Drying of Fibrous Materials

Roger B. Keey

CONTENTS

33.1 Nature of Fibers ............... .......... .......... ............... .......... ............. ............... .......... .......... ............... ...... 755
33.2 Moistu re in Fibers ............... .......... .......... ............... .......... .......... ............... .......... .......... ............... ...... 755
33.3 Moistu re Mo vement in Single Fib ers ... ............... .......... ............. ............... .......... .......... ............... ...... 758

33.3. 1 Steady- State Beha vior ............. ............... .......... ............. ............... .......... .......... ............... ...... 759
33.3. 2 Unst eady-State Beha vior ..... .......... ............. ............... .......... ............. ............... .......... .......... .. 759

33.1 NATURE OF FIBERS

Fibers are regarde d as very elongat ed pa rticles. Staple
fibers that are spun into yarns have length /diamet er
ratios greater than 10,000 . The fibe r lengt hs of co tton
are of the ord er 25 to 75 mm; wool fibe rs may exceed
100 mm and are varia ble in lengt h even when shorn
from the same sheep ; flax fibers may be ava ilable in
length s up to 1 m [1]. The corres pondin g diame ters of
textile fibe rs range betw een 3 an d 5 00 m m.

Fib ers vary in cross-sect ional shape, both natur-

ally and by design. Wo ol fibers are essential ly round
and cotton fibers are elli ptical. Synthet ic fibers made
by melt spinni ng ca n be of a desir ed sh ape. Artifici al
fibers that are spun from solvent s in air or from an
aqueou s medium are usua lly irre gular in shape be-
cause of the skin-core effe ct [2]. Rayon , for exampl e,
can ha ve both regu lar an d irre gular cylindrical form s
composed of hollow as well as solid fibe rs.

The cross-sect ional shape influen ces the way

the fibers pa ck toget her in yarns. Silk fibers, becau se
of their trian gular secti on, can pack compact ly to
give smal l-diameter, de nse yarns. Natur al fibe rs
that grow in short lengt hs and are spu n into staple
yarns are very rarel y stra ight. Cotton and wool en
yarns natural ly ha ve a spiraling crim p. Textile fabri cs

are compo sed of inter locking threads in a gridlike
pattern pro duced by weav ing or knitting individu al
strand s.

W ood consis ts of a large number of fibe rs, to-

gether with cells of othe r types, bonde d togeth er by
lignin to form a solid and rigid struc ture. The fibe rs
are hollow, cylindrical structures , typic ally 1 to 4 mm
in lengt h, with wal ls composed mainl y of cellu lose
and its associ ated polysac cha rides. Most woods
shrink and swell with moisture content, but the
dimensional change is much smaller along the fiber
length compared with the changes across the fiber by
a factor of 50 to 100. Pulping, by chemical or thermo-
chemical means, delignifies the structure, releasing
individual fibers. Paper results from screening, drain-
ing, and drying the macerated mix to give sheetform
material of intertwined fibers. Wood fibers are also
hot pressed with resins, mainly urea formaldehyde,
into reconstituted timber products such as fiber-
boards and hardboards.

33.2 MOISTURE IN FIBERS

The amount of moisture adsorbable by the fibrous
material varie s markedly , as shown in

Table 33.1

Hydrophilic fibers of natural origin can take up

2006 by Taylor & Francis Group, LLC.

considerable amounts of moisture, whereas some ar-
tificial fibers are barely hygroscopic. The variation of
equilibrium moisture content with relative humidity
at constant temperature is shown in Figure 33.1 for a
number of fibers.

At low relative humidities (0 < p/p

< 0.35), water

is adsorbed monomolecularly by many natural fibers.
The equilibrium moisture content X

then relates to

the fraction of available sites taken up, i.e.

¼ fX

(33:1)

where X

is the moisture content for a fully completed

monomolecular layer. Cassie [3,4] considers that water
can be sorbed into hydrophilic fibers in one of two
states: either strongly localized or liquid-like. Through
a statistical thermodynamic analysis this concept leads
to the Brunauer–Emmett–Teller (BET) relationship:

¼ X

¼ Cw=(1 w)(1 w þ C)

(33:2)

in which w is the relative humidity or relative vapor
pressure p/p

and C is a coefficient that relates to a

partitioning between bound and liquid water. Windle
[5] has extended Cassie’s analysis to include three
distinguishable forms of sorbed water. Other elabor-
ations include the possibility of multiple molecular
sorption layers [6].

Schuchmann et al. [7] suggest that Equation 33.2

can be put in a more general form

¼ ax=(1 þ bx)(c þ x)

(33:3)

where a, b, and c are empirical coefficients considered
to be ‘‘shape characteristics.’’ The dependent variable
x is the relative humidity when the parameter is low,
and thus Equation 33.3 reduces to Equation 33.2 with
c

¼ 1. At very high relative humidities,

¼ ln (1 w)

(33:4)

This substitution enables relative humidity data for a
variety of food materials (including apple fiber) to be
satisfactorily correlated up to w

¼ 0.98.

Another modified BET equation has been derived

by assuming that moisture adsorption occurs at ran-
domly located, equal-size active sites and there is no
interaction between adsorbate entities [8]. These as-
sumptions lead to the expression

TABLE 33.1
Smoothed Values of Dry-Basis Moisture Content
(kg/kg) for the Adsorption of Water Vapor at 308C
onto Fibers

Relative Humidity, w ¼ p/p

Fiber

0.2

0.5

1.0

Casein

0.0615

0.1115

1.05

Cotton

0.0305

0.0565

0.23

Cotton, mercerized

0.042

0.0775

0.335

Nylon 6.6, drawn

0.0127

0.0287

0.05

Orlon (508C)

0.0031

0.0088

0.05

Rayon, cuprammonium

0.0515

0.0935

0.36

Terylene yarn

0.014

0.037

0.03

Viscose yarn

0.0555

0.101

0.46

Wood pulp

0.034

0.062

0.25

Wool

0.062

0.11

0.38

Source: Data from Currie, J.A. 1969. Thermodynamic properties
and

irradiation

studies

high

polymers,

Ph.D.

thesis,

Northwestern University, Evanston, IL.

Moisture
content (%)

Relative humidity (%)

100

6
7

FIGURE 33.1 Sorption isotherms for textile fibers: (1)
beryllium alginate, 258C; (2) calcium alginate, 258C; (3)
viscose, cellulose acetate, cupraammonium rayon, and
woolen yarn, 258C; (4) casein fiber, 258C, wool, 35.88C;
(5) jute; (6) mercerized cotton, 208C; (7) flax, 308C, hemp;
(8) steeped cotton, 208C; (9) acetate rayon, 258C; (10) linen;
(11) perlon, nylon, 258C; (12) cellulose acetate; and (13)
Pe–Ce rayon 208C. (From Krischer, O., and Kast, W.
1978. Die wissenschaftlichen Grundlagen der Trocknung-
stechnik, 3rd ed., Springer-Verlag, Berlin, p. 57.)

2006 by Taylor & Francis Group, LLC.

¼ Cw=(1 kw)(1 w þ Cw)

(33:5)

When k

¼ 1, this expression reduces to Langmuir’s

equation for monomolecular adsorption. If 0 < k < 1,
there is a finite maximum hygroscopic moisture con-
tent. While many textile fibers approach such a mois-
ture content asymptotically at high relative humidities,
some man-made fibers such as nylon and viscose appear
to have well-defined maximum hygroscopic moisture
contents [9]. In many cases, the coefficient k is greater
than 1. Jaafar and Michalowski [8] interpret this behav-
ior as the thermal effect of adsorption being equal to the
heat of condensation only after a multimolecular layer
has been formed.

As implied by the proposal of Schuchmann et al.

[7], many adsorption isotherms may be normalized by
plotting the equilibrium moisture content X

against

the free energy change of sorption (

RT ln w) [10,11]. It

is believed that desorption isotherms can be similarly
correlated, particularly at moderate relative humidities
when multimolecular adsorption is the dominant mech-
anism of attachment as the moisture content is directly
related to the thickness of the adsorbate layer. Tests with
particulate materials have shown that there is a linear
relationship between the free energy change and ln X

over a sixfold range in the latter [12]. This correlation
implies an explicit relationship for the equilibrium mois-
ture content of the kind

¼ A exp (BT ln w)

(33:6)

where A and B are empirical coefficients. Equation
33.6 predicts that there is a maximum hygroscopic
moisture content (when w becomes unity) that takes
the value A. In those cases when this moisture content
is ill defined and the equilibrium value increases rap-
idly with relative humidity, a form of Henderson’s
equation [13] is preferred by Papadakis et al. [14]:

¼ A [B=T] ln (1 w)

(33:7)

Henderson’s equation is based on the ratio of the
amount of adsorbed moisture per unit wetted surface
to the energy change on adsorption, this ratio being
assumed to be a function of the equilibrium moisture
content. Papadakis et al. [14] find that Equation 33.7
fits data for two kinds of cellulose over a range of
relative humidity from 0.113 to 0.946 and a range in
temperature from 20 to 938C. An important finding
of their work is that a correlation may fit data over a
limited range in relative humidity very well, but can
give misleading results if extrapolated beyond the
tested range, particularly to higher relative humidities
when different moisture-retention mechanisms take
place. Walker [15] makes the same point with regard

to water in wood. Strictly, the fiber saturation point
corresponds to the maximum hygroscopic moisture
content when the cell walls of the fibers are fully
saturated. However, at relative humidities above
0.98, the lumens and pits of the tracheid fibers begin
to fill by capillary condensation, causing a sharp up-
ward break in the sorption curve.

