Drag Reduction

DRAG REDUCTION

Introduction

The main objective of drag reduction is to reduce the ﬂuid mechanical force known
as “drag,” which is exerted on an engineering system improving its efﬁciency. There
are passive and active techniques to reduce the drag (1). The passive techniques
do not require any energy input to ﬂow; only installation and maintenance costs
are involved. The riblets and large eddy breakup devices fall into this category.
However, the maximum drag reduction is limited up to 10%. The active techniques
require certain energy input. However, level of drag reduction achieved is up to
80%. Among all the techniques, additions of minute amount of high molecular
weight polymers and surfactants have been very active area of research ever since
Toms reported it in 1949 (2).

The discovery of turbulent drag reduction due to particle suspensions goes

back to the 1930s. Forest and Grierson (3) reported the turbulent drag reduction in
pipe ﬂow of wood-pulp ﬁber suspensions of water. Vanoni (4) observed that water
with suspended sand ﬂowed more rapidly in an open channel. Toms (5) and Mysels
(6) independently observed the striking reduction in turbulent drag in pipe ﬂows

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of solutions of high molecular weight poly(methyl methacrylate) (5–10 ppm by
weight) in monochlorobenzene and of aluminum disoaps in hydrocarbon liquids,
respectively. Since Toms (2,5) was the ﬁrst to publish his results, the phenomenon
of turbulent drag reduction is also known as Toms effect. Ever since the reporting
of these results, there has been extensive research activity in this fascinating
ﬁeld of ﬂuid mechanics and polymer science. Nadolink and Haigh (7) compiled
an exhaustive bibliography on the subject containing over 4900 references dating
from 1931 to 1994.

The soluble polymers are the most potential drag-reducing agents of all the

additives mainly because drag reduction of up to 80% can be obtained with the
addition of a few tens of ppm by weight in a particular solvent. The polymer
solution drag reduction has been investigated in aqueous and hydrocarbon liquids,
and a number of excellent reviews have been written by a number of experts
(8–25). Many state-of-the-art papers have also appeared in number of conference
proceedings (26–31).

Drag-reducing polymers have been successfully applied for potential beneﬁts

in various industrial processes and operations, such as long-distance transporta-
tion of liquids, oil-well operations, sewage and ﬂood water disposal, ﬁre ﬁghting,
transport of suspensions and slurries, irrigation, water-heating and [cooling cir-
cuits, jet cutting, and marine and biomedical operations. The developments in the
above] cited ﬁelds are reviewed in the 1990s by Singh (20), Morgan and McCormick
(21), Den Toonder (22), Gyr and Bewersdorff (23), Moussa (24), and Gad-El-Hak
(25).

The most successful application of drag-reduction phenomenon has been in

reducing the drag in crude oil transport through Trans Alaskan Pipelines (TAPS)
and other pipelines in several countries. The ﬁrst large-scale use of hydrocarbon-
soluble drag reducer addition (DRA) in TAPS was accomplished in 1979. The
technology made spectacular advancement since then. Within 10 years, the ef-
fectiveness of additives increased 12 times (32). Because of the effectiveness
of the polymer injection technique, the need of building two delayed pumping
stations disappeared. The 1 ppm of the drag reducer used in the pipeline in-
creased the ﬂow rate by 33%. Several important pipelines such as Tukey-Iraq,
Bas Strait (Australia), Bombay Off Shore (India), etc, have used drag-reducing
additive injection for saving considerable energy. Newer areas are being explored
(23,25,33).

High molecular weight polymers (

>10

) are very effective drag reducers, but

get degraded in turbulent ﬂows and lose their effectiveness after a short interval
of time or ﬂow. Aluminum diasops and other surfactants form aggregates or mi-
celles at a critical micellar concentration (CMC). These micelles are responsible
for drag reduction. These micelles also degrade after critical shear stress though
anionic soaps are found to be good and mechanically stable drag reducers (34). But
when shear stress becomes lower than the critical shear stress, the micelles are
reformed and restore the drag reduction effectiveness. Because of their repairabil-
ity and the capability to withstand higher temperatures, the research activity in
surfactant drag reduction has increased appreciably. The anionic, cationic, non-
ionic, and zwitterionic surfactants have been investigated for their drag-reduction
effectiveness (DRE). Though anionic soaps are found to be good and mechanically
stable drag reducers (34), their use is not favoured because of their vulnerability

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to calcium and magnesium ions normally present in tap and sea water, and their
foam-forming characteristics (35). Nonionic surfactants have narrow temperature
window of applicability around their cloud points (36). Cationic surfactants show
much broader effective temperature window of applicability, and thus have larger
potential for practical applications (37). The drag-reducing characteristics of zwit-
terionic surfactants are being studied (38–40).

The potential application of surfactants exists in district heating and cooling

systems. The characteristics of surfactant drag reducers differ from polymeric
drag reducers in several aspects particularly having higher level of drag reduction
crossing the Virk’s maximum drag reduction asymptote (41,42).

Several attempts have been made to enhance the DRE and mechanical

stability of polymer drag reducers. In general, homopolymers, alternate copoly-
mers, graft polymers, and polyelectrolytes and polysaccharides from natural and
microbial resources are efﬁcient drag reducers in water, organic solvents, and
crude oil (23,25,43). The extent of drag reduction increases with the molecular
weight and length of the polymers, and so does their susceptibility to ﬂow-induced
degradation.

Recently, three approaches have been put forward to enhance the DRE and

shear stability of polymers. The DRE of polysaccharides can be enhanced by graft-
ing synthetic polyacrylamide branches onto their main chains; the resulting graft
polymers combine efﬁciency of synthetic polymers and robustness of polysaccha-
ride chains (44,45). The reversible intermolecular associations in solution increase
the molecular weight of polymer associates and provide mechanical stability
(46–49).

The third approach is by using cross-linking among the polymer molecules.

The drag-reducing polymers such as guar gum can be cross-linked with concentra-
tion below those required for gel formation. The presence of intermolecular cross-
links leads to increased dimensions of the macromolecules resulting in enhanced
drag reduction though the induced degradation of the polymers is not apprecia-
bly affected by the addition of cross-linking agents (50). The ﬁrst and third ap-
proaches have been pursued for water-soluble systems. It has been observed that
in the ﬁrst approach, the level of DRE is higher, that too at low concentrations
(

<100 ppm) of graft copolymers, and that cross-linking is not effective in shear

degradation.

Rheology of polymers and surfactants solutions plays an important part in

drag reduction. Though very dilute drag-reducing solutions have rheological be-
haviors similar to Newtonian solvents except for the anionic polyacrylamide solu-
tions having shear-thinning behaviors at drag-reducing concentration of 50 ppm
(51), their extensional effects may be important. Efforts are still in progress to
measure and correlate the extensional effects to drag reduction (52–60). The
degradation of polymers in turbulent ﬂow needs to be investigated in order
to enhance the effectiveness of polymers by modeling degradation mechanism
(43,61–65).

There are three ways of introducing a polymer solution in the water ﬂow. In

the ﬁrst case of homogeneous drag reduction, the polymer is allowed to mix ho-
mogeneously into the solvent. In the second case of heterogeneous drag reduction,
a highly concentrated polymer solution is injected in the center or at the wall of
the pipe, which disperses completely by turbulent diffusion to yield homogenous

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solution some distance downstream the injector. In the third case, a concentrated
polymer solution is injected into the center line of a turbulent ﬂow at a high
enough concentration that a single coherent unbroken polymer thread forms at
the injector and continuous downstream for several hundred pipe diameters. The
polymer threads have also been injected at the wall or buffer zone of the ﬂow by
Frings (66), who attained highly heterogeneous mixtures downstream. In some
cases (67–69), high concentration strings of polymer develop rather than a single
coherent thread.

All the above forms of drag reduction have been studied in the case of sur-

factant drag reduction as well. The origin of drag reduction in all cases has been
indicated to be similar (70,71). The origin of drag reduction has been extensively
investigated from the very beginning. With the advent of laser Doppler anemome-
try (LDA) (72), and later on with the phase laser anemometry (73), it was possible
to measure and investigate velocity characteristics of ﬂows with precision without
interfering with them. LDA has been extensively used to study various aspects of
drag reduction, particularly in channel ﬂows (74).

Dodge and Metzner (75) developed a correlation between friction factor and

Reynolds number for turbulent pipe ﬂow of purely viscous shear-thinning liquids
based upon a power-law model of shear viscosity. Metzner and Park (76) correlated
the degree of drag reduction in turbulent ﬂow of viscoelastic polymer solutions
with the ratio of elastic to viscous stress, ie with N

, where N

is the ﬁrst nor-

mal stress difference for a given wall shear–strain rate

γ , and τ

the corresponding

shear stress. Though the role of extensional viscosity in causing turbulent sup-
pression or drag reduction is being debated till date, there is a persistent view
that the elongational viscosity, possibly in combination with viscoelasticity, is re-
sponsible for drag reduction.

Gadd (77) was among the ﬁrst to point out that the damping of the turbu-

lence by polymer additives is due to their resistance to elongational strain, which
suppresses shear formation and bursting in near-wall region. Lumley (78,79) sug-
gested that the uncoiling of polymer molecules under ﬂuctuating shear rate in
the buffer region of turbulent ﬂow causes drag reduction because of increase of
extensional viscosity. Gyr (80), Durst and co-workers (81), and Bewersdorff and
Berman (82) provided the extensional viscosity model of drag reduction. Vlas-
sopoulos and Schowalter (51,52) suggested that the origin of DRE is due to the
ﬂuid elasticity inferred from oscillation-induced streaming. Matthys (83) pointed
out the common origin of the extensional viscosity and viscoelasticity. de Gennes
(84) hypothesized that the polymer drag reduction is due to the elastic, rather
than the viscous, phenomenon. Several direct numerical simulations by Orlandi
(85), Den Toonder and co-workers (64,86), and Massah and Hanratty (87) exam-
ined the role of viscoelasticity, extensional viscosity, and stress anisotropy in drag
reduction. Direct numerical simulation (DNS) investigation of Den Toonder and
co-workers (86) points out that drag increases rather than decreases when the
elastic contributions are taken into account.

