Effects of pore size distribution and pore-architecture assembly on drying characteristics of pore networks

E?ects of pore size distribution and pore-architecture assembly
on drying characteristics of pore networks
Somkiat Prachayawarakorn a,*, Preeda Prakotmak b, Somchart Soponronnarit b
a Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Suksawat 48 Road, Bangkok 10140, Thailand
b School of Energy and Materials, King Mongkut’s University of Technology Thonburi, Suksawat 48 Road, Bangkok 10140, Thailand
Received 6 March 2006
Available online 20 September 2007
Abstract
Simulation of isothermal drying using two-dimensional networks comprised of interconnected cylindrical pores is presented. Trans-
port of moisture inside pore segments was described by Fick’s law. The results have shown that the shielding of large pores by the smaller
pores in the stochastic pore network, which is supposed to be representative of real porous medium, causes the lower drying rate and
hence lower e?ective di?usion coe?cient as compared to those predicted from the idealized network of pores with a single size. The
strength of shielding is found to vary with the characteristics of pore size distribution as interpreted by the moisture concentration expe-
rienced by the pores, which is remarkably di?erent amongst the pore size distributions. The ine?cient transport of moisture through the
stochastic pore network can be improved or even better with the suitable architecturally assembled structure. The minimum shielding
archetype network, appearing very high porous at particle surface, is predicted to enhance greatly the drying rate. On the other hand,
the maximum shielding network, which is small pores allocated onto the network exterior, exhibits the slowest drying rate.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Drying; E?ective di?usion coe?cient; Stochastic pore network
1. Introduction
temperature and moisture content with time. By using the
continuum models, the e?ective di?usion coe?cient can
Drying of porous materials has received much attention
experimentally be determined from the drying characteris-
in a number of industrial applications including wood [1],
tic curve. The value of the e?ective di?usion coe?cient var-
pharmaceutical product [2], foodstu?s [3], and paper [4].
ies from material to material although the drying
While material is dried, moisture inside the material trans-
conditions used, i.e. temperature and super?cial air veloc-
ports through its interfacial void spaces to the surface and
ity, are all the same. The summary of the e?ective di?usion
is carried away to the ?owing stream. The transport of
coe?cients for products are given by [8]. However, the
moisture may be occurred by several mechanisms of mass
interpretation of those results have ignored the pore struc-
transfer, such as Knudsen di?usion, molecular di?usion,
tural issues and relied on empirical representations. Such
capillary ?ow, etc. All the drying mechanisms are lumped
empiricisms may not be useful for providing detailed infor-
into the e?ective (apparent) di?usion coe?cient [5–7] and
mation on how moisture di?uses through void spaces, with
the porous material is considered as a continuum. This
di?erent sizes and shapes, which dictate the di?usive path-
consideration leads to formulation of partial di?erential
ways of moisture.
equations which relate to the changes of quantities, i.e.
Thus, it is desirable to obtain the structural models that
are capable of taking into accounts key geometrical and
topological properties such as dead ends and variations
*
in pore size and tortuous trajectories. When the structural
Corresponding author. Tel.: +662 4270 9221; fax: +662 428 3534.
E-mail address: somkiat.pra@kmutt.ac.th (S. Prachayawarakorn).
model is combined with the transport equations, the ?ow
0017-9310/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijheatmasstransfer.2007.03.055