Since adsorbed moisture evaporates more readily

at higher temperatures, the equilibrium moisture con-
tent becomes smaller with increasing temperature at a
given relative humidity. Desorption isotherms, for
instance, of a never dried softwood such as sitka
spruce suggest that the fiber saturation point falls
from about 31% at a temperature of 258C to 23% at
1008C [16]. Under kiln conditions, the equilibrium
moisture content becomes very low: at a dry bulb
temperature of 1208C and a wet bulb depression of
308C, Hilderbrand gives this moisture content as
being only 3%. (Indeed, in using an oven-drying test
to determine the moisture content of a fibrous mass, it
is frequently assumed that the residual ‘‘moisture’’ is
negligible. Difficulties in using weight loss methods
to determine the moisture contents are discussed
in Reference 17.) Shubin [18] presents a useful chart
of equilibrium moisture content for wood covering
vapor pressures to 1 MPa and temperatures to 1808C.

Adsorbed moisture can be held very tenaciously

by natural fibers. Nuclear magnetic resonance studies
have shown that adsorbed water on green and remois-
tened wood can exist in two states, with an immobile
monolayer bonding directly to the cell walls of the
fibers [19]. For most woods the differential heat of
sorption is about half that of vaporization, falling to
about one quarter of that value when a complete
monolayer is formed at about 4 to 5% moisture
content [15].

The heat of sorption is the difference in specific

heat content or enthalpy between the bound moisture
and that freely attached at the same temperature and
total pressure. This enthalpy difference is normally
derived from a form of the Clausius–Clapeyron equa-
tion on the assumption that the moisture vapor phase
acts like an ideal gas and the molal volume of the
condensed phase is negligible compared with that of
the vapor. These considerations lead to the expression

¼ R

ln w

(1=T)

(33:8)

It follows that the heat of wetting can be found by
plotting

ln w against 1/T if sorption data are avail-

able at various temperatures. However, at low equi-
librium moisture contents (for wood fibers <7%),
this procedure is inaccurate and direct calorimetry is
preferable [20].

2006 by Taylor & Francis Group, LLC.

The free energy change –RT ln w is sometimes

used as an approximation to the heat of wetting.
For this approximation to be valid, the equilibrium
relationship must obey a degenerate Antoine expres-
sion

ln w

¼ a=T þ b

(33:9)

where a is a constant and b is zero. In many cases,
b will be nonzero, and a function of moisture content.
The difference between the free energy change and the
enthalpy associated with adsorbed moisture has been
associated with the entropy changes accompanying
the dimensional changes as fibers swell on the uptake
of moisture [21].

Moisture can have a profound effect on the mech-

anical properties of fibers. Water imbibed by the cell
walls of fibers causes swelling and moisture loss
causes shrinkage. Loading, including the develop-
ment of drying stresses, introduces a creep strain
that may not fully recover when the load is released.
This is known as permanent set. With hydrophilic
materials, moisture is found to reduce stiffness and
increase creep, possibly as a result of plasticization.
Variations in moisture content enhance creep.
Changes in the rigidity of wool fibers undergoing
both adsorption and desorption of moisture have
been reported by Mackay and Downes [22]. The
creep of aromatic polyamide fibers at constant mois-
ture content is found to follow the logarithmic rela-
tionship [23]

(t)

¼ a þ b log t

(33:10)

where «(t) is the strain, a function of time t. If the
fibers are exposed to an environment in which the
relative humidity is cycled between limits, then con-
siderably enhanced strain rates are found [24]. At
608C, recycling between 5 and 95% relative humidity
produces the same strain in 2 days as that expected in
5 y when the material is kept at the higher relative
humidity.

Wood fibers shrink anisotropically on drying

below their saturation point. Walker [15] cites some
possible reasons for this behavior, including the pos-
sibility that microfibrils in the cell wall restrain the cell
wall matrix of lignin and hemicelluloses, and differ-
ences in the behavior of earlywood and latewood
between growth rings. The transient effects of mois-
ture on the strength of products composed of wood
fibers are reviewed by Back et al. [25]. The effect of
drying on the properties of wet wood pulp fibers is
summarized by Kumar and Mujumdar [26]. Drying
weakens the fiber mat causing a substantial reduction
in breaking length. However, a study of the drying of

simple, virgin fibers shows an improvement in tensile
strength, but predried fibers of less hemicellulose con-
tent do not [27]. Optical properties are also affected
by drying, with a decrease in light-scattering ability.

Fibrous materials are dried commercially in super-

heated steam as well as air [28]. Materials include cellu-
lose, corn gluten, and sugar beet pulp. Superheated-steam
drying has the advantages of lower energy use compared
with air drying, absence of oxidation, and less contamin-
ation of the product. Bernardo et al. [29] provide some
data on the relative coloration of layers of sugar beet fiber
when dried in air at temperatures up to 1058C compared
with drying in superheated steam at temperatures up to
1508C. The white color of the fibers dried with hot air is
preserved, but yellowing of the fibers occurs with super-
heated steam at dry matter contents >80%. This reaction
may be caused by an initial rehydration, producing traces
of melamines.

33.3 MOISTURE MOVEMENT

IN SINGLE FIBERS

From thermodynamic reasoning we expect the move-
ment of water through a single fiber to occur at a rate
that depends on the chemical potential gradient. For
movement in one direction, the flux of moisture may
be written as

¼ Bc

(33:11)

where B is some coefficient, c is the total concentra-
tion, and m is the chemical potential gradient. Equa-
tion 33.11 can be reexpressed in terms of the
concentration gradient by

¼ BRT

ln a

ln c

(33:12)

on introducing the activity of the sorbed moisture. The
term in parentheses is the diffusion coefficient, and
Equation 33.12 is a form of Fick’s first law of diffusion.

In the hygroscopic moisture regime, when the

activity is not equal to the concentration, the diffu-
sion coefficient can become highly concentration
dependent. Further, at low moisture contents, sorbed
water may form strong bonds with a hydrophilic
fiber, so that simple diffusion can no longer occur.
The concept of sorptive diffusion has been introduced
to describe the way moisture might migrate under
these conditions [30]. Only those molecules with
kinetic energies greater than the activation energy of
the moisture–fiber bonds can shift from one site to
another. The driving force for sorptive diffusion is
considered to be the sorptive pressure, which acts

2006 by Taylor & Francis Group, LLC.

over two-dim ensional regions in a simila r way to
vapor pressur e a cting in three- dimens ional spa ce.

Ho wever, diffusion coeffici ents based on conc en-

tration gradien ts are still commonl y emp loyed as a
means of descri bing the rates of mois ture movem ent.
In general, the diff usion co efficient will be a function
of both con centration an d tempe rature. At constant
tempe rature, the diffusion coeffici ent is only inde-
penden t of concen tration if the moisture isotherm is
linear or the mois ture unbound. Isothe rms for many
fibers are approximately linear over the range of rela-
tive humidi ty from 20 to 80%, as the data in

Figu re

33.1

. Thus , in a number of practi cal ap plications , the

assumption of a concentration-independent diffusiv-
ity can lead to useful results.

Fick’s first law can be expressed in terms of the

dry basis moisture content gradient by noting

¼ (D)

X )

(33:13)

where p

is the density of the solid matrix. This density

is a function of the moisture content as the fiber swells
or shrinks in response to the moisture present. Gen-
erally, only the bone-dry fiber density n˜

is known,

and Equation 33.13 is transformed into Equation
33.14:

¼ (D)p

(33:14)

The diffusion coefficient is now concentration depen-
dent, reflecting dimensional changes in the fiber. Such
changes can be accommodated by appropriate defin-
itions of length coordinates to avoid shrinkage effects
within the diffusion coefficients [31].

Notwithstanding a variety of cross-sectional shapes

that are found, a fiber may be viewed, to a first ap-
proximation, as a long circular cylinder, either hollow
or solid. Under these conditions, the moisture concen-
tration is a function of fiber radius r and time t only,
and mass balance over an elemental isotropic volume
yields a form of Fick’s second law of diffusion:

(33:15)

Coumans and Thijssen [32] derive a form of Fick’s
second law that can describe the drying of either solid
or hollow cylinders exhibiting linear volumetric shrink-
age. The space coordinate is taken as the relative radial
distance at any time, while the diffusion coefficient is
assumed to increase as a power law function of volu-
metric moisture content. This implies that the diffusion
vanishes as the fiber approaches equilibrium.