For the case of viscous anisotropic polymer model, almost all turbulence

statistics and power spectra calculated agree in qualitative sense with experimen-
tal results. Dimitropolous and co-workers (88) did DNS for fully turbulent chan-
nel ﬂow of a polymer solution using the ﬁnitely extensible nonlinear elastic head
spring dumbbell model with Peterlin approximation (FENE-P) and the Giesekus

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DRAG REDUCTION

523

model. They demonstrated that the solution extensional viscosity plays the pri-
mary role in turbulent drag reduction. Comparing the mean velocity proﬁles and
statistical features of the turbulent ﬂow showed agreement with well-established
experimental observations, such as enhanced buffer zone, increase in the spacing
of the streamwise streaks, decrease in the streamwise vorticity ﬂuctuations, and
increase in the streamwise velocity ﬂuctuations. This demonstrated the onset of
drag reduction in a turbulent ﬂow at a sufﬁciently high level of viscoelasticity in
the ﬂow and reinforced previously held hypothesis that one of the prerequisites for
the phenomenon of drag reduction is sufﬁciently enhanced extensional viscosity.

However, Sreenivasan and White (89) point out that the connection between

ﬂuctuating strain rates and large extensional viscosity is circumstantial. Further
polymer coils can only be partially stretched in a random ﬁeld of strain rate.
Sreenivasan and White (89) point out that the elastic theory proposed by de
Gennes (84) is compatible with at least two experimental observations; ie, the
dependence of drag reduction onset on polymer concentration and maximum drag
reduction asymptote.

On the other hand, DNS of turbulence in channel ﬂow based on FENE-P

bead-spring chains in the presence of large-enough velocity gradients by Massah
and Hanratty (87) indicates that polymers cause drag reduction by selectively
changing the structures of eddies that produce Reynolds stresses. Their calcula-
tions (87) support the suggestions by Lumley (78) that the polymers can become
unravelled by the turbulence in the buffer region. The calculated unravelling of
a bead-spring chain in the viscous sublayer could explain the increased viscosity
observed by Vismann and Bewersdorff (90) and by James and co-workers (91) in
elongational ﬂow when the solution is presheared in laminar Couette or chan-
nel ﬂow. Thus these investigations point out the basis of further research on the
origin of drag reduction and explanation of its various manifestations in both
polymeric and surfactant drag reduction. A large number of reviews are available
in literature till 1990. In this review, emphasis will be given on the researches
reported since then, with comprehensive accounts of materials, mechanisms, and
applications in the ﬁeld of turbulent drag reduction in liquids.

Characteristics of Turbulent Drag Reduction

Mathematical Description.

Lumley’s (92) deﬁnition of drag reduction,

“drag reduction is the reduction of skin friction in turbulent ﬂow below that of
the solvent,” will be followed in this review. Most of the studies on drag reduction
have been conﬁned to hydraulically smooth pipe ﬂows or channels; hence various
physical parameters will be described in terms of smooth pipe ﬂows.

Reynolds was the ﬁrst to ﬁnd out that transition from laminar to turbulent

ﬂow takes place in cylindrical-pipe ﬂows of water at a particular value (

=2300)

of a dimensionless parameter known as the Reynolds number (R

), where R

given by the following relation:

(1)

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where ¯

u is the mean ﬂow velocity, D is the pipe diameter, and

υ( =

) is the kine-

matic viscosity.

υ is equal to the ratio of viscosity η and the density of the liquid, ρ.

The pressure loss in pipe is due to ﬂuid friction resistance. The friction factor

f may be derived as

pD

ρ ¯u

(2)

where

 p is the pressure drop and L is the pipe length. The wall shear stress,

, in a fully developed pipe ﬂow is related to the pressure drop by the following

equation:

pD

(3)

Hence the Fanning friction factor:

1
2

ρ ¯u

(4)

The friction velocity u

can also be evaluated as

(5)

Prandtl–Karman coordinates (f

− 1/2

vs R

) are, in general, used to

present the drag reduction data because in these coordinates Prandtl–van Karman
law for Newtonian turbulent pipe ﬂow appears as a straight line in a semiloga-
rithmic diagram (see Fig. 1).

− 1/2

√

as ordinate

and

√

as abscissa

represent ratios of bulk to turbulent velocities and pipe to turbulent length scales
respectively (10).

The drag-reducing polymers, such as poly(ethylene oxide) or polyacrylamide,

exhibit drag reduction at such low concentrations that the solution viscosity is
close to solvent viscosity. In laminar ﬂows, the majority of drag-reducing polymer
solutions obey Poisseulli’s law, ie

− 1/2

16
R

(6)

In case there is no drag reduction, the friction factor is given by the Prandtl–

van Karman law for Newtonian turbulent pipe ﬂow, ie

= 4.0 log

− 0.4

(7)

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525

Fig. 1.

(a) The variation of f

− 1/2

with log

) in case of dilute drag-reducing poly-

mer solutions. The various regimes are depicted as follows: 1 by the Newtonian laminar
region; 2 by the Prandtl–Karman curve for Newtonian ﬂuids in a smooth pipe; 3 by Virk’s
maximum drag reduction asymptote; 4 by a typical curve for polymer solutions.

δ is the

slope increment. Adapted from Figure 1.3 of the Ref. 23. (b) The variation of friction fac-
tor with Reynolds number in case of drag-reducing surfactant solutions. 1, Laminar; 2,
von Karman Linc; 3, Virk asymptote; 4, Zakin and co-workers asymptote. Adapted from
Figure 2 of the Ref. 42.

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Virk (10) observed that the maximum possible drag reduction asymptote

(MDRA) is given by the following equation, where the drag reduction is insensitive
to polymer properties:

= 19 log

− 32.4

(8)

In the regime below the maximum drag reduction asymptote, the friction

factor varies with polymer properties and ﬂow variables:

= [4.0 + δ] log

− 4.0 − δ log

√

(9)

where

δ and w are polymer solution parameters.

In case of surfactant solutions, friction factors signiﬁcantly lower than the

predicted by MDRA for high polymer solutions are predicted. Zakin and co-
workers (93) provided an equation given below for maximum drag reduction
asymptote for surfactant solutions

≈ 0.32 R

.55

(10)

The velocity proﬁles in terms of universal dimensionless coordinates

and y

y u

] offer an alternative representation of drag reduction be-

havior. The local velocity u varies with y, the distance from the wall. There are
three distinct regions that can be represented by the following equations:

Close to the wall, the ﬂow in the viscous sublayer and in the buffer layer are

represented by equations 11 and 12 respectively.

= y

< y

< 5) (viscous sublayer)

(11)

= y

< y

≤ 30) (buffer layer)

(12)

The logarithmic layer is given by

= 2.5 ln y

+ 5.5 (y

> 30)

(13)

The velocity proﬁles of drag-reducing ﬂows in many cases show a peculiarity.

A logarithmic proﬁle starts at the intersection with a steeper slope and describes
the velocity at maximum drag reduction. Virk’s (10) maximum drag reduction
proﬁle is given by

= 11.7 ln y

− 17

(14)

For drag-reducing polymers, the velocity proﬁle is parallel to the Newtonian

proﬁle and is separated by a factor

B depending on the polymer, and on pipe and

ﬂow characteristics (see Fig. 2).

= 2.5 ln y

+ 5.5 + B

(15)

The ﬁrst region (viscous sublayer) extends to about y

= 5. The drag-reducing

ﬂows intersect the maximum drag reduction line instead of u

= y

. The region

between the viscous sublayer and Newtonian plug is known as the elastic sublayer

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DRAG REDUCTION

527

Fig. 2.

Main stream velocity proﬁle for drag-reducing ﬂuids according to Virk’s model: 1,

viscous sublayer; 2, elastic buffer layer; 3, turbulent core.

since the solution in this zone exhibits an elastic ﬂow behavior. In case of maxi-
mum drag reduction, the elastic region extends to the center of the pipe and the
Newtonian region disappears. By integrating the equations, we obtain the total
volumetric ﬂow rate and friction factor:

= 4 log

(R f

)

− 0.4 −

√

(16)

In the 19th century, Reynolds established the basic approach to analyze the

turbulent ﬂow. He introduced in the momentum equations the time ﬂuctuating
velocity whose average value over a period of time is zero but whose time-averaged
squares and products are not zero. The relation for velocity components and pres-
sure can be written as follows:

= ¯u + u

(17)

= ¯v + v

(18)

= ¯w + w

(19)

= ¯p + p

(20)

where u

, v

, and w

are ﬂuctuating velocity components in turbulence in x, y,

and z directions, respectively, and p

is the ﬂuctuating pressure component in

turbulence. The time average at a ﬁxed point in space can be given as

1
t

u dt

(21)

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DRAG REDUCTION

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u can be further split into time average mean and a phase-locked average

(91), where ˜

u is thought to be an oscillatory part of the velocity ﬁeld and u

is the

remaining turbulent ﬂuctuation.

= ¯u + ˜u + u

(22)

The components of stress tensor due to the turbulent velocity components of

the ﬂow are given by

= − ρ

(23)

The diagonal components u

, v

, and w

denote twice the average kinetic

energy per unit mass of the respective velocity components. The nondiagonal terms
u

, u

, and v

denote negative components of turbulent and Reynolds shear

stress.

The correlation coefﬁcient

between the longitudinal and transverse ﬂuc-

tuations at the same point is deﬁned as

(24)

Taylor (95) pointed out that in order to quantify special structure of turbu-

lence, the velocity ﬂuctuations at two neighbouring points, 1 and 2, in ﬂow ﬁelds
have to be observed. This will deﬁne correlation function ¯

R as

(25)

The integral of the correlation function ¯

R is known as scale of turbulence.

/2 D

R(r) dr

(26)

If the second quantity u

is measured at the same location but at a different

instant of time (u

at instant t

and u

at instant t

= t

+ τ), we obtain the

auto-correlation function

κ. The x component of κ, ie κ

, can be written as

,t)u

,t + τ)

(27)

These functions are equivalent to a spectral decomposition of the kinetic

energy of the ﬂuctuations, K.

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DRAG REDUCTION

529

The alternate description of the structure of turbulence is obtained when a

frequency analysis of the motion is provided instead of a correlation function.

These functions are equivalent to a spectral decomposition of the kinetic

energy of the ﬂuctuations in the respective directions, eg

2
1

∞

,ω) du

(28)

into components for each frequency

ω, the so-called power spectrum. It follows

from this deﬁnition that

(

χ,ω) =

∞

− ∞

,ω) e

− iωτ

(29)

and vice versa:

(

χ,ω) =

∞

− ∞

(

χ,τ)e

− iωτ

(30)

A complete insight into the statistical turbulence and turbulence process

not only requires the study of the axial and transverse ﬂuctuations but also to
measure space and time correlation functions.