---

Nomenclature
C
moisture content (decimal dry basis)
Greek symbols
C
average moisture content (decimal dry basis)
r
standard deviation (m)
D
di?usion coe?cient (m2/s)
l
mean pore radius (m)
Fo
Fourier number, DDt
C
gamma function
Dx2
N
drying rate, kg water/s, or number of pores in
j
adjustable parameter of uniform distribution
network
w
adjustable parameter of uniform distribution
Pr
probability distribution function
a
adjustable parameter of bimodal distribution
L
material thickness (m)
b
adjustable parameter of bimodal distribution
l
pore length (m)
r
pore radius (m)
Subscripts
t
drying time (s)
e
equilibrium
x
distance along the pore length (m)
e?
e?ective
of substances through pore segments inside porous solid
an array of lattices (shown in 2-D in Fig. 2). Each pore in
can numerically be predicted [9–11] and hence the e?ective
the real solid becomes a bond in one of the lattices and each
properties are calculated, thereby providing the under-
pore junction becomes a node. In this study, the pore shape
standing of macroscopic properties. In such a way, net-
assigned onto the network is assumed to be cylindrical
work models can be used in the modeling of transport
geometry and all pores in the network are assumed to have
processes such as single-phase and two-phase ?uid ?ow
and pore di?usion [12–15].
In this work, the drying of the random or stochastic
pore network, which is supposed to be representative of
pore spaces of real porous particle, is investigated. The
moisture movement inside the pore segments is described
by Fick’s law and the drying process occurs under isother-
mal condition. The e?ect of pore size distributions on the
drying characteristic curve and subsequent e?ective di?u-
sivity is theoretically determined. In addition to the pore
size distribution, the geometrical con?guration of the
pores, which is a full set of pores assembled in di?erent
ways onto the network, is explored how the di?usion of
moisture through such geometrical structure exhibits di?er-
ent to that predicted from the stochastic pore network.
This geometrical structure, sometimes called as pore archi-
tecture in this work, has similar pore size distribution to
that employed in the stochastic pore network.
2. Network model
Fig. 1 shows an example of scanning electron micro-
graph (SEM) views of dried durian chip obtained from
the freeze and hot air dryings. Pores shown in Fig. 1 are
represented by black color and tissue by grey color. Poros-
ity of the material appears to consist of a randomised
assembly of pore spaces, which are more or less randomly
interconnected. As shown from the ?gure, di?erent drying
techniques can produce remarkably di?erent microstruc-
tures. Durian chip dried by the freeze-drying technique is
more porous and larger pore sizes than that dried by hot
air. With the hot air dried sample, the dense layer is formed
and the small pores appear at the surface.
To understand the transport of moisture through the
Fig. 1. SEM images of durian chip obtained from di?erent drying
pore spaces, the pore sizes of the real solid is mapped onto
techniques.

---

along the length, the forward ?nite di?erence is applied
and Eq. (1) is thus expressed as


Cpþ1 ¼ Fo Cp
þ Cp
þ ð1 À 2FoÞCp
ð2Þ
m;ri;j
mÀ1;ri;j
mþ1;ri;j
m;ri;j
where Fo is the Fourier number, Fo ¼ DDt, p and m the
Dx2
respective indexes of the present drying time and of nodal
position along the pore. Eq. (2) is stable when Fo ranges
between 0 and 0.5. The transfer rate Ni,j of moisture, for
any time t, di?using into a pore with radius of ri,j can be
calculated by