Crank [33,34] provides numerous solutions to

Fick’s second law for a variety of boundary condi-
tions. Some of the more important solutions follow.

33.3.1 S

TEADY

-S

TATE

EHAVIOR

At steady state, when the diffusion coefficient is inde-
pendent of position, Equation 33.15 reduces to

¼ 0

(33:16)

which has the general solution

¼ A þ B ln r

(33:17)

where A and B are constants to be determined from
the boundary conditions.

One solution, which sometimes corresponds to an

early period in the drying process, is the condition
that the upper surface at r

¼ R

is kept at a constant

concentration c

and at the outer surface (r

¼ R)

evaporation takes place in the atmosphere for which
there is an air–surface equilibrium concentration of
c

. A mass balance at this outer surface (r

¼ R) gives

¼ b(c c

)

(33:18)

where b is a mass transfer coefficient. This boundary
condition leads to the solution

þ a ln (R=r)] þ ac

ln (r=R

)

þ a ln (r=R

)

(33:19)

in which a

¼ bR/D and is a Sherwood number.

The loss of moisture per unit length of fiber is

given by

¼ (2pR)D

¼ 2pD

þ a ln R=R

)

(33:20)

which reduces to the expression

¼ (2pR)b(c

)

(33:21)

for thin-walled fibers.

33.3.2 U

NSTEADY

-S

TATE

EHAVIOR

The expression

¼ u exp (Da

(33:22)

2006 by Taylor & Francis Group, LLC.

is a solution of

Equat ion 33.15

for constant diffusiv ity

provided u is a functio n of the radial dimens ion r only
satisfy ing

þ a

¼ 0 (33 : 23)

which is a Bes sel’s equati on of ord er zero. Sol utions
of Equat ion 33.23 may be fou nd in term s of Bessel
functio ns, ch osen to satisfy initial and bounda ry
conditi ons.

Cra nk [33, 34] has present ed a numbe r of such

solution s. If the cylind rical fibe r is initially at a
unifor m co ncentra tion c

, and there is a surface

conditi on

@ c

@ r

¼ b( c

) (33 : 24)

where c

is the actual surfa ce conc entration at so me

time t and c

is the final c oncentra tion at the surfa ce at

equilibrium , then the requir ed solution is

¼ 1

2LJ

( ra

)

( a

þ a

) J

)

exp (

2
n

Dt=R

)

(33 : 25)

In this expression , J

( x) is a zero-ord er Bessel func-

tion of the first kind, a is the nondimens ional qua n-
tity bR/D , an d the coefficien ts a

are roots of the

equati on

( a)

¼ 0 (33 : 26)

in whi ch J

(x ) is a first-order Bessel fun ction. The

fractional reductio n in moistness , M

, compared

with the amount lost after infinite time when the fibe r
reaches equilibrium is given by

¼ 1

exp (

Dt=R

)

( a

þ a)

(33 : 27)

Newman [35] pro vides tabula r v alues of M

which Crank [33] has plotted in graphic al form , re-
produced he re as Figure 33.2.

Anothe r useful solut ion of Bes sel’s e quation oc -

curs with the case of a cylin drical fibe r initially at
unifor m concentra tion c

and sub jected to the co ndi-

tion that there is a co nstant transfer rate at the surface
(corresponding to constant drying rate conditions).
This boundary condition may be written as

¼ J

¼ cst

(33:28)

Macey [36] gives the solution at large times for the
fractional reduction in moisture content as

¼ 1

A
R

(33:29)

where A

¼ @c/@r at the surface, r ¼ R. Values of the

concentration distribution given by Crank [33] are
plotted in

Figu re 33.3

wi th the Four ier number Dt/ R

as a parameter.

1.0

0.8

0.6

0.4

0.2

M∞

Dt/R

√

FIGURE 33.2 Fractional loss of moisture (M

) from a cylindrical fiber, as a function of (Dt/R

)

1/2

. The parameter is the

Sherwood number a

¼ b/D. (From Crank, J. 1956. The Mathematics of Diffusion, Oxford University Press, Oxford and

Newman, A.B. 1931. Trans. AIChemE, 27:203–220.)

2006 by Taylor & Francis Group, LLC.

Desorption 0.33 to 0.146 Regain

Desorption 0.146 to 0 Regain

Desorption 0.33 to 0.146 Regain

Desorption 0.146 to 0 Regain

Bed length in mm as parameter

Bed length in mm
as parameter

(a)

(b)

(c)

(d)

2.5

0.35

Regain

Time (min)

0.30

0.25

0.20

0.15

0.10

0.05

Regain

Temperature

(8C)

Temperature

(8C)

FIGURE 33.3 Response of a 30-mm thick wad of wool to environmental changes: (a) moisture content (regain) changes from
0.33 to 0.146 kg

; (b) moisture content (regain) changes from 0.146 to 0 kg

; (c) temperature changes on drying

from 0.33 to 0.146 kg

; and (d) temperature changes on drying from 0.146 to 0 kg

. (From David, H.G., and

Nordon, P. 1969. Text. Res. J., 39(2):166–172.)

2006 by Taylor & Francis Group, LLC.

The moisture diffusion coeffici ent wi thin a single

wool fiber is of the order 10

[34] . When

there is no su rface resi stance,

Figure 33.2

indica tes

that for fiber diame ters, typic ally 20 mm for wool , the
fiber will respond to a change in mois ture co ndition s
very quickly , being abo ut 98% complet e within 2 5 s.
Experim ental ly, King and Cas sie [37] ha ve measur ed
the mois ture uptake in vacuo by a sliver of Merino
wool (havi ng a fiber diame ter of 21 mm). A tempe ra-
ture of 65 8 C was obs erved afte r 30 s but, by correct ing
the effe ct of the heat of adsorpt ion, the authors co n-
clude that the fiber would reach equilib rium in a time
less than 15 s. Clearl y, a mass of fibe rs will react
rapidly to its surroundi ng en vironm ent, and local
hygrothe rmal equ ilibrium may often pertain.

33.4 RESPONSE OF A FIBER MASS

TO ENVIRONMENTAL CHANGES

Henry [38,39] first provided a theoretical framework
to describe the response of a fiber mass to step changes
in humidity or temperature in the surrounding
environment. He assumed that the amount of moisture
held by unit mass of fiber was a linear function of the
water vapor concentration c

in the air space between

the fibers and the temperature T:

¼ X

þ s c

þ v T (33 : 30)

in which X

and the coefficien ts s and v are

constant s. Thes e coeffici ents have the meani ng of
(@ X /@ c

)

and ( @ X/ @ T)

, respectivel y. Alth ough

Henry assum ed constant values for these coeffici ents,
they ha ve be en found to be strong functio ns of
moisture content an d tempe ratur e for both co tton
[39] an d wool [40]. The co efficien t X

may be regarde d

as da tum mois ture con tent. Local hygrothe rmal
equilibrium is assum ed. The equ ations for the diff u-
sion of moisture vap or and tempe ratur e through the
mass in the longit udinal direction reduce to the pair
of exp ressions

@ x

@ t

( c

lT ) ¼ 0

@ x

@ t

( T

)

¼ 0

(33 : 31)

in whi ch

¼ gv=(1 þ gv) with g ¼ (1 «) =«r

(33 : 32)

and

¼ hs=(1 þ hv ) with h ¼ DH

(33 : 33)

It foll ows from the previous eq uations that g

1 and

thus l is also smal l: the concen tration chan ges are
scarce ly influ enced by tempe ratur e. Fur ther, h

and

jnj ! js/vj, so the tempe ratur e ch anges depend

upon the mois ture con centration shifts.

As air is passed through a bed of moist hygroscopic

fibers, the temperature fronts are seen to sweep through
[41]. Associated with these temperature fronts are
moisture concentration fronts, of which the second is
the greater. Both fronts travel at widely different, but
constant, velocities. The first front travels at a fraction
of the air velocity, while the second front moves at a
velocity of several orders of less magnitude. The slow
second front is normally the one of principal concern in
drying technology, being associated with majority of
the moisture content change.

Nord on [42] mod els the passage of these front s on

the assump tion that the moisture trans fer in the fibe r
is very fast co mpared with the diffusion within the
interfib er space. The mo isture co ntent and tempe ra-
ture pro files calcul ated by him for the drying of a
thick wad of wool are present ed in

Figu re 33.3a

and

Figure 33.3b for the exposure of fully saturated
material to air of 65% relative humidity, and that of
material equilibrated to perfectly dry air. The corre-
sponding moisture contents are 0.33 kg/kg at w

¼ 1

and 0.146 kg/kg at w

¼ 0.65. Nordon’s calculations

apply to the case in which the wad is relatively exten-
sive (a thick bed or a slow airflow rate) and would not
be applicable to high-intensity drying of thin webs. In
that case, the number of transfer units (in the airflow
direction) is very small and the drying air no longer
emerges saturated for most of the drying time, as in
the example evaluated by Nordon.