Experimental Results: Investigations of Drag Reduction and

Turbulence Parameters.

In the last decade, a large number of experimental

articles have appeared on polymer drag reduction in pipe and channel ﬂows, where
LDA and 2D LDA have been used to measure various velocity components and
Reynolds stresses. Pinho and Whitelaw (96), Harder and Tiederman (97), Wei and
Willmarth (98), Walker and Tiedermann (99), Tong and co-workers (100), Codot
and co-workers (101), Den Toonder and co-workers (86), Dimitropoulos and co-
workers (88), Hoyer and co-workers (102), Fortaine and co-workers (103), Nieder
Schulte and co-workers (104), Bewersdorff and co-workers (105), and Massah
and Hanratty (87) reported various measurements on velocity components and
Reynolds stresses. The most important ﬁndings reported in these articles are that
the polymers not only suppress the turbulent motion but also increase the stream-
wise turbulent intensity, while the normal turbulence intensity is decreased. Wei
and Willmarth (98) reported that the energy in the normal turbulence intensity is
drastically suppressed over all frequencies while there is redistribution of energy
from high frequencies to low frequencies for the streamwise component.

The drag reduction (DR) for pipe ﬂow of an incompressible ﬂuid additive

system (20,23) is deﬁned as

= (1 − P

/P

)

(31)

where

is the pressure drop with a ﬂuid additive system, and

is the pres-

sure drop with a pure ﬂuid, measured at constant ﬂow rate. It may be assumed

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DRAG REDUCTION

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Fig. 3.

Various methods of polymer addition for manifestation of the turbulent drag re-

duction phenomenon (63).

that small additions (at the ppm level) of the additives do not change the ﬂuid
density and shear viscosity. The ﬂuid additive system is called drag-reducing if
DR is positive.

Methods of Drag Reduction.

There have been three basic methods for

adding a polymer to the turbulent ﬂow, and consequently three types of drag-
reduction methods (70) (see Fig. 3). In homogeneous drag reduction, the polymer
is mixed into the solvent and it disperses uniformly before it is allowed to ﬂow in
the pipe, and measurements are taken for various parameters of drag reduction.
In another form of homogeneous drag reduction, the diffusive ﬂow of the polymers
takes place. Here the polymer is injected into the centre or at the wall of a pipe
at a concentration which disperses completely by turbulent diffusion to yield a
homogeneous solution some distance downstream the injector. In the second case,
known as heterogeneous drag reduction, concentrated drag-reducing polymer so-
lution is injected into the centerline of a turbulent ﬂow so that a single coherent
unbroken polymer thread forms at the injector and continues downstream for
several hundred pipe diameters. The third type of drag reduction takes place (67)

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DRAG REDUCTION

531

when the injection is such that many high concentration strings of the polymer
develop, rather than a single coherent thread from the centerline injector. Frings
(66) used very high polymer concentrations in a wall injector and obtained highly
heterogeneous mixtures downstream. Most of the wall injector studies yield ﬂows
similar to the second case, and the ﬁrst case describes majority of the drag reduc-
tion studies.

Two other type of drag reduction (10,106) within the polymeric regime have

been observed. In type A drag reduction, a family of additive solutions yield
friction factor segments fanning outwards from a common “onset” point on the
Pradtl–Karman line, their slopes increasing with increasing concentrations and
drag reduction increasing with increasing R

. This is characteristic of random

coiling macromolecules. In type B drag reduction, a family of additive solutions
yield segments that are roughly parallel to that displaced upwards from the P-K
line, with drag reduction essentially independent of R

but increasing with

increasing concentration. This behavior is exhibited by a variety of additives in-
cluding extended polyelectrolytes, ﬁbers, soaps, and clays. This drag reduction
occurs without any discernible onset effect where the macromolecules causing the
effect are already in the extended state and do not need to be stretched by a strong
ﬂow.

The various investigations on heterogeneous drag reduction carried out up

to 1987 have been discussed by Singh (20) and Gyr and Bewersdorff (23). Hoyer
and Gyr (71) have provided the critical analysis of heterogeneous drag reduction.
Usui and co-workers (68,107,108) have investigated the velocity proﬁle of the
injected polymer phase and the surrounding water phase separately by seeding
both liquids with tracer particles. They monitored the ﬂow using a video camera,
which was moved with ﬂow velocity (see Fig. 4). On the basis of their results (68,
107,108), Usui and co-workers (108) suggested that the main interaction between
polymer thread and the turbulence which results in drag reduction takes place
in the central part of the ﬂow and suppresses the large-scale motions of the ﬂow
in agreement with earlier results by Vleggar and Tells (109,110) and Bewersdorff
(23,69,105). Gyr and Bewersdorff (23) showed that by varying the ratio of polymer
injection velocity to the bulk velocity and by mounting contractions in pipe, the
drag reduction increases with the elongation of the polymer thread as long as the
thread stays intact and is not broken into pieces. Hoyt and Sellin (111) investigated
the thread injection techniques using various viscoelastic solutions ranging from
water-soluble polyacrylamide (PAM) and PEO and surfactant tetradecyltrimethyl
ammonium bromide

+2% sodium salycilate (C

TASal) and hexadecyl trimethyl

ammonium bromide

+2% sodium salycilate (C

TASal), as well as water-insoluble

FLO (commercial pipeline drag reducer), polyisobutene, and PEO dissolved in
dichloromethane. They attributed that the drag reduction effect is due to dissolved
molecules removed from the thread at high Reynolds numbers, whereas at low
Reynolds number an interaction of the thread with large-scale eddies should be
responsible for the observed drag reduction.

A number of very precise measurements by Smith and Tiederman (70) and

Hoyer and co-workers (71,102) reveal that the mechanism of polymer thread drag
reduction is caused by a modiﬁcation at or near wall, or by modiﬁcation in the
central portion of the ﬂow. The drag reduction is ascribed to minute quantity of
polymers removed from the thread and dispersed into the bulk of the ﬂuid. Smith

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DRAG REDUCTION

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Fig. 4.

Experimental setup for measurement of (a) drag reduction and (b) tracer par-

ticle trajectories; (c) proﬁles of turbulent intensity in the longitudinal direction:

, Wa-

ter;

䊊

, polymer injection (water phase);

䊉

, polymer injection (polymer thread); , premixed

ﬂow;

Pennel and co-workers (Newtonian ﬂuid, R

= 11400);

McComb–Rabie

(injection); – – – – Reishman–Tiederman (premix, 100-ppm Separan AP-273, R

= 44500,

= 39%).

and Tiderman (70) measured drag reduction, radial location of thread, and the
polymer concentration in the near-wall region. The concentration was measured
by laser-induced ﬂuorescence utilizing ﬂuorescin dye as tracer. In their experi-
ment, the polymer injected was 500 ppm by weight of Separan AP273 dyed by 8.8
ppm by weight of ﬂuorescin; the unbroken threads existed for more than 200 pipe
diameters downstream the injector and produced drag reduction of the order of
40%. They found that the thread did not appear in the region y

< 100. When there

was no polymer at y

= 50, there was no drag reduction. As soon as measurable

amount of polymer was found at y

= 50, there was drag reduction. The major

conclusion arrived at by Smith and Tiderman (70) was that low concentrations of

Vol. 9

DRAG REDUCTION

533

Fig. 4.

(Continued).

polymer in the near-wall region are sufﬁcient to cause drag reduction measured
in the polymer thread experiments. The polymer that is diffused from the thread
is the major cause of the drag reduction.

In the experiment of Hoyer and co-workers (102), the thread was sucked

out and drag reduction downstream of the withdrawl point was measured, and
in a second series of measurements near wall, the ﬂuid was withdrawn and the
drag reduction of that ﬂuid in a bypass was measured (see Fig. 5). The thread
trapping and bypass experiments indicate that the heterogeneous drag reduction
is at least partly due to minute amounts of polymers removed from the thread
and dispersed in the bulk of the ﬂuid. It was found that the effect decreases if the
thread ruptures into pieces instead of being enhanced as expected for a diffusion
process. With decreasing u

∗

, the effect increases and the onset point is lowered.

This suggests that diffusion is not the mechanism by which the polymer enters
the bulk of the ﬂuid. Further, it was observed that the drag reduction occurred
whenever the thread started forming loops. In these loops, the thread unravelled
locally into various strands which uniﬁed again when the thread was stretched.
Hoyer in further experiments (71,102) collected near-wall ﬂuid from 30-mm inner
diameter circular pipe (D

) using a slit suction device of height 0.25 mm and

integrated in a 4-mm pipe for drag-reduction capability. The average thickness of
collected wall layer never exceeded 22 viscous units and thus ensured that no part
of the concentrated polymer thread was sampled. He observed the following:

534

DRAG REDUCTION

Vol. 9

Fig. 5.

(a) A typical experimental setup for measuring drag reduction using a bypass

pipe; (b) inﬂuence of the injection ratio u

∗

on the friction behavior in round pipe with c

0.8% and c

= 5 ppm:

䊊

, Commercial guar gum;

䊉

, puriﬁed guar gum;

. Adapted

from Ref. 102.

(1) The near-wall ﬂuid collected just before the onset in the main pipe showed

no drag reduction.

(2) The ﬂuid collected within increasing levels of drag reduction in the main

pipe showed increasing drag reduction capabilities in the small pipe.

Polymeric Drag Reduction.

The following macromolecular parameters

seem to inﬂuence the drag-reduction characteristics, ie chemical and physical
structure, molecular weight, length, extension, ﬂexibility, and elasticity. Both syn-
thetic and natural linear polymers having molecular weight of 5

× 10

or more

have been found to be good drag reducers (19–24,112).

The lower molecular weight polymers capable of forming higher molecular

weight aggregates have also been found to be effective drag reducers (46–48).
Lodes and Macho (113) reported that the aqueous solutions of a 19000 kg/mol
partially sponiﬁed poly(vinyl acetate) with various degrees of hydrolysis exhib-
ited drag reductions close to the MDRA. In case of still lower molecular weight

Vol. 9

DRAG REDUCTION

535

Fig. 5.

(Continued).