dCr ðx; tÞ
N
i;j
r
¼ pr2 D
:
ð3Þ
i;j
i;j
dx
x¼l
2.2. Mass balance in the network
After drying starts, the pore ends positioned at the exte-
rior network are exposed to the drying medium and have
Fig. 2. 2-D 30 Â 30 random pore network.
moisture equal to equilibrium moisture content, assuming
negligible convective mass transfer resistance. This assump-
the same length. The pores with di?erent sizes are
tion allows the moisture contents of the exterior pores at
randomly placed onto the network and this approach pro-
any drying time to be calculated directly. For the interior
vides pore at any positions within the network independent
pores, the calculation of their moisture contents is not
to the neighboring pores. Fig. 2 illustrates 2-D pore net-
straightforward since the moisture contents at the two ends
work with a size of 30 Â 30, consisting of 1860 pores. Each
of pore is not known. To determine the internal moisture
pore junction has a connectivity of 4. Real pore sizes of
contents, the mass balance of moisture content at inner
solid, which may determined by nitrogen adsorption or
nodes of the network is made, assuming the size of pore
mercury porosimetry, are assigned to the bonds so that
junctions being zero and no accumulation at the pore junc-
the real structure and the network model have the same
tions within the network. The sum of all in and out?ows,
pore size distribution. Let L is the average particle size of
for a small time interval, at any node is accordingly zero.
material. The length of each pore, l, is then calculated by
That is,
dividing L by N + 1, where N is the network size. Moisture
X
leaves from the network via all the pores at the network
N r ¼ 0
ð4Þ
i;j
periphery, which open onto the drying medium.
j2fig
where {i} refers to the set of i-adjacent nodes which are
2.1. Di?usion in single pores
connected to node (i) in the network. By solving the mois-
ture in every node together the speci?ed boundary condi-
When the pore network is established, the di?usion
tions around the network periphery, the average moisture
problem is solved by calculating the moisture content
content Cnetwork of the network can readily be calculated.
inside the individual pore in conjunction with the mass bal-
The calculation, based on the volume average, can be ex-
ance of moisture at the pore junctions. It is assumed that
pressed by
the moisture di?using through pore with radius ri,j, occurs
PN
R l
under isothermal condition. The isothermal condition
r2
Cr ðx; tÞ dx
CðtÞ
¼
n¼1 i;j
0
i;j
P
ð5Þ
occurs when heat required for evaporation balances with
network
N Á l
N
r2
n¼1 i;j
heat from conduction and convection. The change of mois-
ture inside individual pores of the network is described by
where N is the number of pore in the network and l is the
the following equation:
pore length (m).
oC
o2C
¼ D
ð1Þ
2.3. E?ective di?usivity
ot
ox2
where C is the moisture content (decimal dry basis), D the
If the di?usion is occurring through the slab-shaped por-
di?usion coe?cient (m2/s), t the drying time (s) and x the
ous solids, the e?ective di?usivity can be determined by
distance along the pore length (m). The di?usion coe?cient
Fick’s second law of di?usion, which is expressed by
is assumed to be a constant value and the moisture concen-


CðtÞ À C
8 X
1
1
tration in the pores at the beginning is specially uniform
e ¼
exp Àð2n þ 1Þ2 p2Deff t
ð6Þ
C
p2
along the pore axis. To determine the moisture pro?le
i À Ce
ð2n þ 1Þ2
L2
n¼0

---

where CðtÞ is the average moisture content of material (dec-
Bimodal size distribution :
imal dry basis), C




i the initial moisture content, Ce the equi-
ra1À1
r
ra2À1
r
librium moisture content, D
f ðrÞ ¼
exp À
þ
exp À
;
e?
the e?ective di?usion
Cða
b
Cða
b
coe?cient and L the material thickness. Eq. (6) presents
1Þba1
1
1
2Þba1
2
2
the di?usion of moisture in one direction. The drying of
0 6 r 6 1
ð12Þ
pore network at the present study is, however, occurred
where r is the standard deviation, l the mean pore radius,
in two directions and the solution is obtained from the
C(a) the gamma function and j, w and a all the adjustable
product of the above di?usion equation itself, thus eventu-
parameter.
ally yielding
Before investigating the di?usive ?ow behaviour within
  

  


the network of pores, pore sizes are generated by the map-
CðtÞ À C
2
e
8
D
2
D
¼
exp À2p2 eff  t
þ
exp À10p2 eff  t
ping of a sequence of uniformly distributed numbers in the
Ci À Ce
p2
L2
9
L2
 



range of 0 and 1 on the corresponding probability distribu-
2
D
þ
exp À26p2 eff  t
þ Á Á Á
ð7Þ
tion function Pr(r
25
L2
i) and then are randomly distributed to
the bonds.
The ?rst three terms of in?nite series of Eq. (7) are em-
ployed to quantify the e?ective di?usivity and a trial-error
3. Results and discussion
method is used. The e?ective di?usivity is obtained when
the di?erence between the value of moisture content pre-
Drying simulations were performed on the pore network
dicted by Eq. (7), CðtÞ, and that calculated from the net-
model. At the beginning, every pore within the network is
work, CðtÞ
, is less than the acceptable value. By this
network
assumed to have equal moisture content, with the value of
method, the evolution of moisture content at pore level di-
0.35 dry basis. When the drying starts, moisture content at
rectly re?ects on the e?ective di?usivity.
the periphery pores immediately equilibrates to the sur-
rounding air, which is assumed to be 0.165 dry basis in this
study. The di?usivity value used in the simulations was
2.4. Pore size distribution
1 Â 10À10 m2/s. To minimize the e?ect of periphery pores
on the transport of moisture, size of the network should
Pore size distribution de?ned in the range from a mini-
su?ciently be large. In addition, it enables to capture the
mum to a maximum pore radius, rmin and rmax, is described
moisture transport inside the large network closed to that
in terms of the number diameter probability density func-
occurring inside the real porous materials, consisting of
tion which is given by
 