For the purpose of calculating the propagation of

the changes in humidity and the moisture content, the
effects of the first, essentially thermal front can be
neglected. The lowest temperature attainable in desorp-
tion is greater than the adiabatic saturation tempera-
ture, but only by a small amount. The drying of the bed
as a whole can show a long constant-rate period that is
only slightly smaller than the constant-rate period when
the fibrous material containing free water is dried. This
behavior is the characteristic of drying webs with large
extensiveness (large number of transfer units).

Nordon’s predictions have been subsequently con-

firmed in tests on changes in moisture content and
temperature in response to hygrothermal changes in
the surrounding air, and in the changes that accom-
pany the Hoffmann pressing and heat through fabrics
during changes in moisture content [43].

In another work, Nordon and David [44] have

modified their analysis to take account of the two-
stage sorption behavior of a textile material and
moistness dependence of the transfer rate. Use of

2006 by Taylor & Francis Group, LLC.

this elaboration does not alter the essential conclu-
sions of Henry’s linearized analysis. A wad of textile
material exposed to a sudden rise in ambient relative
humidity experiences the passage of the fast tempera-
ture front with a rise in temperature, and a slow front
with a drop in temperature of equal magnitude. Of
the two corresponding humidity fronts, only the slow
one is obvious as the fast one is very small and super-
imposed on the major one.

Henry’s linearized analysis, with averaged values

for the coefficients s and w, has been used by Walker
[99] to estimate changes in temperature and weight of
wool bales, both open and enclosed, when exposed to
an environmental change in temperature and humidity.
The method is able to follow the response in core tem-
perature and bale moisture to the new equilibrium level.
Walker also used the technique to determine the equili-
bration of overdried fleece wool in an undisturbed bin.
After 1 day, the moisture uptake is calculated to pene-
trate 150 mm into the fibrous mass, reaching 700 mm
after 10 days and 1.1 m after 100 days.

More recent work by Cudmore et al. [45] high-

lights difficulties in using Henry’s methods in analyz-
ing the behavior of modern high-density bales of
scoured loose wool in which there may be pockets of
relatively wet material, and significant unbound mois-
ture transport may prevail. When fiber is packed at
high density, its equilibrium moisture content and
the apparent moisture diffusion coefficient appear to
fall, and data obtained with materials packed loosely
may no longer apply. Moisture diffusion in the bale
approaches that in a single fiber. Under these condi-
tions, Cudmore et al. describe the moisture redistri-
bution in terms of Fickian movement between slabs
at different moisture content, employing diffusion
coefficients that are a function of temperature and
packing density [46]. Temperature changes were ex-
perimentally found to be insignificant.

The influence of the openness of a fiber matrix on

the effective moisture diffusion is also observed in the
diffusion of water vapor through wood pulp and
paper sheets.

Nilsson et al. [47] find that the apparent moisture

diffusion coefficient falls from 5.4

to 2.1

as the density increases from 500 kg

(softwood pulp) to 1530 kg

(coated and

calendered paper).

33.5 CONVECTIVE DRYING

OF FIBROUS MASSES

Moisture migration in fibrous and porous media can
occur in a number of ways: (a) by liquid diffusion
along the fibers due to moisture and temperature

gradients; (b) movement due to capillarity and gravity
within interfiber spaces; and (c) vapor diffusion due
to variations in moisture vapor pressure throughout
the mass. Knudsen flow or effusion exists when the
mean free path of the vapor molecules is of similar
dimensions to the space between the fibers. This is
unlikely under most commercial drying situations.
Surface diffusion of sorbed moisture may also occur,
but such movement may not significantly influence
the transport of moisture as the migrating material
may simply recirculate around a single air-filled
pocket [48]. Transport of sorbed moisture through
fibers, however, does appear to take place [49].

It is normally assumed that large fiber masses,

fiberboards, and webs are macroscopically homoge-
neous so that it is possible to apply conservation and
constitutive equations over sufficiently small control
volumes to obtain smooth profiles of temperature and
moisture, as implied in the work de scribed in

Se ction

33.4

. Shoul d no detai led infor mation on these prop -

erties be needed, it is possible to fit a simple diffu-
sional equation to the drying process, often with a
concentration-dependent diffusion coefficient [50]. In
the hygroscopic moisture region, tests with glass fiber-
boards suggest that temperature gradients can make a
significant contribution to the total moisture transfer,
with a thermal gradient coefficient in the order of 2

[51].

The relative success of the concept of the charac-

teristic drying curve has led to the investigation of
whether the concept describes the drying of beds of
loose fibers. This concepts derives from van Meel’s
idea [52] that for a given material the rate of drying,
relative to the value when only the external boundary
layer controls the process, is only a function of the
volume-averaged moistness, expressed as the relative
free moisture content. In other words, the drying
kinetics may be described by a function of the kind

¼ f (F)

(33:34)

where

¼ N

and F

¼ (X X

)/(X

), subject

to the boundary conditions

¼ 1, F ¼ 1 at the critical moisture content

¼ 0, F ¼ 0 at equilibrium with

¼ 1 for F $ 1 (unhindered drying period), and

thus

0 # f # 1 over the range, 0 # F # 1 (falling rate

period).

With some hygroscopic fibers, however, an initial,

constant drying rate period is uncertain, giving rise to
doubts about the estimation of an appropriate critical
moisture content. Walker’s data [40], for drying wool in
cans under constant external conditions, show a

2006 by Taylor & Francis Group, LLC.

maximum drying rate, but no period in which the drying
rates remained constant. Moreover, a mass of loose
fibers do not constitute a simple capillary-porous
bo dy , a nd th e m ec ha ni sm s t ha t g iv e r is e t o a c ons ta nt -
rate period in a porous network [53] do not arise in a
touching fibrous assembly. Recent experiments [54] on
the transport of water and n-propanol through samples
of Kraft pulp and filter paper confirm lack of import-
ance of capillarity. Even with knitted fabrics, drying has
been envisaged in terms of evaporation at all depths in
the material and vapor diffusion there from [55].

If there is no critical point, Lang rish et al. [56]

suggest that it might be possibl e to derive normal -
ized drying rate curves based on the init ial rather
than the critical mois ture content . A function al
relationshi p

¼ g( G) (33 : 35)

where g

¼ f/ f

and G

¼ F /F

will be found if the

origina l charact eristic drying curve takes the sim ple
algebr aic form ,

¼ A F

(33 : 36)

in which A and n are coeffici ents. It is also somet imes
possibl e to estimat e an app arent crit ical point from
data obtaine d whol ly in the fall ing rate period in
drying thin layer s of mate rial [12] .

Tubbs [57] finds a characteristic drying curve

for loose wool hung in minibales in an airstream over
a limited range of humidity potential and air velocity.
Later work by Keey and Wu [58] on through-circulating
thin layers of saturated wool over a temperature range
from 60 to 858C, indicates that the concepts hold ap-
proximately for these conditions, with n

¼ 0.6. The

fractional dryness of the surface will be a limiting factor
in the cross-circulation drying of thin veneers and webs,
as noted in the experiments of Peck et al. [59] who find
n

¼ 2/3 in the drying of thin slats of balsa wood. The

internal resistance to moisture movement is essentially
negligible with porous materials less than 6 mm in
thickness.

A single characteristic drying curve is unlikely to be

found in the drying of bulk fibrous material, such as
timber boards. However, Keey and Pang [60] note that
the high-temperature drying of softwood boards of a
given thickness can be described by two common curves
for commercial kiln ranges in temperature and humid-
ity. One curve relates to the period when an evaporative
front at the boiling point sweeps through the material;
the other to the period when cell wall and bound water
diffusion takes place below the fiber saturation point.

W ith bulk y stuff, such as bound bobbi ns of cloth

and yarn, capillary trans port of mois ture is possibl e.

Nissan et al. [61] hav e investiga ted the drying of a
127-mm wide piece of Ter ylene cloth (a polyester
fiber) wound on a spool to give ab out 25-mm
depth of material and the drying of a sim ilar
wound bobbi n of wool co mposed of bulk ed yarn in
heavy and felted cloth. A critical mois ture con tent at
0.73 kg

was found with the Tery lene bobbin ,

but for the wool the value was 2.96 kg

. A

feature of these an d other tests rep orted by Bel l
and Nis san [62] was the app earance of a pseudo
wet bulb tempe rature, a quasisteady tempe rature
determined by the thermal balance betw een the in-
ward trans fer of heat and the outw ard evapo ration
of mois ture from the body of the wind ing, as illus-
trated in

Figure 33.4

. Such resul ts su ggest that the

drying can be modeled in term s of an evaporat ive
plane recedi ng from the exposed surfa ce.