(

=6000), 0.4 and 0.6% by weight aqueous solutions of Tylose, a methylhydroxy

cellulose from Hoechst, Pereira and Pinho (114) showed drag reductions (

=25–

35%) of the half that reported to occur with other low elasticity, shear-thinning,
high molecular weight aqueous solution of CMC (molecular weight 300000 kg/mol)
(96). The drag reduction caused by Tylose may be either due to the high molec-
ular weight fractions present in its sample or associated complexes, which may
be present at such high concentrations as tens of ppm (by weight) of polymers.
On the other hand, rigid shear stable polymers such as polysaccharides (ie, guar
gum, carboxymethylcellulose, and xanthan gum in the form of natural gum or
formed by algae and bacteria) cause maximum drag reduction of up to 60% at the
concentrations of a few hundred ppm by weight (20,23,115).

Among the synthetic polymers, poly(ethylene oxide) is the most efﬁcient but

relatively lesser shear stable than polyacrylamide. Molecular weight, length, and
coil dimensions are the chief attributes of polymers to drag reduction (21). It
has been shown by Olivier and Bakhtiyarov (116) that polyacrylamide of very
high molecular weight, ie M

= 20–25 × 10

, causes drag reduction in as low as

536

DRAG REDUCTION

Vol. 9

0.02-ppm solution. Gampert and Wagner (117) have prepared highly fractionated
samples of polyacrylamide. They have shown that drag reduction increases with
molecular weight. In mixtures of various fractions, it is the highest fraction that
contributes the most in drag reduction.

Drag reduction is shown by polysaccharides, which are linear in nature.

Highly branched materials such as gum arabic and dextran do not seem to reduce
drag (17). Polyelectrolytes, such as partially hydrolyzed polyacrylamide (64,106),
polyacrylic acid (118), acrylamide sodium acrylate copolymer (119), and sodium
alginate (120), show higher drag reduction when the chain is extended or there is
increment in coil dimensions. The coil expansion takes place because of coulom-
bian repulsion and solvent steric hindrance of side group and main chain (119).

Virk and Wagger (106) reported that drag reduction results in case of par-

tially hydrolyzed polyacrylamides (PAMH) of molecular weight M

= 15 × 10

When the charge neutralization was obtained by adding 0.1 M NaCl, the additive
solutions yield friction factor segments fanning out from a common “onset” point
on Prandtl–Karman line, their slopes increasing with increasing concentrations
and drag reduction increasing with increasing R

. This is the characteristic of

random coiling macromolecules. Virk designated it as type A drag reduction. In B
type of drag reduction, obtained without adding any NaCl or adding up to 0.001
M NaCl to 0.0003 M NaCl (practically no or very little charge neutralizations
took place), a family of additive solutions yield segments that are roughly paral-
lel to, but displaced upwards from, the P-K line, with drag reduction essentially
independent of R

but increasing with increasing concentration. This type

of behavior is exhibited by additives such as extended polyelectrolytes (PAMH),
ﬁbers, and soaps, and clays such as asbestos, xanthan, asbestos, paper-making
ﬁbers, and nylon ﬁbers.

Among the polymers that show drag reduction in nonaqueous solvent and

crude oil, polyisobutylenes, polyisoprene, polystyrene, homo and copolymers of
alkylstyrene, acrylates, methacrylates, and FLO are the prominent ones. A de-
tailed catalog of drag-reducing polymers has been given by Singh (20) and Gyr
and Bewersdorff (23). The recently studied drag-reducing polymers are listed in
Table 1.

In search for better drag-reduction efﬁciency and shear stability at low cost,

a systematic investigation has been made in the author’s laboratory by grafting
efﬁcient drag reducer such as polyacrylamide chains onto robust polysaccharide
backbones to develop graft polymers having drag-reduction efﬁciency of synthetic
polymers and shear stability of polysaccharides main chains (121–128). The max-
imum in drag reduction is also obtainable at the concentrations ranging from
50 to 100 ppm (see Fig. 6). As the grafting alters the regularity of the molec-
ular structures, it inhibits the enzyme attack on main chain, thus enhancing
the biodegradation resistance of graft copolymers and increasing the shelf life
(44). Starch and low molecular weight (125000) poly(vinyl alcohol) are not drag-
reducing. However, on grafting polyacrylamide branches, the graft copolymers
show drag reduction efﬁciency and shear stability. A large number of graft poly-
mers of amylose/amylopectin/CMC/guar gum/poly(vinyl alcohol)/starch/xanthan
gum) have been synthesized. The graft polymers having longer and fewer poly-
acrylamide branches have been found to be more drag-reduction effective and
shear stable. It has also been observed that puriﬁcation of guar gum and xanthan

Vol. 9

DRAG REDUCTION

537

Table 1. Recently Investigated Drag-Reducing Additives

The reducing polymers

Molecular weight

Reference

Carboxy methylcellulose (CMC)

High viscosity grade OSA Co.

115

Xanthan gum (XG)

A food grade applied by Kelco Div of

Merck and Co., Inc.

115

Polyacrylamide

Floerger/Dow Chemicals

99,115

Separan AP273

6–8

× 10

g/mol

22,65,86

Superﬂoc A110, partially

hydrolyzed polyacrylamide

Cytec Co.

Anionic polyacrylamide

× 10

– 17

× 10

g/mol

Acrylamide-co-acrylic acid
Cyanatol-750
Poly(ethylene oxide)

Union Carbide Corp.

51,53,65,80,

151,152

Nonionic polymer

× 10

g/mol

Poly OX WSR-303

× 10

g/mol

Poly OX WSR-301

× 10

g/mol

Xanthan gum (XG)

Sigma Chemical Co.

Hydroxy propyl

Dowell Schlumberger 2.5

× 10

g/mol

50,52

Guar gum HPG

Alliburton

Guar gum
Polyisolutylene

Aldrich Chemical Co. 3.79

× 10

g/mol

Polyacrylamide/separan AP-30,

AP-302

Dow Chemical Co.

Commercial drag reducer (CDR)

Esso Australia

Magnaﬂoc 866A 50% hydrolyzed

PAM

× 10

– 19

× 10

g/mol American

Cynamid

PAM-Nonionic

× 10

– 6

× 10

g/mol Polysciences

Poly OX WSR-301

× 10

g/mol Union Carbide

Cetyl trimethyl ammonium

bromide (CTAB) and sodium
silicate

BDH Ltd.

Poly OX WSR-303

Union Carbide 7

× 10

g/mol

Anionic PAM

(acrylamide-co-acrylic acid
30%) Cyanatrol 750

American Cynamid Co. 14.25

× 10

gm/mol

gum enhances their drag-reduction efﬁciency as removal of low molecular weight
ingredients like fats and proteins increases the fraction of high molecular weight
polymers, and hence improves their drag-reduction ability. The drag-reduction
ability of grafted polymers is not affected by the salts present in seawater. These
graft copolymers also have synergetic ﬂocculation characteristics (44,45).

Bello and co-workers (50) have recently reported the effect of cross-linking

agents on the drag-reduction efﬁciency of hydroxylpropyl guar and guar gum so-
lutions in turbulent ﬂow through a horizontal pipe. The results show that the ad-
dition of cross-linking agent (borax) to solution with concentrations below those
required for gel formation enhances the drag reduction due to increased dimen-
sions of the macromolecules in the presence of intermolecular cross-links. The

538

DRAG REDUCTION

Vol. 9

Fig. 6.

The variation of drag reduction percentage with concentration in commercial,

puriﬁed, and polyacrylamide grafted guar gum (GM

) at R

-14000:

Water; × diameter =

1 mm, u

∗

= 0.57;

䊊

diameter

= 3 mm, u

∗

= 0.06 (116,118).

ﬂow-induced degradation of the polymers is not appreciably affected by the addi-
tion of cross-linking agent. The intermolecular bonds are stable to ﬂow-induced
degradation since their presence does not signiﬁcantly alter the degradation rate.
The enhancement of drag reduction also takes place at concentration of the macro-
molecules above 500 ppm. The enhanced drag reduction is up to 35%. On the other
hand, grafting and puriﬁcation enhance the drag reduction up to 68%, that too
at concentrations below 100 ppm (121,123,128,129). Hence, it is worth investi-
gating the effect of cross-linking of graft copolymers for further enhancement of
drag-reduction efﬁciency.

McCormic and co-workers (130–136) have investigated the DRE of polyacry-

lamide copolymers. The various copolymers studied by this group include polyelec-
trolytes [(PAM-co-sodium-2-acrylamido-2-methylpropane sulphonate (NaAMPS);
PAM-co-sodium-3-acrylomido-2-methylbutenoate

(NaAMB)];

polyamphotytes

[(poly-2-acrylimido-2-methyl propyl) dimethyl ammonium chloride-co-NaAMPS
(ADAS);

poly(acrylimide-co-2-acrylimido-methylpropenedimethyl

ammonium

chloride-co-sodium-2-acrylimido-methyl-propane

sulfonate

(ADASAM)];

and

hydrophohically modiﬁed acrylamides [(PAM-co-diacetone acrylamide) (DAAM);
PAM-co-N-n-decrylamide;

PAMCO;

(PAM-C

N-isopropylacrylamide-co-

acrylamide (1PAM) copolymers]. Several of these copolymers showed better
drag-reduction efﬁciency than PAM.

Kowalik and co-workers (46) and Malik and co-workers (47–49) presented a

new approach in development of shear stable and efﬁcient drag reducers based
on intermolecular associations and intermolecular complexes based on secondary
interactions. These systems displayed higher drag-reduction efﬁciency and shear
stability. The associations may be caused by electrostatic, hydrogen-bonding, or

Vol. 9

DRAG REDUCTION

539

hydrophobic interactions. The increased shear stability was attributed to the re-
versible breakage of secondary bonds in preference to cleavage of polymer back-
bone. Malik and co-workers (47–49) introduced chemical moieties with interacting
functionalities on the backbone of a polymer to cause association effects. These
interpolymer complexes were based on a copolymer of 97 wt% dodecyl acrylate
and 3 wt% methacrylic acid (proton-donating polymer), and a terpolymer is con-
stituted by 50 wt% dodecylacrylate, 46 wt% styrene, and 4 wt% 4-vinyl pyridine
(proton-accepting polymer). These hydrogen bonding mediated interpolymer com-
plexes exhibited higher drag reduction and shear stability; though low molecular
weight donor polymer is more shear stable than proton-accepting polymer, it is
not an effective drag reducer. The shear stability has been discussed in terms of
mechanistic considerations. It is apparent from the above discussion that though
a lot of experimental results based on commercially available polymer drag reduc-
ers have been reported, the development of new drag-reducing agents with higher
drag-reducing efﬁciency and shear stability is limited.