many thousands of pores. A network size of 45 Â 45, con-
d NðrÞ
sisting of 4140 pores in the network, was used in this study.
N T
f ðrÞ ¼
;
r
For each set of results reported, 20–30 realisations were
d
min < r < rmax
ð8Þ
r
carried out and the average value was presented.
where NT is the total pores in the network and N(r)
3.1. In?uence of pore size distribution width
presents the number of pores between r and r + dr. The
integration of Eq. (8) from rmin to rmax equals to unity,
R
Pore size distribution is the important parameter not
rmax f ðrÞdr ¼ 1. The probability distribution function of
rmin
only in quality of foods but also in transport of moisture
all pores in the network with radius larger than a particular
[16]. Their structures are given by a nature or through pro-
radius, Pr(ri), is
cessing. To simplify the problem, this work assumes that
Z rmax
the structure of foods does not change with time. Two case
PrðriÞ ¼
f ðrÞ dr
ð9Þ
studies were performed; the ?rst deals with the width of
ri
pore size distribution and the latter deals with the in?uence
of characteristics of pore size distribution (see Section 3.2).
The values of Pr(ri = rmin) = 1 and of Pr(ri = rmax) = 0. In
In the ?rst case, the simulations were performed with the
this study, the following three types of pore size distribu-
normal size distribution to determine the e?ect of pore size
tion, i.e. normal distribution, uniform distribution and bi-
distribution width on the average moisture content. The
modal distribution were used:
width of distribution can be made by varying the value
Normal size distribution :
of standard deviation. A mean pore radius was given, with


a size of 40 lm. The average moisture contents of the net-
1
1 hr À li
f ðrÞ ¼ p?????? exp À
;
À1 < r < 1
ð10Þ
works versus time are plotted in Fig. 3 for the values of
r 2p
2
r
standard deviation (r) of 1, 7, and 12 lm. The moisture
content of the network, for a given standard deviation, is
Uniform size distribution :
rapidly decreased at the early drying period and slowly
1
f ðrÞ ¼
;
w 6 r 6 j
ð11Þ
decreased afterwards. This trend is generally found in dry-
j À w
ing curve of porous materials.