Gummel [63,64] has examined the through-circula-

tion drying of textile and paper webs. These are
regarded as regular porous networks, with the threads
composed of multiple strands of individual fibers
(

Figure 33.5

). Some values of characteristic dimensions

reported by Gummel are given in

Table 33.2

. The

textiles were through-circulated in the range of temper-
atures from 20 to 708C, and the paper tissue from 20 to
908C at air velocities between 0.06 and 1.5 m

. The

results for textiles could be expressed in the form of
normalized drying curves, with a critical point of
0.41 kg

for the textile fabrics. The normalization

was less convincing for the data involving paper tissue,
with highly variable critical moisture contents in the
range of 2.6 to 4.0 kg

being recorded.

In a later work, Albrecht [65] showed that char-

acteristic drying curves could be drawn up for the
through-circulation drying of cottonlike fabrics over
a range of incident velocities from 0.1 to 0.6 m

The critical moisture content was defined by the inter-
section of the constant rate and linearized falling rate
curves. One has

¼ KX ¼

(33:37)

where K is an empirical drying coefficient. It follows
that the critical moisture constant becomes

(33:38)

with

( ln X )

(33:39)

and N

is the maximum unhindered drying rate.

2006 by Taylor & Francis Group, LLC.

More advanced models of the drying of fibrous

webs take into account the interaction of water and
the solid matrixes [66]. For example, dry paper fiber
consists of about 100 lamellae, but is not porous [67].
Water can diffuse into the fiber and dissolve within
the cellulose and hemicellulose, causing swelling
across the fiber but not along it. Completely wet
paper consists of moisture between fibers and bound
water within the solid matrix.

Only when the moisture content reaches the fiber

saturation point does the intrafibrous moisture vanish
and the paper begins to shrink.

Pores within the fibrous mass may not lead to the

exposed surface, but may have dead ends or simply be
occluded. Methods of estimating capillary motion in
such porous structures are considered by Neiss and
Winter [68].

Air speed 5.25 m/s

Air temperature

Drying rate

(g/min)

Depth (mm)

200

400

600

800

1000

Time (min)

Calculated wet bulb temperature

Calculated pseudo wet bulb temperature

1200

1400

Consistent rate

Temperature

(8C)

First falling rate

Second falling rate

FIGURE 33.4 Temperature profiles on drying a 28-mm diameter bobbin of wool at a dry bulb temperature of 808C, a
wet bulb temperature of 308C, and an air velocity of 5.5 m

. (From Bell, J.R. and Nissan, A.H. 1959. AIChemE J.,

5:344–347.)

FIGURE 33.5 Model of a textile web (d ¼ yarn diameter; and s ¼ thread spacing). (From Gummel, P. 1977. Durchstro¨-
mungsrocknung. Experimentalle Bestimmung und Analyse der Trocknungsgeschwindigkeit und des Druckverlustes luft-
durchstro¨mster Textilen und Papiere, Dr. Ing. thesis, University Karlsruhe, TH.)

2006 by Taylor & Francis Group, LLC.

Besides any capillary transport of liquid moisture

and vapor diffusion, there is sorptive or bound mois-
ture diffusion within the fibers when they are less than
fully saturated [49]. At relative humidities below 0.8,
the sorptive transport coefficient diminishes exponen-
tially with decreasing values of relative humidity.

The use of such a detailed mechanistic picture of

the pore structure in modeling the convective drying
of paper is described by Harrman and Schultz [69].
The alternative approach is to consider the capillary-
porous web as a continuum having equivalent ther-
modynamic properties to the pore system [70]. This
approach has recently been described in detail by
Lampinen and Ojala [71].

33.6 THROUGH-CIRCULATION

OF LOOSE FIBERS AND WEBS

Kro¨ll [72] reviews the kinds of commercial through-
circulation dryers that can treat loose fibers and
fibrous webs, and Watzl [73] presents a more recent
overview of these kinds of dryers with particular

reference to energy conservation and environmental
protection.

Originally, cloth was stretched out on a wooden

framework or tenter in the open air to dry, the edges
being firmly held by hooks. To be on ‘‘tenterhooks’’ has
entered the English language as a figurative expression
for being held in suspense under tension. Today the
tenteryards have been replaced by enclosed dryers
through which the cloth is moved over pegs. Loose
fibers can be conveyed by perforated bands through
which the drying air is circulated. Most modern drying
systems, however, incorporate rotating perforated
drums that take up less floor space than horizontal
band dryers. Single-drum dryers can be adapted for
the drying of paper tissue and carpet lengths, while
multiple-drum units can handle loose fibers such as
fleece wool. Table 33.3 gives an indicative comparison
of the major dryer types. Cylinder machines offer ad-
vantages in space needs and thermal economy.

The evaporative capacities in Table 33.3 are some-

what higher than the corresponding values given by
Stewart [74] for fleece wool dryers, namely, 10 to
15 kg

for belt (or brattice) dryers and 20

TABLE 33.2
Characteristic Dimensions of Some Textile and Paper Webs

Material

Number Threads (mm

)

Thread Diameter (mm)

Pore Width (mm)

Thickness (mm)

Weight (g m

)

Polyester PES626

2.68

324

424

194.6

1.97

324

184

Polyester PES611

2.80

300

439

192.8

1.98

300

205

Wool fabric

2.15

326

130

644

204.9

1.41

352

357

Acrylic-wool fabric

2.11

323

151

590

203.3

1.28

448

332

Paper tissue
Light

200

257

50.0

Heavy

150

258

23.1

Source: From Pander, J.R. and Ahrens, F.W. 1987. Drying Technol., 5(2):213–243.

TABLE 33.3
Comparison of Equipment to Dry Loose Fibers and Webs

Type

Specific Evaporative Energy Use (kJ kg

)

Evaporation Rate (kg m

)

Relative Floor Space

Flat tenter

4610

Perforated band

3600

0.85

Drum tenter

3440

44.8

0.4

Sieve drum

3250

44.8

0.4

Source: From Watzl, A. 1991. Melliand Textilberichte, 72(6):470–479.

2006 by Taylor & Francis Group, LLC.

to 30 kg

for sucti on-drum dryers . How ever,

Stewart ’s fig ures probably relate to old er dr yers of
lesser pe rformance. The electrica l power use for brat-
tice dryers is less than that for units involving rotat ing
drums, being abo ut 250 kJ

(evapor ation) for

the ba nd driers and 400 kJ

for the drum dryers .

Howev er, the latter is still only abo ut 12% of the
therma l load.

Thes e data are con sistent with guarant eed ope ra-

tive capacit ies (pres umably minimum values ) of one
manufa cturer reported by Kro¨ ll [72] for suction -drum
dryers an d are reprod uced in Tabl e 33.4.

Gardiner and Dietl [75] describe the single-drum

dryers for thin permeable paper sheets in which drying
rates in the range of 50 to 200 kg

were meas-

ured with inlet air temperatures of 170 to 4508C. The
drying is accomplished in a matter of seconds. There is
sufficient pressure drop across the perforated cylinder

and pressing sheet to hold it to the drum, as the sheet is
pulled through, without leaving marks. The principle of
the process is illustrated in Figure 33.6.

M ultiple-d rum dryers for ha ndling loose stuf f

may be a rranged wi th rotat ing cylinders in a hor izon-
tal or vertical array, although the former is more
common. The vertical arrangement has advantages
if the material has to be shifted from one level to
another. A comparison in layout between brattice
and suctio n-drum drye rs is shown in

Figure 33 .7

Up to 20 drums may be used in series, although

commonly about 5 would be employed. Normally,
drums are supplied in the range of 1.4 to 2.0 m
diameter, with widths up to 6.0 m. The principal
operational problem with these dryers for loose fibers
relates to the difficulty of securing a feed of uniform
openness and thickness. Scoured fleece wool, for ex-
ample, after passing through the final squeeze roll at

TABLE 33.4
Average Drying Rates of Selected Materials in Through-Circulated Perforated-Drum Dryers

Material

Air Temperature (8C)

Moisture Content Dry Basis (%)

Mean Drying Rate (kg m

)

Inlet

Outlet

Wool, spun

13.0

Wool, squeezed

15.8

Cotton, spun

90–100

18.2

Cotton, squeezed

90–100

100

24.2

Rayon, spun

110

21.9

Rayon, squeezed

110

180

25.2

Sisal

120

25.8

Jute

110

18.5

Source: From Kro¨ll, K. 1978. Trockner und Trocknungsverfahren, 2nd ed., Springer-Verlag, Berlin.

FIGURE 33.6 Perforated cylinder for drying thin paper sheets: (a) paper sheet; (b) sieve drum; (c) exhaust; and (d) hot air
distributor. (From Kro¨ll, K. 1978. Trockner und Trocknungsverfahren, 2nd ed., Springer, Berlin.)

2006 by Taylor & Francis Group, LLC.

the outlet of the scouri ng bowl , is then combed out
into a spiked feedi ng co nveyor to present to the dr yer
a fairly unifor m, tangl ed mat of fibers.