Mechanism of Drag Reduction

The effect of polymers on turbulence has been discussed by Singh (20), Gyr and
Bewersdorff (23), and Gad-El-Hak (25), and several research articles have been
published in 1990s. The gist of the past and present researches is being provided
below and is the status of still eluding origin of drag reduction.

(1) The turbulent intensity of streamwise components has been reported for

drag-reducing ﬂows. All experiments indicated that the position of the max-
imum is further away from the wall than for Newtonian ﬂuids and is gen-
erally found at y

∼

= 30–60.

(2) For transverse intensity component in the presence of drag-reducing addi-

tives, the radial ﬂuctuations are strongly damped in the buffer region and
(

)

maximum is shifted to y

∼

= 200 or even to the centre of the pipe if large

drag reduction is there. In the core region, the intensity is the same as for
the solvent. The xy component of Reynolds shear stress is the measure of
intensity of turbulence transport. In the pipe ﬂow of Newtonian ﬂuid, it
starts growing from zero at the wall to a maximum at y

∼

= .05d

and de-

creases nearly to zero at the pipe axis. In drag-reducing ﬂow, the intensity
is reduced and the maximum is shifted further from the wall.

(3) The frequency spectra of wall shear stress ﬂuctuations for drag-reducing

ﬂows show the relative attenuation of high frequency components. The de-
crease in high frequency content and increase in low frequency are observed
in the frequency spectra of axial as well as transverse ﬂuctuations for drag-
reducing ﬂows.

(4) As streak spacing is a measure of the size of coherent eddies in viscous

and buffer layers, the drag-reducing polymers change the structure of the
ﬂow. There is an increase in the nondimensional streak spacing as the drag
reduction increases.

540

DRAG REDUCTION

Vol. 9

(5) The bursting period is an indication of time between occurrences of sec-

ondary instabilities. The burst produces extensive Reynolds stresses. The
bursting is more energetic and its frequencies decrease as the drag reduc-
tion increases. In the maximum drag reduction region, the bursting period
becomes two to three times as large as that of the Newtonian ﬂuid at the
same Reynolds number.

(6) In homogeneous drag reduction, only in the buffer region, the Reynolds

stresses are produced in contrast to the case of heterogeneous drag reduction
where there is a much larger region where the Reynolds and viscous shear
stresses are of the same order of magnitude. The characteristic time of big
eddies is of the same order as that of relaxation times of injected polymer
solutions for shear rates of 10–10

− 1

, indicating an interaction between

big eddies and polymer threads.

(7) The polymer threads inﬂuence the large-scale structures; it appears that

highly elastic polymer threads restrict their motion leading to reduced
transport of momentum from this region to the dissipating small eddies,
and thus causing the observed drag reduction.

(8) According to the Lumley (78,79,92,137), the large eddies are formed in

the viscous sublayer and are extended into the buffer layer. The polymer
molecules are extended when subjected to ﬂuctuating strain rate outside
the viscous sublayer. This causes an increase in the extensional viscosity.
This high extensional viscosity damps the small dissipating eddies. Because
of the decreased intensity of small eddies, stress in the buffer layer delays
the reduction in the mean proﬁle slope, resulting in the thickening of the
buffer layer. As the molecules are not extended in the viscous sublayer, it is
not affected by polymer.

(9) The change in mean velocity proﬁle causes the expansion of large eddies.

The expanded large eddies produce an increased streamwise ﬂuctuating
velocity, primarily in the buffer layer. In the maximum drag reduction re-
gion, only large eddies are supposed to remain. According to the Lumley
(78,79,92,137) hypothesis, the eddies in the buffer layer that are primar-
ily responsible for Reynolds stress production are those associated with
secondary instability on inﬂectional proﬁle. These eddies are presumably
damped.

(10) Luchik and Tiderman (138) postulated that turbulence and the polymer

molecules in dilute polymer ﬂows reach statistical equilibrium, where the
remaining turbulent stretching keeps the molecule extended so that lower
threshold motions can be damped by the viscoelastic properties of the dilute
polymer solution. Gyr (80) was more speciﬁc and attributed the required
molecular extension to a wall-layer structure of vortices.

(11) It seems that the high shear rates of a turbulent ﬂow in the near-wall

region are necessary to deform the spherical polymer molecule to an el-
lipsoid which becomes aligned with its long axis in ﬂow direction. These
deformed and aligned molecules are able to exhibit an increased resis-
tance against vortex stretching and, therefore, can interact with turbulent
structures.

Vol. 9

DRAG REDUCTION

541

(12) In the drag reduction by the surfactant solutions when a critical shear gra-

dient is exceeded, the shear viscosity suddenly increases because of the
formation of the so-called shear induced state (SIS). In SIS, the micelles be-
come aligned in ﬂow direction. Furthermore, in the SIS, the micelles have
to build up larger, super-order structures. The critical shear rate for the
occurrence of the SIS can be related with the onset of drag reduction (139),
and it seems that drag-reducing surfactant solutions appear to exhibit an
increased shear viscosity in the buffer zone of a turbulent velocity proﬁle.

(13) The various theories explaining drag reduction may be divided into three

categories: ﬁrst, an explanation in which the increase in extensional viscos-
ity for the polymer solution is the main ingredient; second, a theory that
stresses the importance of anisotropic effects introduced by the extended
polymer molecules; and third, a proposed explanation in which elastic ef-
fects are responsible for drag reduction.

(14) On the basis of DNS, a large number of investigations have been undertaken

to explain the drag-reduction. Den Toonder (22,54,65,86) has proposed the
following mechanism for the drag reduction by polymer additives. The poly-
mers become extended by the ﬂow at a certain Reynolds number, depending
on the time scale of the polymer molecules in relation to the time scale of the
turbulence. Hence, this “onset” phenomenon is determined by elastic prop-
erties of the ﬂuid. When the polymers are extended, viscous anisotropic
effects introduced by the extended polymers in the relation between the
stress and the deformation cause a change in turbulent structure and the
anisotropy production leading to a reduction in drag. At this stage, elasticity
plays a counterproductive role in the drag-reduction process.

(15) Dimitropolous and co-workers (88) pointed out that previous work on nu-

merical simulation on drag reduction has focused on the investigation of the
role of elongational viscosity through the use of generalized Newtonian mod-
els. They used the nonlinear elastic model with the Peterlin approximation
(FENE-P) and the Giesekus model (140) of viscoelasticity for the solution
at high extensional rates. In both the cases, comparing the mean velocity
proﬁles and the statistical features of the turbulent ﬂow showed agreement
with well-established experimental observations, such as the increase in
the spacing of the streamwise streaks and the increase in the streamwise
vorticity ﬂuctuations. In addition, the hypothesis that drag reduction is pri-
marily an effect of the extension of the polymer chains, where the increase
in the extensional viscosity leads to the inhibition of turbulence-generating
events, was once again reinforced.

(16) Sreenivasan and White (89) recently invoked the theory based on the elas-

tic behavior of stretched polymers of de Gennes (84), who states that coil-
stretch transition does not occur in turbulent ﬂows in randomly ﬂuctuating
strain rates and that, if moderately stretched, the polymers produce no
measurable change in viscosity. Sreenivasan and White (89) were able to
explain the onset of drag reduction and maximum drag reduction asymp-
tote on the basis of the elastic theory, and their results qualitatively explain
the existing experiments.

542

DRAG REDUCTION

Vol. 9

Degradation and Shear Stability Mechanisms

Though the DRE of polymers is very high at extremely low dose, the practical
problem in widespread applications of polymer additives is the degradation of
polymers in turbulent ﬂow. The degradation leads to a marked loss of the drag-
reducing capability of the polymer.

There are two types of degradation, chemical degradation and mechanical

degradation (65). Chemical degradation causes change in the structure of poly-
mers by chemical reactions. It can occur, for example, by the presence of metal or
any free-radical initiators when oxygen is present. The high salinity or calcium
concentrations in solvent can also cause chemical degradation (141).

Mechanical degradation is caused by mechanical energy input to the poly-

mers in solutions, which means passing the solution through pumps or pipes or
both. Mechanical degradation has long been associated with shear ﬂow. To some
extent, the shear ﬂow causes the degradation of dilute poly(enthylene oxide) so-
lutions (14). Bueche (142) showed in his pioneering work that the elongational
stresses which exist in some regions of turbulent pipe ﬂow are more severe and
cause scission of polymer molecules. A molecule in a shear ﬂow is subjected to
both rotation due to the presence of vorticity and to stretching and compressive
stresses. Bueche (142) showed that in simple shear ﬂows, the molecule is rotated
past principle axes much too fast to allow the ﬂow to stretch it to a large extent. On
the other hand, in elongational type of ﬂows, the vorticity is much less relative to
the stretching and aligning action of the strain than in shear ﬂows. A large num-
ber of investigations have been reported, which convincingly indicate that the
molecules are fully extended followed by mid-chain scission under elongational
ﬂow ﬁeld (143–147).

Mechanical degradation of polymers in turbulent ﬂow has been extensively

investigated and reviewed by Pollert and Sellin (148), Singh (20), Moussa and co-
workers (149), Moussa and Tiu (43), Gyr and Bewersdorff (23), Den Toonder and
co-workers (65), Nguyen and Kausch (146), Brostow and co-workers (62–64), Choi
and co-workers (141), Rho and co-workers (150), Kim and co-workers (151–155),
and Choi and co-workers (156–159).

It is well established that the extent of drag reduction increases with the

molecular weight and length of polymers, and so does their susceptibility to ﬂow-
induced degradation (20). The rate of mechanical degradation increases with the
increasing molecular weight. In most of the cases, it is possible to represent degra-
dation by an exponential expression using ﬂow time or number of passes as an
independent variable. In turbulent ﬂow, the degradation is more in poor solvent
at low Reynolds number, whereas the opposite was observed at high Reynolds
number. For constant wall shear stress and pipe diameter, the degradation rate
was found to be directly proportional to the molecular weight of polymers. For
constant wall shear stress and polymer concentration, the degradation rate was
found to be inversely related to pipe diameter. For constant wall shear stress
and pipe diameter, the degradation rate was found to be inversely propotional
to polymer concentration. For constant polymer concentration and pipe diameter,
the degradation rate was found to increase with wall shear stress. In general,
the shear stability increased with solvation number. The higher the ratio of total
length to the width of the polymer molecule, the faster will be the degradation. In

Vol. 9

DRAG REDUCTION

543

Fig. 7.