---

Fig. 4. In?uence of pore size distribution width on transport property
(l = 40 lm).
Fig. 3. In?uence of pore size distribution width on moisture content
(normal size distribution with l = 40 lm).
capillary and viscous forces. However, Segura and Toledo
[19], who studied the isothermal drying of pore networks
by assuming the dominant contribution of capillary forces
As shown in Fig. 3, di?erence in drying rate amongst
over the viscous forces, reported the opposite results to the
pore size distribution widths is clearly evident after which
above studies. In their work, the simulation showed an
moisture content of the networks is reduced below 0.25
insigni?cant e?ect of pore size distribution on the drying
dry basis. The moisture content is reduced faster with the
curves of the pore networks.
narrower pore size distribution, corresponding to smaller
Fig. 4 shows the in?uence of width of pore size distribu-
standard deviation. When the standard deviation becomes
tion on the e?ective di?usivity with a mean value of 40 lm.
unity, the decrease of moisture content is almost identical
The e?ective di?usivity of the network reduces as the value
to that of the network of single-sized pore. The single-sized
of r/l increases. The value of e?ective di?usivity decreases
network is an ideal network where the moisture di?using
from 9.4 Â 10À11 m2/s at the r/l of zero to 8.3 Â 10À11 m2/
through any pore in the network is not interfered by their
s at the r/l of 0.3. These results respond to the similar way
adjacent pores. These simulation results emphasize the less
found in the drying curves, showing the faster drying rate
e?cient transport of moisture within the network consist-
with lower value of standard deviation.
ing of large and small pores, which are randomly con-
nected. The poor transport is due to the larger pores
3.2. In?uence of type of pore size distribution
shifted behind smaller ones and this e?ect is named as pore
‘‘shielding” [17]. Such shielding results in the moisture
In this section, the change in moisture transport, while it
existing in the shielded pores di?cult to move from the
di?uses through the network with di?erent distributive
interior to the exterior because of the strong di?usional
pores, i.e. uniform, normal and bimodal distribution, is
resistances in the surrounding pores.
studied. In comparison, the networks of pores, which are
However, the pore shielding e?ect is insigni?cant at the
characterized by di?erent types of pore size distribution,
early drying period since the main portion of moisture
have equal total pore volume and the network length is
removed at this time is present near the network periphery
equal. The structural parameters required to generate pore
in which the moisture movement is not interfered by the
size distributions are given as follows:
disorder of void spaces within the network. Thus, the
reduction of moisture content with time is nearly the same
Normal size distribution: l = 40 lm and r = 10 lm
for the networks of pores that possess di?erent standard
Uniform distribution: j = 74.13 lm and w = 4.97 lm
deviations of pore size, as shown in Fig. 3.
Bimodal distribution: b1 = 3 lm, b2 = 10 lm, a1 = 2 lm
The in?uence of the pore size distribution width on the
and a2 = 4.9 lm
drying curve presented in Fig. 3 is similar to that reported
by Metzger and Tsotsas [18], exhibiting the strong e?ect of
For the single-sized network, which is used as a baseline,
standard deviation of pore sizes on the drying behaviour.
the pore size of 40 lm was employed. Fig. 5 shows the
In their model, voids in porous material were represented
number diameter probability density function of pores gen-
as cylindrical shape and their arrangement was in parallel
erated from di?erent types of pore size distributions using
direction to ?uid ?ow. The parallel capillaries were con-
the above structural parameters. In the bimodal distribu-
nected all along their length with no any resistance and
tion, the pore sizes are generally characterized by two
?uid present in the capillaries was transported by the
groups, small and large pores. Pore sizes produced from

---

Fig. 6. In?uence of type of pore size distribution on moisture content.
Fig. 5. Number diameter probability density function generated from
di?erent types of pore size distribution under the same total pore volume.
for 64% of total number of pores. For the uniform distribu-
tion, the generated pore sizes ranged between 1.9 and
the structural bimodal parameters were given in the range
71 lm.
of small pores from 0.34 to 17.3 lm, accounting for 36%
Fig. 6 shows the in?uence of type of pore size distribu-
of total number of pores allocated onto the network, and
tion on reduction in moisture content, indicating the strong
in the range of large from 17.3 to 121.8 lm, accounting
impact of pore size distribution on the moisture change.
Fig. 7. Moisture content in 2-D pore networks with di?erent distributions of pore sizes.