Band dryers and tente rs lose signifi cant amoun ts of

heat through the co oling of the ba nd or chain as it
passes out of the hot zo ne an d throu gh the extens ive
chamber wall area. Drum dryers are thermally more
efficien t, as

Table 33 .3

indica tes. Conven tionally, these

dryers are fitted with internal steam, finned heaters,

which are prone to collect fluff and loose fiber. Direct
firing of the inlet air has the advantage of avoiding such
heating elements that need periodic cleaning and may
be the site of incentive pockets of stuff.

If the standard drum-drying system does not pro-

vide adequate capacity, the newly developed, high-
capacity drum with a fractional free area of 96%
may be specified as a possible alternative unit having
evaporative capacities up to 400 kg

[76].

Air exhaust

Wool out

Wool in

Air inlet

B - B

A - A

Wool

Conveyor

Wool

Blown wool

Wool out

Air in

Air from blower

(a)

(b)

FIGURE 33.7 Dryers for loose wool: (a) brattice (band) dryer; and (b) suction-drum dryer. (From Stewart, R.G. 1983.
Woolscouring and Allied Technology, Wool Research Organization New Zealand, Christchurch, New Zealand.)

2006 by Taylor & Francis Group, LLC.

33.7 VARIATION OF PROCESS

CONDITIONS AND MOISTURE
IN THROUGH-CIRCULATED DRYERS

A detai led analys is of the through- circul ation of loo se
material s is g iven by Keey [17] . The an alysis is also
valid for webs of fibro us material s. Consi der an elem -
ental vo lume within fibe rs on a pe rforated band as
shown in Figure 33.8.

A mois ture balance betw een that lost by the fibe rs

and that gained by the drying air yields

@ Y

@ y

¼ r

«) u

@ X

@ z

(33 : 40)

where the symbols ha ve the meani ngs illustr ated in
Figure 33.8. The movem ent of so lids may be direct ly
related to the band speed if the fibers do not redis -
tribute on the band during drying:

¼ z =u

(33 : 41)

The longitud inal mois ture content gradie nt is found
by consider ing the rate of dr ying of the fibe rs wi thin
an increme ntal volume in the layer:

« )u

@ X

@ z

¼ f bf

a( Y

) (33 : 42)

where b is the m ass transfer coefficient, f

is t he

hum idi ty potential c oefficient, and ( Y

) is

the h um idity d ifference b etween the wet bulb and the
bulk gas values.

Equat ion 33 .40 and Equation 33.42 can be co n-

venient ly recast into dimens ionless form

(33 : 43)

and

¼ f P (33 : 44)

in whi ch one has a characteris tic mois ture con tent

(33 : 45a)

a relative tim e of drying

F ( X

)

t (33 :45 b)

a relative hum idity potential

(33 : 45c)

the extens ivenes s of the fiber mass

¼ bf

ay =G (33 :45 d)

In the foregoing definitions, subscript cr refers to the
transition from unhindered to hindered drying in the
falling rate period, e to equilibrium, 0 to the air inlet face
of the fiber mass, G to the bulk air, and W to the wet
bulb conditions. The holdup of solids on the band is F.

The solut ion of Equat ion 33.43 and Equation

33.44 for a first-ord er drying process (linear falling
rate period) is given in detai l by Keey [17]. The drying
can be divide d into three stages:

1. The moisture content s everyw here are above

the critical point. The drying rates fall off in
the airflow direct ion, resul ting in a mois ture
content pro file normal to the band .

2. Part of the fibr ous mass , adjacent to the ban d,

is dried be low the critical mois ture content .
Some enhancement of drying rates within this
occurs, changing the shape of the moisture
content profile somewhat.

3. All of the materials are below the critical mois-

ture content, and the moisture content differ-
ences normal to the band gradually diminish,
although the relative difference DF/

hFit, where

hFi is some average value, does not.

The variation of the characteristic moisture con-

tent F and the drying rate f as a function of relative
time u is sho wn in

Figu re 33.9

for the case when F

2 and j

max

¼ 1.

FIGURE 33.8 A perforated band dryer.

2006 by Taylor & Francis Group, LLC.

The moisture content variations that arise at right

angles to the direction of the band movement can lead
operators to overdry stuff so that the absolute residual
moisture content differences are acceptable. The rela-
tive moisture content differences are never reduced.
However, by periodically changing the airflow direction
along the band, the streamwise variation in moisture
content can be restricted to a considerable degree.
Suction-drum dryers automatically incorporate this
feature, and suitable baffling and placing of fans can
also affect airflow reversal in brattice (horizontal band)
dryers, as illustrated in

Figure 33.10

The effe ct of a single a irflow revers al at u

¼ 1

for the case illustrated in Figure 33.9 is depict ed in

Figure 33.11

. At a co ntact tim e of u

¼ 2 the max-

imum moisture co ntent difference DF has been re-
duced to one fifth the value that is found withou t
any revers ing of the airflow, with the wettes t material
now being in the middl e of the mass an d the oute r
portio n of the drier . In the sucti on-drum dryer, the
radial mois ture con tent profiles are e ssential ly negli -
gible after the fourt h dr um (three airflow revers als)
[58].

It is difficul t to ensure even feedi ng of loose

fibers to a dry er as combing and oth er prefee ding
techni ques are only pa rtially effecti ve in unta ngling
fibers that have interlocked . The effe ct of such
unevenn ess in mat thickne ss an d/or open ness has
been invest igated by Keey a nd Wu [77], who co nsider
that an actual suctio n-drum dry er can co nceptual ly
be replac ed by a n eq uivalen t unit co nsisting of a
number of na rrow dryers in parall el, each being fed
unifor mly with mate rial. Expe rimental transverse
profiles of thickne ss can be discretiz ed so that the
individu al feedi ng rates are de terminabl e. Gas dy -
namic consider ations yiel d the corres ponding gas
flow throu gh each of the narrow dryers to maintain
across the dryer a unifor m pressur e dro p that is
known. The resulting nonuni form ity in the e xtent
of the drying implies that the material woul d be
underdrie d unless add itional heatin g were supp lied
or the capacit y redu ced or both. Experim ental ob-
servations suggest that the relative thickne ss on the
band is given by

¼ exp ( k=w) (33 : 46)

over the region P

< P( w) < 1, wher e w is e ssential ly the

relative effe ctive width of the dryer and is evaluat ed as

P( w)

(33 : 47)

with P( w) being the probabil ity that the relative
depth is d or less . The coeffici ent k has been
called the ‘‘unev enn ess factor,’ ’ and is a measur e of
the v ariation in thickne ss. A repres entat ive value of k
for one sucti on-drum dryer ha ndling loose wool is 0.2
[78].

33.8 AIR IMPINGEMENT OF FIBROUS

MATERIALS

The drying of heavy fabrics, including broadloom car-
pets, can be assisted by the use of air jets. The design of
air-impingement systems to improve the efficiency of
drying textile fabrics is reviewed by Gottschalk [79]
with reference to one commercial arrangement. The

2.0

1.6

1.2

0.8

1.0

0.8

0.6

0.4

0.2

0.4

0.8

Critical

point curve

1.2

1.6

2.0

0.4

Critical point

(a)

(b)

dF
dq

FIGURE 33.9 Through-circulation of a fibrous mass on a
band for an initial moisture content F

¼ 2 and a mat

thickness j

max

¼ 1: (a) variation of moisture content F

with relative time (or distance) u along the band; (b) vari-
ation of drying rate dF/du with relative time (or distance) u.
(From Keey, R.B. 1992. The Drying of Loose and Particu-
late Materials, Hemisphere, Washington, DC.)

2006 by Taylor & Francis Group, LLC.

optimum clearance of circular air jet nozzles is given as
5 times the nozzle diameter, with the nozzle occupying
about 2% of the ventilated area of the fabric. The
optimal design resulted in a set of round nozzles set
in individual fingers of nozzle boxes.

Korger and Krizek [80] present detailed results on

the variation of local mass transfer coefficients
on surfaces impinged with jets from slotted nozzles
at different pitches and clearances. Their findings

indicate maximum enhancements of the transfer
rates at clearance/slot width ratios in the range of
8.0 to 9.5, with minimum values in the region of 3.5
to 4.5. Maxima in the transfer coefficients are found
immediately below each nozzle and at a position mid-
way between adjacent nozzles. These variations are
superimposed on the general changes in process con-
ditions that accompany cross-circulated, conveying
dryers, which are analyzed in detail by Keey [17].
Recently, Polat [81] has given a review of the effects
of flow-cell and nozzle geometry, as well as jet-to-
surface and jet-to-jet spacing on the surface transfer
rates. In a confined jet system, with a symmetrical
exhaust of the spent flow between jet nozzles, cross-
flow effects on the evaporative process become sig-
nificant. Saad [82] notes that there is a 15 to 30%
decrease in the average Nusselt number when the
crossflow was only 1 to 2 times the jet flow. How-
ever, the crossflow does not significantly affect the
heat transfer within a region up to 3 to 5 jet rows
[83]. Exhaust ports are normally provided at wider
intervals in industrial systems.