The variation of relative drag reduction with time for mixtures of pure xanthan

gum (10 ppm) and polyacrylamide (10 ppm):

×, Theoretical (Brostow Polymer Flow Model);

䊉

, experimental (59).

high turbulent ﬂow, the degradation is not caused not only by scission of polymer
chains, but also by a radical propagation reaction initiated by scission of polymer
chains.

The critical Reynolds number R

∗

or apparent shear/extension rate (v/d)

∗

was

found to increase with polymer concentration and molecular weight as represented
by the dimensionless concentration c[

η]. Most of the degradation takes place at

the entrance region because of high extensional straining of polymers.

The molecular degradation in turbulent ﬂow is also explainable by the theo-

retical model of Brostow (62–64) (see Fig. 7). The mid chain scission in turbulent
ﬂow has been experimentally and theoretically explained (143–145,147). Recently,
Kim and co-workers (153) studied the mechanical degradation of high molecular
weight polystyrene under turbulent ﬂow using a rotating disk apparatus for three
various solvent systems. They found that the extent of the degradation depended
on the solubility parameter of the solvents. Their experimental data for molec-
ular degradation in turbulent ﬂow gave an excellent ﬁt with the Brostow model
(62–64). Brostow (62) obtained the following relation:

DR(t)

+ w (1 − e

)

(32)

where DR(t) and DR

are the percentage drag reductions at times t and t

= 0,

respectively. A large value of h indicates fast degradation, and a large value of w
implies a low shear stability. Their data give excellent ﬁt to the equation.

Choi and co-workers (158) observed the following correlation between time-

dependent drag reduction and mechanical degradation:

DR(t)

= exp( − t/λ

)

(33)

544

DRAG REDUCTION

Vol. 9

where DR(t) and DR

are the percentage drag reductions at times t and t

= 0

respectively, and

is an adjustable parameter. 1/

measures the rate of degra-

dation. It describes the degradation mode very well for shear-resistant polymers
such as various CMC and CMC-based graft copolymers (125) and xanthan gum
(160).

However, the exponential equation deviates from the experimental data for

drag reducers such as ﬂexible PEO. Recently Sohn and co-workers (161) and Kim
and co-workers (155) have studied the drag-reduction characteristics of polysac-
charides such as xanthan gum and guar gum respectively. They are found to be
reasonably shear-stable drag-reducing agents (123,162,163). They are highly sus-
ceptible to biodegradation. To overcome this disadvantage these polysaccharides
have been grafted by ﬂexible polyacrylamide branches (122,123). The solutions
of both polymers conform to the empirical relationship between drag-reduction
efﬁciency and polymer solution properties (156) at a ﬁxed Reynolds number, ie

K[C]

max

(34)

where DR

max

is the maximum drag reduction, K is the characteristic parameter

which depends on the polymer solvent system, and C is the intrinsic concentration
(W

ppm

) deﬁned by

[C]

max

Lim

→0

(

)

(35)

and the universal curve for drag reduction when normalized by the hydrodynamic
volume fraction of the polymer solution (% DR/[

η]C vs [η]C) is due to McCormic

and co-workers (130–137).

They reported that volume fraction normalization allows the comparison of

drag-reduction efﬁciencies of polymers of widely differing structures. Xanthan
gum molecules in deionized water exhibit higher drag reduction in the range of
50–60

◦

C than at room temperature because of conversion to individual xanthan

gum molecules from aggregated helics. In case of guar gum, it was conﬁrmed that
K is a characteristic constant of a particular polymer/solvent system and does not
depend on molecular weight.

The turbulent drag reduction and drag reduction of DNA has been recently

investigated by Choi and co-workers (164). Double-stranded DNA is found to be a
good drag reducer when compared with the other normal linear polymers. How-
ever, the drag-reducing power of DNA disappears when DNA denatures into two
single-stranded molecules. DNA is always cut in half by the turbulence. Its degra-
dation is different from that of the normal ﬂexible long-chain polymers.

In a number of graft copolymers (122,124,165,166), it has been found that

the grafting increases the shear stability. However, in some cases, the grafting has
been found to reduce the shear stability of graft copolymers (123,125,126), which
supports the mechanistic analysis of Agrawal and Mashelkar (167).

A highly branched polymer of high molecular weight amylopectin and its

graft copolymer with polyacrylamide have been investigated by subjecting the
solutions by intensive turbulent ﬂow in turbulent rheometer at Reynolds number

Vol. 9

DRAG REDUCTION

545

Fig. 8.

The variation of viscosity ratio versus pass number at concentrations of 500 ppm

(a) and 100 ppm (b) respectively in case of solutions of polyacrylamide grafted amylopectin
(

䉬

), amylopectin (

) and polyacrylamide ( ) (R

= 14000), and at 50 ppm (c) for polyacry-

lamide (

) experimental and ( ) theoretical according to Brostow model (R

= 14000). (161).

of 14,000 (168) (see Fig. 8). The solutions were investigated in the concentration
range of 50–500 ppm, and mechanical degradation was monitored by measuring
absolute viscosities of sheared solutions from 10 to 50 pass numbers in turbulent
ﬂow rheometer. As is evident from Figure 8, the results contradict the Agrawal
and Mashelkar theory (167) and support the Brostow polymer model (62–64).
Apart from grafting, two other approaches have been put forward to enhance the
shear stability. The reversible intermolecular association in solution increases the
molecular weight of polymer and provides enhanced shear stability (46–49). The
drag-reducing polymers can be cross-linked to enhance drag reduction; the ﬂow

546

DRAG REDUCTION

Vol. 9

Fig. 8.

(Continued).

induced degradation of the polymers is not appreciably affected by the addition of
cross-linking agents (50).

Drag Reduction by Mixed Systems

The earlier work on drag reduction by ﬁbers, polymer/polymer, polymer/ﬁber, and
polymer/soap mixtures has been reviewed by Singh (20) and Gyr and Bewersdorff
(23). It has been noticed that ﬁbers with high aspect ratio (l/d), ﬂexibility, and
surface roughness show good drag-reduction effectiveness. At equal aspect ratio,
ﬁbers with smaller diameter cause more drag reduction. This can be attributed
to the improved ﬂexibility due to decrease in diameter of the ﬁbers. The ﬁbers of
nylon, wood pulp, acrylic, glass, and asbestos have been reported to cause drag
reduction in suspensions.

Both positive and negative deviations from the linear additive line have been

observed in drag reduction caused by polymer/polymer mixtures depending upon
their composition, ﬂow rate, and polymer species. The maximum synergism is
obtained at a speciﬁc composition. The random coil size, rigidity, and salvation of
polymer molecules appear to be responsible for the synergism in drag reduction
by polymer/polymer mixtures (169).

The maximum drag reduction caused by polymer/ﬁber mixtures is more than

predicted by Virk’s maximum drag reduction asymptote (170). Kale and Metzner
(171,172) explained the reasons for synergism in drag reduction by high exten-
sional effects on polymers along with ﬁbers and consequent high extensional vis-
cosities of polymer solutions. Reddy and Singh (169) found strong synergistic effect

Vol. 9

DRAG REDUCTION

547

with both guar gum and xanthan gums in combination with asbestos ﬁbers. A
50:50 mixture by weight gave the maximum in both cases. As observed by Hoyt
(17), both mass and length are responsible for suppression of turbulence by these
systems.

Recently, Inaba and co-workers (173) pointed out that it is possible to reduce

the pumping power, to downsize the transport system, and to decrease the heat loss
to environment by using surfactant water solution as a thermal energy transport
medium. The environmental pollution caused by discarding the used surfactant
solution has become a serious problem. It is required that the new additive have
the same ﬂow drag reduction effect as surfactant solution, and also that little envi-
ronment load be used. They used pulp ﬁber as the new type of ﬂow drag reduction
additive in a circular pipe. The pulp ﬁber consists of a vegetative ﬁber that forms
paper. Therefore, pulp ﬁber does not have harmful effects on the environment.
The ﬁbers were of the diameter range 6.45–29

µm and had an aspect ratio of 50:1.

The ﬂow resistance and heat-transfer characteristics of water suspensions with
pulp ﬁbers were measured. The velocity distribution of the pulp ﬁber suspension
was similar to the plug ﬂow in the laminar ﬂow. The ﬂow drag reduction effect
was observed. The enhancement effect of heat transfer in the laminar ﬂow and
the heat-transfer reduction effect in the turbulence were observed. The nondimen-
sional correlation equations of pipe ﬂow resistance and heat-transfer resistance
were derived in terms of various nondimensional parameters in the above study
(see Fig. 9).

Fig. 9.

Relationship between pipe friction coefﬁcient

λ and Reynolds number for various

pulp water suspensions. I depicts the theoretical equation of the ﬂow resistance in laminar
ﬂow in pipe and II depicts the Blasius resistance formula of turbulent ﬂow. C

, %:

䊉

, 0

(Water); , 0.30

;

䊉

, 0.55

;

, 0.72— - —. Adapted from Figure 9 of Ref. 166.

548

DRAG REDUCTION

Vol. 9

Drag reduction caused by passive devices such as riblets has been conﬁrmed

for various boundary layers and pipe ﬂows (174–178). However, riblets have a nar-
row range of the effective ﬂow rates, and if the ﬂow rate is higher than this effec-
tive range, the riblets increase the friction drag just like normal rough wall (179).
Walsh and co-workers (175–177) found that the triangular grooves of roughly
equal height and azimuthal spacing, ie h/s

≈ 1, provided the optimal drag reduc-

tion performance. They further found that relative to a smooth wall, riblets with
h/s

≈ 1 exhibited two general ﬂow regimes:

(1) For nondimensional riblet height h

< 25, the riblets reduced drag with the

largest reduction of the order of 10% at h

≈ 15.

(2) For nondimensional riblet height h

> 25, the riblets enhanced the drag by

as much as 30% at h

≈ 50.

It has been established that interﬂows of air and water in riblet-lined pipes

(180–183) show the same behavior as the external ﬂows over riblets. According to
Walsh (175,176), riblets act as fences to isolate the low speed streaks that exist
near the wall (184), and thus retard their bursting.