---

The rate of moisture reduction is lowest with the bimodal
rate can be changed when the physical structure of material
distribution and it becomes faster with the following uni-
is modi?ed. Two illustrative structures are given to show
form and normal distributions. Moreover, the fastest rate
the scope for this.
of moisture reduction exhibits in the single-sized network
The ?rst structure is shown in Fig. 8a whereby the full
for which the shielded pores are absent. The moisture
set of random pores, generated from the normal distribu-
transport through the bimodal network is least e?cient in
tion (r = 10 lm and l = 40 lm), is assembled in rank order
spite of the larger pore sizes and higher pore volume in
and then spirally wound into positions in the network, with
the large pore assembly, both of which normally serve high
the largest pore at the exterior and the smallest at the cen-
?ow of moisture because of low resistance of moisture dif-
tre. This architectural structure, namely minimum shield-
fusion in the large pores. However, the slowest drying rate
ing network, exhibits very more porous at the exterior
for the bimodal pores can be attributed to the fact that the
large pore assembly ine?ectively communicates itself
throughout the network and some of them possibly allo-
cate behind the smaller pores. Thus, the moisture di?usion
from the inside to the outside for this pore size distribution
is strictly limited. This description can be interpreted
through the representation of network moisture gradients
in voids which will be shown in Fig. 7.
The changes of average moisture content of the net-
works, with di?erent pore size distributions, shown in
Fig. 6 are selected for a particular drying time of 4500 s
to visualize the moisture content of each pore positioned
within the networks. The pictorialized representations of
local moisture content are shown in Fig. 7. Each pore
was colored according its moisture content. The represen-
tative colors with 21 shades from light grey to black were
used for the corresponding range of moisture content from
less than 0.16–0.34 dry basis. After drying is passed, di?er-
ence in the detailed moisture contents amongst the net-
works of pores is shown up. As shown in Fig. 7d for the
‘‘bimodal” network, the ine?cient connection of large
and small pore assemblies exhibits the delay of moisture
in percolating through the network once the drying front
approaches the smaller pores. Irregular pattern of moisture
content is also found with the bimodally distributed pores.
The results from the simulations also indicate that the
moisture at the innermost pores of the ‘‘bimodal” network
for the illustrative drying time of 4500 s is the same content
as at the initial one (black), implying that drying at that
area does not commences. With the other networks, the
moisture at the innermost had already decreased, reducing
from 0.34 to 0.32 dry basis which corresponds to the dark
grey color.
3.3. E?ect of structure re-ordering on the drying kinetics
The food materials in particular fruit possess dense
physical structure and sugar content. When it is conven-
tionally dried, the crust or dense layer may possibly be
formed near the material surface. This created structure
does not facilitate internal moisture movement, thus result-
ing in long drying time, browning and darkening of prod-
uct and large energy consumption. One approach to
improve the drying rate is to change its physical structure,
for example, making it more porous. This can be made by
the foaming of fruit before drying [20]. In this section, the
concept of pore network is utilised to show how the drying
Fig. 8. Illustrative pore architectural structures.

---

Fig. 9. E?ect of pore architectural structure on the drying kinetics.
surface as shown in Fig. 8a. On the other hand, if the pores
are allocated into the network, with the smallest size at the
exterior surface and the largest at the centre, it can be visu-
alized as a dense layer at the surface, which is shown in
Fig. 8b, which is named as maximum shielding network.
The outer dense layer of the later pore structure may pos-
sibly be similar to that occurring in the biomaterials con-
taining high sugar content when dried with hot air. Both
pore structures shown in Fig. 8 have exactly identical pore
sizes used in the stochastic pore network. The simulation
results obtained from the above archetypal pore structures
are shown in Fig. 9. The transport of moisture through dif-
ferent con?gurations of pore assembly is strikingly di?er-
ent. The reduction of moisture content is very fast with
the pore structure appearing very porous at the exterior
(D) and extremely slowest with the dense structure at the
exterior (A). The corresponding e?ective di?usivities are
1.57 Â 10À10 m2/s and 3.81 Â 10À11 m2/s.
The moisture content of each pore for the architectural
con?gurations is shown in Fig. 10, for the illustrative dry-
ing time of 4500 s which is the same time as presented in
Fig. 7. As shown in Fig. 10a for the minimum shielding net-
work, the moisture content of the exterior pores at that
time lies in between 0.16 and 0.2 dry basis, corresponding
to the shade of grey color which increases intensity from
light to medium grey. This result implies the architectural
pore structure with very high porous at the outer surface
facilitating the high di?usive ?ux of moisture, thereby
enhancing the rapid fall in moisture content.
Fig. 10. Moisture content in 2-D network with di?erent arrangements of
Because of high resistance of moisture di?usion in the
pore assembly.
small pores at the periphery for the maximum shielding
network, the di?usion of moisture is restricted and this is
4. Conclusions
clearly evident from Fig. 8b, showing the grey color shade
only at the periphery pores whilst most inner pores have
A 2-D pore network for the drying of moisture content
moisture contents above 0.3 dry basis.
under isothermal condition has been studied. The transport