The use of high-velocity impinging airstreams to

improve the through-drying of semipermeable webs is
considered by Randall [84], while Loo and Mujumdar
[85] developed a model for the case when superheated
steam is the drying medium. There are considerable
difficulties in making experimental measurements
under high-speed situations in which, for example, a
paper sheet may be moving at a speed of 25 m

and being impinged with a jet issuing at 100 m

and experiments in the laboratory with static surfaces
can yield misleading information about possible
transfer rates. In drying permeable continuous sheets

Out

(a)

Out

(b)

FIGURE 33.10 Airflow reversals in through-circulation drying: (a) horizontal band arrangement; (b) suction-drum
arrangement.

0.6

0.4
0.2

Airflow reversal

0.8

0.2

FIGURE 33.11 Moisture content variation in a through-
circulated dryer with a single airflow reversal at u

¼ 1;

initial moisture content F

¼ 2; and material thickness

max

¼ 1. (From Keey, R.B. 1992. The Drying of Loose

and Particulate Materials, Hemisphere, Washington, DC.)

2006 by Taylor & Francis Group, LLC.

of pap er or textile s, impingemen t drying rates can be
enhanc ed furt her by drawing some of the hot dry ing
gas throu gh the web.

M artin [86] provides design correlati ons for

multiple -slot and roun d jets besides reco mmendation s
for the spati al arrange ment of jet noz zles on the basis
of maxi mizin g he at trans fer per unit fan energy. The
optima l ratio of the pitch of the noz zles compared
with the distan ce ab ove the surfa ce (0.7 ), which is
recomm ended by Marti n, is close to the report ed
critical value at which jet-to- jet interactio ns star t in-
fluencing the heat trans fer at the stagna tion poin t
under the jet axis [83] .

33.9 DRYING OF PULP AND PAPER

All paper and wood- based boards are made from a
suspensi on of fibers in wat er, with relative ly smal l
quantit ies of nonfibr ous additives and filter s to give
particu lar finishes to the dried product. Most of
the wate r is drained away in a combinat ion of ro lls,
foils, and sucti on box es. In pa permaki ng, the pulp is
admitted to a wire secti on through a flow box, from
which it leaves having a water-to-fibe r ratio of abo ut
6:1. Henc e, the pul p passes to a press section in which
the water is squ eezed into endless belts during
traverse betw een loaded nips, so removi ng abo ut
70% of the water. A diagra mmatic layout is sho wn
in Fig ure 33.12.

The web then passes to the drying section, from

which the sheet emerg es a t abo ut 8% mois ture co ntent
(dry basis), essential ly in eq uilibrium with the ambi-
ent atmos phe re. Norm ally, the drying section con sists
of a series of rotating cylinders, internally heated by
steam, grouped in double banks of about 10 units
each. The wet sheet passes alternately between the
upper and lower ranks of cylinders in an endless
web. Contact is assisted by pressing dry felts, which
also retain shrinkage and hinder wrinkling of the

sheet (

Figur e 33.13

) . The sheet passes through

the machine at high speed, the peripheral velocity of
the rotating cylinders reaching 10 m

or higher

[87], to be taken up by an end reel when dried.

Semipermeable tissue can be dried by through-

circulation over a single cylinder [84,87]. Much light-
weight paper is dried in this way. The very large
steam-heated cylinder, up to 6 m in diameter, is run
at extremely high speeds (more than 20 m

), and

may be worked with a small number of fore and aft
cylinders. Gardiner and Dietl [75] give details of the
performance of these single-cylinder dryers.

Nissan [88] has divided the drying over each drum

of the multiple-cylinder drying section into a cycle of
four phases:

1. The paper sheet contacts the outer surface of

the cylinder, but is uncovered by the felt.

2. The sheet is pressed onto the cylinder’s surface

by the felt.

3. The sheet remains in contact with the cylinder,

but the felt has now left.

4. The sheet, no longer in contact with the cylin-

der, traverses freely to the next drum in the
adjacent bank.

To obtain the moisture profile in the machine

direction, Nissan et al. [89] have made several as-
sumptions about the drying process, principally that
the drying was a first-order process (linear falling
rate period) and that the pressing felt in phase 2 of
the drying cycle reduced the evaporation rate to
one tenth that in the sheet’s free traverse between
cylinders under similar temperature driving forces.
Over each of the periods when the sheet touches
the cylinder, it is assumed that the sheet tempera-
ture is constant (or linearly varying about an arith-
metic mean), both in the plane of the sheet and
normal to it. These concepts lead to a relatively

19,400

Water removed

per 100 kg fiber

kg water

kg fiber

Flow
box

Wire
section

Press
section

Reel
up

Multicylinder drying section

200:1

6:1

1.5:1

0.08:1

450

142

FIGURE 33.12 Layout of a papermaking machine. (From From Kirk, L.A. 1984. Advances in Drying, 3:1–37.)

2006 by Taylor & Francis Group, LLC.

simple relat ionship for the sheet tempe ratur e after a
time inter val t :

¼ T

) exp [U D=M

þ C

X )]

(33 : 48)

where T

is the initial sheet tempe ratur e at the begin-

ning of the co nsidered pha se, T

is the steam tempe ra-

ture, U is the overal l heat trans fer coeffici ent, M

the amount of dry solids pe r unit sheet a rea, C

is the

specific heat of dry fiber, C

, is the specific heat of

moisture, an d X is the dry ba sis moisture co ntent.
Over phase 4, the tempe rature changes are obtaine d
by evaluat ing the sum of conve ctive, evaporat ive, and
radiative heat losse s.

Thes e ideas led to the pre diction of a saw -

toothed temperatur e profile, tracki ng the succes-
sive heati ng and cooling of the she et as it pa sses
over and unde r the trains of cyli nders. Most of the
moisture loss is predict ed to take place dur ing the
free trave rse (phase 4), but a significan t fraction
occurs over pha se 3 when the felt has left the cylind er
(

Figur e 33.14

) .

Ho wever, later experi ments have indica ted that a

consider able fract ion of water is remove d in phase 2
[90], prob ably as liquid into the felt . Subs equen t
analogue computa tions by Deploy [91] suggest that
the felt does indeed hind er evaporat ion, wi th the
wet web leavin g the cy linder at a higher tempe rature
than when the cylind er was unf elted. The net effe ct
is that a felted cyli nder has sli ghtly less mois ture
loss than an unfelted one for the same initial
conditi ons.

Bel l e t al. [90] explai n the diff erences in the relat ive

impor tance of each phase of the cycle in term s of the
difference in the felting action be tween various ma-

chines. Nis san [92] , in co nsider ing the way the felt
remove s water in a paperma king mach ine, attr ibutes
such diff erences to the composi tion of the felt and the
extent to which the felt is heated and dried between
cylind ers.

M ore ad vanced models of the drying process are

discus sed by Kir k [87]. More recen t revie ws include
those writt en by Nederv een et al. [93] and W ilhelms-
son et al. [94]. The latter authors identi fy 20 models
that have been propo sed to simulat e mu lticylinder
paper dryers . In so me of these models , the physica l
transfer pro cesses are simu lated in detail, whi le others
adopt a less detai led viewpo int and rely on more
empirical coefficien ts to fit the data.

In practice , the major ity of the evaporat ion (abo ut

80%) oc curs in the draw s, with a dispropor tionat ely
large num ber of cyli nders needed for the relat ively
small amo unt of evaporat ion in the falling rate
period. Thi s feat ure is a general observance for pro -
gressive drying, as illu strated by the moisture pro files
in

Figure 33.9

. Wilhelms son et al. [94] note that abo ut

two thirds of the hea t demand in a mu lticylinder
machi ne is used direct ly in evapo ration, whi le abo ut
22% is lost from the c ylinders to the environm ent in
various ways . About 6% is lost from the web by
convective heat exchange with the air.

Ventilation of the sheet as it passes through the

drying section is important as an inadequate air supply
can result in the conversion of a uniform cross-web
moisture profile into one with a markedly wetter mid-
section at the take-up reel. The efficiency of various
pocket ventilation systems is investigated by Kirk [95].

Comparative values of drying rates and steam use

with multicylinder dryers for paper are given in

Table 33.5

. The data prob ably do not reflect modern

practice, with its higher machine speeds and better

Upper
felt

Felt dryer

Lower
felt

Paper

Stretching
device

FIGURE 33.13 Multicylinder drying section showing felt runs. (From Kirk, L.A. 1984. Advances in Drying, 3:1–37.)

2006 by Taylor & Francis Group, LLC.

energy savings, but merely give some indication of the
relative performance of these kinds of drying units
with various grades of paper.