Bechert and co-workers (185) and Choi (186) have proposed that the riblets

impede spanwise motions of streamwise vortex pairs associated with sublayer
streaks, resulting in weakened bursts and lower shear stress. Choi and co-workers
(187) and Pullese and co-workers (188) conducted measurements of three rms tur-
bulence intensities and turbulence shear stress over riblet surfaces in their drag-
reducing regimes. These physical entities were reduced relative to their respective
magnitudes over smooth surfaces at the same force stream velocity. However, axial
to transverse correlations near the riblets surface remain much the same as those
near a smooth surface. This is in contrast to polymer drag reduction, where signif-
icant reductions in the axial to transverse velocity correlations relative to solvent
are observed (10). The drag enhancement by riblets at high h

was attributed

by Walsh (175,176) to adverse effects of the increased riblet wetted surface area
overwhelming the riblet-induced drag reduction. However, Tani (189) observed
the riblet drag enhancement as being akin to that by sand-roughened pipes and
estimated the equivalent sand roughness of riblets to be about a quarter of their
actual height.

Choi and co-workers (190) have carried out direct numerical simulation

of turbulent ﬂow over riblets at h

≈ 20 and 40, respectively, in drag-reducing

and drag-enhancing regimes. Interpreting their calculations in terms of coherent
structures, they pointed out that riblets reduce drag when the streamwise vortices
above them are aligned such that only a small portion of a riblet, near the tip, is
exposed to their downwash at higher h

; the streamwise vortices become smaller

relative to the riblets; and their downwash affects a greater fraction of the riblet
surface, enhancing drag.

The combined polymer additives and riblets are expected to cancel out the

drawbacks associated with applying each of these systems and to produce a
positive synergistic effect. The effect of combined experiment would also eluci-
date the respective drag-reduction mechanism. Choi and co-workers (190) experi-
mented on a ship model with riblets and then coated the model with polymer. The

Vol. 9

DRAG REDUCTION

549

measured drag of the model revealed that the combined system caused 2% higher
drag reduction than the additives of each systems effect. Rohr and co-workers
(191) measured the friction factor for dilute PEO in a pipe lined with 0.076-mm,
V-groove riblets (3MCO). He found that the combined system produced the same
drag reduction ratio as the polymer additive alone. Christodoulou and co-workers
(192) and Anderson and co-workers (180) carried out similar experiments. In both
experiments, results obtained for combined systems using PEO solutions showed
that the drag-reduction rates were less than the sum of two systems. In contrast,
Anderson and co-workers (180) observed for combined system using guar gum
that the drag rate was greater than the sum of the drag-reduction rates of the
individual systems and that the critical shear stress of the additive was lowered.
Koury and co-workers (178) carried out a systematic experiment for a combined
system of polyox and a riblet pipe. The positive synergistic effect was observed to
occur.

Recently, Mijunuma and co-workers (179) investigated the drag reduction

for combined system of polymer additives and riblet pipe. The riblet groups were
V-shaped, the spacing of which was 1.3 mm and the height 1.01 mm. For higher h

a triangular riblet system including other geometries increases the drag to levels
similar to those of normal transient roughness. The polymer additives were Aron-
ﬂoc N-110 and separan AP-31. The critical shear stress,

∗

, at which N-110 started

the drag reduction was approximately eight times higher than

∗

for AP-30. In

the combined system, the synergistic drag reduction for higher h

∗

was discussed

under the assumption that additives suppressed the drag increase resulting from
riblets. Since additives thicken a wall layer covering the region from a viscous
sublayer to a buffer layer, the relative height h to this wall layer thickness is
lowered. Another cause of the synergistic effect is the ﬂow enhancement due to
additives, which suppresses the riblet-induced drag increase. Hence the combined
effects almost cancel out the drag increase due to riblets. This synergistic effect
exceeds 10%. The analysis based on velocity proﬁles indicated that these effects
can produce synergistic drag reduction for higher h

∗

Drag reduction can be achieved by direct injection of microbubbles through

slots or porous skin (193–196) or the generation of hydrogen by electrolysis at
the wall (197). The primary parameters, independent of gas type and Reynolds
number, appear to be the actual gas ﬂow rate referenced to injector conditions
of temperature and pressure (198–200) and the location of the bubbles in the
turbulent boundary layer (198,199,201–203). Merkle and Deutsch (196) have pro-
vided a comprehensive review on skin friction reduction by microbubble injection.
Mahadevan and co-workers (204) postulated that microbubbles like polymer so-
lution destroy turbulence production by selectively increasing the viscosity near
the buffer region. They increase the local dynamic viscosity. Pal and co-workers
(205) demonstrated that microbubble and polymer solution shear stress statistics
as measured by ﬂush mounted hot ﬁlm sensors are similar at equivalent value of
drag reduction.

Fontaine and co-workers (206), on the basis of these similarities, envisaged

that high levels of drag reduction can be achieved by combining low concentra-
tions of polymer and surfactants with microbubble injection at low injection rates.
The inﬂuence of homogeneous surfactant (Aerosol OT) and homogeneous poly-
mer (PEO) solutions on the performance of microbubble skin friction reduction

550

DRAG REDUCTION

Vol. 9

was investigated on an axisymmetric body. Carbon dioxide was injected in wa-
ter, homogeneous surfactant solution, and homogeneous polymer solutions. The
integrated skin friction measurements were obtained at two free-stream veloc-
ities as a function of gas injection rate and PEO concentration. At similar gas
injection rates, microbubble injection exhibited more drag reduction. At low gas
injection rates, the results of this investigation indicate that the combination of
microbubble injection with polymer additives can yield drag reduction levels ex-
ceeding those of the individual systems. Maximum drag reduction in the combined
system was greater than 80% for 20-ppm polymer concentration and higher gas in-
jection rates. This level of drag reduction is higher than the levels obtained with
either polymer or microbubbles separately at these concentrations or injection
rates. In this study, synergism between microbubble and polymers was not ob-
tained. Reducing the bubble size through addition of surfactant did not affect the
characteristics of microbubble drag reduction. The resulting size of microbubble
is still large compared to turbulent scales and, thus, may explain the lack of effect
on drag-reduction characteristics of microbubbles with and without surfactant.

Watanabe and co-workers (207–210) reported drag-reduction phenomena in

different geometries having highly water-repellent walls in laminar region. The
basic material of the highly repellent wall is ﬂuorine alkane modiﬁed acrylic resin
with added hydrophobic silica, and the contact angle of the wall is about 150

◦

Watanabe and co-workers (207) reported for the ﬁrst time the laminar drag re-
duction of Newtonian ﬂuids ﬂowing in a channel with square and rectangular
ducts with highly water-repellent walls. The maximum drag reduction ratio of
water was 22% for the square duct. The drag-reduction phenomena were also ob-
served for the frictional resistance of an enclosed rotating disk with highly water-
repellent walls. The maximum drag reduction ratio for tap water was about 25%
at the Reynolds number of 2

× 10

. In their recent investigation (208–210), the

drag-reduction phenomenon in which 14% drag reduction of tap water ﬂowing in a
16-mm diameter pipe occurring in a laminar region has been explained. This phe-
nomenon occurred because of the presence of ﬂuid slip at the wall. The measured
velocity proﬁle gives the slip velocity at the pipe wall, and it was shown that the
shear stress is directly proportional to the slip velocity. The friction factor formula
for a pipe ﬂow with ﬂuid slip at the wall has been obtained analytically from the
exact solution of the Navier Stokes equation, and it well agrees qualitatively with
the experimental data. The main reasons for the ﬂuid slip have been pointed out.
In these cases, the molecular attraction between the liquid and the solid surface is
reduced because the free energy of the solid is very low, and the contact area of the
liquid is decreased compared with conventional smooth surface because the solid
surface has many ﬁne grooves. A liquid cannot ﬂow into the ﬁne grooves owing
to surface tension. These concepts are supported by the experimental result that
the drag reduction does not occur in the case of surfactant solutions.

Turbulent Drag Reduction by Surfactants

Recently, turbulent drag reduction by surfactants has been extensively reviewed
by Gyr and Bewersdorff (23), Zakin and co-workers (42), and Myska and Zakin

Vol. 9

DRAG REDUCTION

551

(41). The main features of the surfactant drag reduction and their industrial ap-
plications are summarized here.

The polymer solutions are strongly affected by mechanical degradation dur-

ing turbulent ﬂow which limits the lifetime of their DRE. The surfactants have
been found to reduce the frictional drag by 70–80%. At high stress, the surfactants
also suffer temporary mechanical degradation of their microstructure, but they
have the ability to repair themselves in the order of seconds (42).

The drag-reducing surfactant solutions are characterized by the presence of

rod-like micelles which are formed by single surfactant molecules above a certain
characteristic concentration (139). This critical concentration depends strongly
on temperature and electrolyte concentration. As mentioned earlier, critical wall
shear stress, a shear induced state (SIS), is achieved when the micelles are co-
alesced to form larger structure aligned in ﬂow direction. This is also the onset
stress of drag reduction by surfactant. The observed loss of drag reduction be-
yond this critical wall shear stress is reversible. The drag reduction is caused by
anionic, cationic, nonionic, and zwitterionic surfactants. Nonionic surfactants are
chemically stable, endowed with low toxicity, and biodegradable. However, their
effective temperature range is limited. Zwitterionic surfactants are more useful
as they have a larger effective temperature range. As they have both positive and
negative charges in single surfactant molecule they may be sensitive to ions exist-
ing in water. The cationic surfactants with the organic counterions are excellent
drag reducers in aqueous system. They have fairly wide temperature ranges and
are not sensitive to calcium or magnesium ions present in water. Because of their
potential for practical applications, they have been extensively investigated in the
1990s.

The DRE of cationic surfactant is greatly dependent on their chemical struc-

tures, surfactants, and counterion concentrations. Surfactants with short alkyl
chains are effective at low temperatures, while those with long alkyl chains are
effective at high temperatures. The dramatic effect of the counterion to surfactant
concentration ratio on ﬂuid characteristics of surfactant solutions has been found
recently. The proper combination of both can extend the effective range widely.

The surfactant drag reducers may exhibit strong viscoelasticity and high

extensional viscosity. Excess counterions in cationic surfactant may make the
solution still nonviscoelastic with distinct extensional viscosity. This suggests the
correlation between drag reduction and extensional viscosity.

The surfactant drag reduction may exceed Virk’s drag reduction asymptote

for high polymers, and velocity proﬁles may be steeper than his elastic sublayer.
The turbulence in radial and tangential directions is suppressed by surfactants.
The zero Reynolds stress proﬁles have been observed for surfactants. Though the
drag reduction mechanism is not established for surfactant drag reduction like
polymer drag reduction, its mechanism may be different.

Along with the reduction in momentum transport, drag-reducing ﬂuids have

also been found to reduce the heat-transfer coefﬁcients particularly in tube-in-
tube heat exchangers. The heat-transfer reduction accompanying drag reduction
may be caused by the thickening of the viscous boundary near the wall, which
increases the thermal resistance between wall and bulk ﬂuid and reduces the
radial turbulence intensity. Heat exchangers with ﬂow channels which disturb the
ﬂuid more, such as plate exchangers, show less heat-transfer reduction. Despite

552

DRAG REDUCTION

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several successful ﬁelds tests in district heating and district cooling systems, no
commercial scale applications of surfactant drag reduction have been undertaken
so far (23,31,42).

Applications of Drag Reduction

Introduction.

Ever since the discovery of the drag-reduction phenomenon,

efforts have been made for its industrial applications. In the last ﬁve decades, the
range of applications of drag reduction has increased tremendously. The possible
areas include oil-well fracturing operations, crude oil and reﬁned petroleum prod-
uct transport through pipelines, ﬁre ﬁghting, sewerage and ﬂood water disposal,
irrigation, hydrotransport of solids, water-heating circuits, jet cutting, hydraulic
machinery, and marine and biomedical applications. The detailed progress made
in these areas has been reported in various reviews (14,15,17,20,23,42,44,112,211,
212).

In crude oil transport and storm sewers, because of the economic beneﬁts,

the drag-reducing polymers have been put into practice in Trans Alaska Pipeline
and other 100 pipeline sites, as well as in other pipelines transporting reﬁned
petroleum products (213,214). Similarly, drag-reducing polymers in storm sewers
for Knowle and Dallas sewers (15) have been put to practice. Exigency require-
ments are in favour of applications of the drag-reducing polymers in ﬁre ﬁghting.
Hence the practice has been accepted by New York City Council and the City of
Hamburg. Large-scale ﬁeld experiments have shown the efﬁcacy of using drag-
reducing polymers in hydrotransport of ﬂy ash and sludge, heating circuits, water
power stations, and irrigation from Czechoslovakia (211). Use of drag-reducing
polymers has been made in short diversion tunnels and culverts in Yugoslovakia
(215). Drag-reducing polymers have been used in energy requirements of sprin-
kler irrigation, reduction of percolation losses, and development of slow-release
urea in India (33,44).

The efﬁcacy of drag-reducing polymers in reducing the drag, hull of a 42.7-m

long HMS Highbortor has been reported from the United Kingdom (216). In other
cases, laboratory scale experiments have been performed, indicating beneﬁcial
use of drag reduction. Large-scale applications are inhibited in many cases be-
cause of the high cost of polymers and their degradation. Large-scale laboratory
experiments as well as ﬁeld trials have been reported indicating efﬁcacy of cationic
surfactants in district heating circuits (42). Economically feasible applications are
described in some important cases.

Crude Oil Transport and Reﬁned Petroleum Products.

The most

spectacular success of the application of drag-reducing polymers has been in the
Trans Alaskan Pipeline (TAPS) in 1979, where the throughput capacity has been
above 2 million barrels of oil per day (BPD) from pipeline capacity of 1.5 million
BPD without the use of polymeric drag reducers (DRA) at present. The pioneer-
ing use in TAPS was to increase throughput while pump stations were being
constructed and commissioned. As the effectiveness of the DRAs improved in the
period 1979–1984, the need to build pumping station nos. 5 and 11 of the 12 disap-
peared. Present day DRAs are 12 times as effective as the initial materials used
in TAPS in 1979.

Vol. 9

DRAG REDUCTION

553

In the Iraq-Turkey pipeline, DRA is injected downstream from each of the 15

pump stations. The injections of 40–50 ppm of DRA at each pump station allowed
for an increase in throughput to 1 million BPD from a base ﬂow of 0.7 million
BPD.

A similar application of DRA has been undertaken to oil being pumped from

the offshore platforms to shore facilities (217). Since 1983, some pipelines have
used DRA for pipeline transportation of reﬁned petroleum products (213). Treated
ﬂuids include gasoline, diesel, heating oil, and C

carbon. Today, approximately

100 pipeline sites use DRA for increased throughput (213,214). Typical dose rates
for 10–30% ﬂow improvement in these pipelines are no more than 1–2 ppm poly-
mer per injection. Tests indicate excellent drag reduction without adverse effect on
engine (218). In 1994, DRAs were 14 times more effective than the initial material
used in TAPS in 1980.

The rapid and completely dissolving formulation will increase DRA effec-

tiveness and improve application predictability. In addition, the incorporation of
DRA into the design status of new pipeline construction deserves consideration
for either downsizing pipes or reducing the number of pumping facilities.

Applications of Drag-Reducing Agents in Agriculture.

Drag-

reducing polymers reduce the drag in a turbulent ﬂow and increase the drag
in laminar ﬂow because of an increase in shear viscosity. This feature of drag-
reducing polymers has been utilized in reducing the energy requirement of
sprinkler irrigation system in which the ﬂow is in turbulent region in laterals,
risers, and jets. Their use also increases the throughput and the area of cover-
age of sprinkler irrigation system (33,44,219–226). Water containing the drag-
reducing polymers percolates slowly in the soil. This is due to increased shear
and elongation viscosities of aqueous polymer solutions. The increased elonga-
tional viscosity produces a higher resistance in the porous media ﬂow in the soil.
Utilizing this aspect, a slow-release urea has been developed by blending urea
with guar gum (33,223), which has boosted yields of wheat and paddy by 20–
25% in ﬁeld trials at IIT Kharagpur. It also increased the yield of vegetables
such as cauliﬂower and brinjal in another ﬁeld trial done in IHRI, Ranchi, India
(227).

As guar gum is biodegradable, it does not affect the soil adversely. As a matter

of fact the residual positive effects in yield in subsequent crops have been observed
by Kar and Sahoo (228). There have been considerable developments in materials
and polymer solution injection systems in sprinkler irrigation system.

Singh and co-workers (229,230) have developed a series of polyacrylamide

grafted polysaccharides as drag reducers which are biodegradable and shear sta-
ble. Of these, polyacrylamide grafted amylopectin has been found to be the most
effective drag reducer, and it reduces percolation losses most effectively by 50%
at a concentration of 100 ppm.

In most of the reported investigations on sprinkler irrigation system, homo-

geneous drag reduction has been used in which the drag-reducing polymers are
dissolved in the inlet source itself. In ﬁeld conditions, the main water source for
sprinkler irrigation can be tubewell, open well, reservoir, or a running stream
or canal. In case of such sources, the polymer solution is required to be in-
jected either at the inlet or outlet of the main pump. As evident from Fig-
ure 10, outlet injection is most effective as the drag-reducing polymers are not

554

DRAG REDUCTION

Vol. 9

Fig. 10.

Effect of injection method on drag-reduction characteristics of 50 ppm of poly-

acrylamide grafted amylopectin (AP-g-PAM) and 100 ppm of AP-g-PAM

Inlet;

Ventury

(224).

degraded by the centrifugal pump (231). The cost beneﬁt analysis shows that
using drag-reducing polymers in sprinkler irrigation allows reduction in the
pipe diameter and the power of centrifugal pump, which reduces the installa-
tion costs as well as the energy required. The reduction in the percolation losses

Vol. 9

DRAG REDUCTION

555

brings down the amount of water needed. This integrated technology is impor-
tant for all those countries in the world which suffer from a shortage of water
(23).

Storm Sewer Augmentation.

Many sewers face overloading for a short

duration during storms or heavy rains or because of increase in catchment area
over the years owing to continued development. The capacity of sewers can be
increased by drag-reducing polymer dosing. It has been shown by Sellin and co-
workers (15) that the capital cost of dosing installations, recurring cost of polymers
and maintenance, etc, are much lower than the capital cost involved in laying down
a new sewer of 381-mm diameter in place of the existing 305-mm diameter sewer
(in the rate of 1:15 according to prices in 1979). Fully automatic polymer dosing
stations have already been installed in Buchman Creek (Dallas, Tex.) and Knowle
(Bristol, U.K.). In these installations, drag-reducing polymer powder poly(ethylene
oxide) water slurry is injected in the sewer. Bewersdorff and co-workers (232,233)
showed that polyacrylamide suspensions (SEDIPUR AL436 containing 25% ac-
tive material PAM by weight) can be injected economically to enhance the out-
put of a sewer in Dortmund (Hohensyburg Sewer). During storms, 20–30 ppm of
poly(ethylene oxide) or polyacrylamide can augment the ﬂow capacity by 20–30%;
economic feasibility studies together with 5-year data from an automatic dosing
station (234) demonstrate that this is a viable and practical solution to many
ﬂooding situations.

Conclusions and Future Scope

The origin of drag-reducing polymers still remains enigmatic though consider-
able progress has been made in understanding it at the molecular level. Now it is
possible to measure the extensional viscosity and other rheological properties of
drag-reducing polymers at drag-reducing concentrations. The numerical simula-
tions are also revealing other facets of the turbulent drag reduction phenomenon.
Various molecular models such as FENE-P are being tested. As has been pointed
out by Zhou and Akhavan (235), the most promising approach to accurate com-
putation of polymer drag reduction at present is through stochastic simulations.
However, on the application side, drag-reducing polymers are being used, as a
routine practice, in crude oil and other petroleum product transport. The most
prominent application seems to be yet realized in agriculture (236). On the ma-
terials side, the hydrolyzed and nonhydrolyzed grafted polysaccharides seem to
have a bright future, because these materials have not only distinguished drag-
reducing characteristics in turbulent ﬂow of water but also distinguished ﬂoccu-
lation and viscosifying attributes. Cationic surfactants seem to offer a shear- and
heat-resistant material for district heating and cooling systems (31,34). Further
research to identify a stable, low toxicity, and rapid biodegrading surfactant drag-
reducing system is being focused for the coming decades (31,42,237–241). Biomed-
ical applications of drag-reducing polymers also have a very bright future. In the
years to come, turbulent drag reduction would remain an exotic ﬁeld of research
and applications.

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RAKASH

INGH

Indian Institute of Technology

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