Hardboard, which is produced from coarse ther-

momechanical pulp, and similar dense products are
dried batchwise by pressing. The fiber mat is fed to a
press, where the mass is compressed over a heated
platen. The main effect of press drying is the thermal

softening of lignin and cellulose components. If tem-
peratures 25 to 508C above the glass-transition point
of lignin is reached, then bonding can takes place.
This condition entails a temperature in the order of
1508C or above in the wet web. With a further in-
crease in temperature, the lignin viscosity slowly
declines and lesser pressures are needed to attain a
given board density [96].

100

150

200

250

Cycle number

Sheet
temperature
(

°F)

Change in
cylinder
temperature

Water/solids
ratio 0.4

Change in
cylinder
temperature

0.5

1.0

1.5

2.0

Water/solids

ratio

p = 0.4

(a)

(b)

(c)

2.50

5.00

7.50

10.00

Water
evaporated
per cycle
(10

–4

lb/sq.ft)

Whole cycle

Ratio
of 0.4

Phase III

Phase IV

Phase II

Phase I

Evaporation
rate
(lb/sq.ft.h)

FIGURE 33.14 Calculated variation in sheet properties in the drying section of a papermaking machine: (a) temperature
profile, 8C

¼ (8F 32) 5/9; (b) water/solids ratio; (c) water loss rate, kg m

¼ 4.882 lb ft

. (From Nissan, A.H., Kaye,

W.G., and Pilling, D.E. 1958. Trans. IChemE, 36:107–114.)

2006 by Taylor & Francis Group, LLC.

33.10 SUPERHEATED-STEAM DRYING

Superh eated-ste am drying is a specia lized techni que
that uses superheat ed steam rather than mois t air as
the drying medium. The a dvantage s are that the med-
ium no longer provides an environm ent in which
heated loose fibe rs can bum or potentiall y form ex-
plosive mixtures and there are econ omies in ene rgy
use. The he at us ed in vaporiz ation can be partially
recover ed elsewhere in a pro cess by the cond ensation
of the vapor. On the other ha nd, a potenti al draw -
back is that the elevated tempe ratures that are asso-
ciated wi th supe rheated -steam drying may cause
therma l damage to the fibe rs. For exampl e, both
Nichol ls [100] a nd Sweetman [101] found that therm al
damage to wool fibe rs in the presence of steam in-
crease d with temperatur e, exposure time, a nd the pH
of the exami ned mate rial. Presen ce of water in the
material enhanced the degradat ion. Thes e tests, how-
ever, exp osed the mate rial for longer than one might
expect in any drying installation. Othe r tests [102]
with the throu gh-drying of small samples of wool
fabric showe d that very littl e y ellowing of the fibe rs
occurred at tempe ratures be low 150 8 C, but very wet
sample s (at initial moisture con tents abo ve the critical
value) sho wed a signi ficant color change at the begin-
ning of the process within the first 30 s.

At a suffici ently high tempe rature, the evap oration

rate from a wet ted surface into its pure superhea ted
vapor is higher than into perfec tly dry air. The tem-
peratur e at which this trans ition rate occurs is called
the invers ion value. Expe rimental values for this tem-
peratur e ran ge be tween 160 [103] and 230 8 C [104] in
compari ng steam with air. The invers ion occurs be-
cause of the difference in pro perties between steam and
air (which have different tempe rature coefficien ts) and
the ab sence of a gas side mass transfer resistance when

a liqui d evaporat es into its pur e vap or. At low tempe r-
atures, the evaporat ive process is he at transfer con -
trolled and eva poration into perfec tly dry air is the
faster process ; wher eas at higher tempe rature s, the
mass transfer resistance be comes relative ly significa nt
for evapo ration into air an d the superheat ed-vapor
process then be comes fast er. The actual magni tude of
the invers ion temperatur e depends upon the geomet ry
of the evaporat ing surfa ce an d the tempe rature and
humidi ty ch anges in the direct ion of the gas flow.

As pointed out by Schwartze [102], the inversion

temperature is also a function of gas composition.
There is a different ‘‘point’’ inversion temperature in
the way the comparison is evaluated. A comparison of
the evaporation into perfectly dry air with that into
moist air with diminishing humidity from the limit of
pure steam (T

0,1

) is different from comparing the

evaporation into pure steam with that into moist air
with increasing humidity from the limit of dry air
(T

1,X

Figure 33.15

shows the results of calculating

the inversion temperatures for evaporation within a
wetted-wall column with a gas core of 29 mm diameter
in turbulent flow. The point inversion temperatures
range from 1558C for (T

0,1

) and 3008C for (T

1,1

)

respectively. The two kinds of point inversion
temperatures have a common value of 198.68C, repre-
senting the condition, (T

0,0

)

¼ (T

1,0

) , when evapor-

ation into steam is compared with evaporation into
pure air from an infinitesimally small surface.

Bond et al. [103] discuss the drying of paper by

impinging jets of superheated steam. Svensson [105]
discusses applications in the drying of wood pulp
while Amoux et al. [106] consider the use of superheated
steam in the drying of softwood biomass.

Stubbing [107] describes the use of drying at

atmospheric pressure in a steamy environment, which
he terms airless drying, with the tower density of the

TABLE 33.5
Drying Rates and Steam Use in Multicylinder Dryers for Paper

Material

Basis Weight

(g m

)

Mean Drying

Rate (kg m

)

Energy Use

(kg steam/kg dry s)

No. of Sections

No. of

Cylinders/Section

Condenser paper

8–12

3–5

5–7

Vellum

40–60

5–7

4–6

Writing paper

50–70

16–28

1.9–2.5

8–10

Newsprint

50–52

20–23

1.8–2.2

8–16

Packaging

60–120

20–24

2–3

8–10

Carton

200–700

14–20

2.2–3.0

6–8

Calculated in terms of the web-covered surface (about 60% of the total surface).

Upper and lower cylinders separated.

Source: From Meinecke, A. 1974. Wochenblatt f. Papierfabr., (102):41–52.

2006 by Taylor & Francis Group, LLC.

steam relative to the air being used to seal the chamber,
so that the air is progressively displaced. A possible
application in the drying of cloth is suggested.

ACKNOWLEDGMENT

Parts of this chapter are based on a review, ‘‘The
Drying of Textiles,’’ Review of Progress in Coloration,
Vol. 23, 1993, published by the Society of Dyers and
Colourists, Bradford, United Kingdom, and are re-
produced with permission.

NOMENCLATURE

a, b, c

coefficients

activity

exposed surface per unit area

coefficient

moisture flux coefficient

moisture concentration

equilibrium moisture concentration

initial moisture concentration

surface moisture concentration

moisture vapor concentration

moisture liquid concentration

coefficient

specific heat of liquid moisture

heat capacity at constant pressure

specific heat of dry solids

yarn diameter

moisture diffusion coefficient

relative drying rate function

solids holdup

reduced relative drying rate function

specific dry gas rate

total transfer flux

zero-order Bessel function

first-order Bessel function

mass transfer coefficient

coefficients

drying coefficient

characteristic length

mass of sheet

mass of moisture at time t

mass of moisture at infinite time

drying flux

drying flux in first drying period (constant-
rate period)

drying flux in first period at the air inlet

moisture vapor pressure

saturation vapor pressure

P(w)

probability of depth having a value w or less

radial distance

radius of fiber

universal gas constant

a parameter

spacing between threads

time

temperature

ambient temperature

fiber temperature

initial temperature

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300

Point inversion temperature (8C)

Humidity

0, 1

−X

1, X

FIGURE 33.15 Variation of the point inversion temperature as a function of air humidity in a wetted-wall column. (T

0,1

is temperature on comparing evaporation into perfectly dry air with evaporation into moist air of diminishing humidity; T

1,X

the temperature on comparing evaporation into pure steam with evaporation into air of increasing humidity. (From Schwartze,
J.P. 1999. Evaluation of the Superheated Steam Drying Process for Wool, D 82, Diss. RWTH Aachen, Shaker Publisher, p. 89.)

2006 by Taylor & Francis Group, LLC.

steam temperature

moisture vapor temperature

moisture liquid temperature

moisture concentration function

conveying band speed

gas velocity

solids velocity

overall heat transfer coefficient

width function

relative humidity function

distance

moisture content (dry basis)

critical moisture content

equilibrium moisture content

moisture content for complete monolayer

normal distance

humidity

bulk gas humidity

bulk gas humidity at air inlet

wet bulb humidity

longitudinal distance

total longitudinal distance

Greek Symbols

a Sherwood number

mass transfer coefficient

voidage function

relative free moisture content (based on
initial value)

nondimensional layer depth

strain

voidage

volumetric heat of wetting

relative extent or time

thermal diffusivity

a function

relative distance or NTU

humidity potential

density

bulk density

fiber density

gas density

solids density

change of moisture content with vapor
concentration

a ratio

humidity potential coefficient

characteristic moisture content (based on
critical value)

initial value of characteristic moisture
content

change of moisture content with
temperature

relative humidity

latent heat of vaporization

heat of wetting

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Document Outline

Table of Contents
Chapter 033: Drying of Fibrous Materials

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