---

of moisture within individual pore segments is described by
[5] G. Efremov, T. Kudra, Calculation of the e?ective di?usion coe?-
Fick’s second law. The simulation results have been shown
cients by applying a quasi-stationary equation for drying kinetics,
Dry. Technol. 22 (2004) 2273–2279.
that the e?ect of shielding inherent in typical random pore
[6] Md. Raisul Islam, J.C. Ho, A.S. Mujumdar, Convective drying with
network results in slower decrease of moisture content and
time-varying heat input: simulation results, Dry. Technol. 21 (2003)
hence lower value of e?ective di?usion coe?cient as com-
1333–1356.
pared to the single sized network for which the shielding
[7] S. Prachayawarakorn, P. Prachayawasin, S. Soponronnarit, E?ective
is absent. Degree of shielding is di?erent among pore size
di?usivity and kinetics of urease inactivation and color change during
processing of soybeans with superheated-steam ?uidized bed, Dry.
distributions and this e?ect causes the value of e?ective dif-
Technol. 22 (2004) 2095–2118.
fusion coe?cient to be dependent on the distribution types.
[8] N.P. Zogzas, Z.B. Maroulis, D. Marinos-Kouris, Moisture di?usivity
The strongest shielding e?ect is found with the pore net-
data compilation in foodstu?s, Dry. Technol. 14 (1996) 2225–2253.
work characterized by bimodal pore size distribution and
[9] M. Blunt, Flow in porous media-pore – network models and
this in?uence consequently results in drying of bidisperse
multiphase ?ow, Curr. Opin. Colloid Interface Sci. 6 (2001) 197–207.
[10] R. Mann, Development in chemical reaction engineering: issues
porous structure relatively longer time than the other illus-
relating to particle pore structures and porous materials, Trans.
trative pore size distributions, i.e. uniform and normal dis-
IchemE 71A (1993) 551–561.
tribution. The drying rate of the stochastic pore network
[11] M. Sahimi, G.R. Gavalas, T.T. Tsotsis, Statistical and continuum
can be improved through the proper pore structure. This
models of ?uid–solid reactions in porous media, Chem. Eng. Sci. 45
superiority is greatest with the network of pores appearing
(1990) 1442–1502.
[12] S.C. Nowicki, H.T. Davis, L.E. Scriven, Microscopic determination
highly porous at the exterior. On the other hand, porous
of transport parameters in drying porous media, Dry. Technol. 10
particles, with a dense layer at the surface or consisting
(1992) 925–946.
of small exterior pores, can be dried with lowest rate.
[13] J.B. Laurindo, M. Prat, Numerical and experimental network study
of evaporation in capillary porous meida. Drying rates, Chem. Eng.
Acknowledgements
Sci. 53 (1998) 2257–2269.
[14] M. Prat, Isothermal drying of non-hygroscopic capillary-porous
materials as an inversion percolation process, J. Multiphase Flow 21
The authors express their sincere appreciation to the
(1995) 875–892.
Thailand Research Fund and commission on higher educa-
[15] V.G. Mata, J.C.B. Lopes, M.M. Dias, Porous media characterization
tion for ?nancial support.
using mercury porosimetry simulation. 1. Description of the simula-
tor and its sensitivity to model parameters, Ind. Eng. Chem. Res. 40
(2001) 3511–3522.
References
[16] M.S. Rahman, O. Al-Amri, I.M. Al-Bulushi, Pores and physico-
chemical characteristics of dried tuna produced by di?erent methods
[1] D. Elustondo, S. Avramidis, S. Shida, Predicting thermal e?ciency in
of drying, J. Food Eng. 53 (2002) 301–313.
timber radio frequency vacuum drying, Dry. Technol. 22 (2004) 795–
[17] G.P. Androutsopoulos, R. Mann, Evaluation of mercury porosimeter
807.
experiments using a network pore structure model, Chem. Eng. Sci.
[2] K.H. Gan, R. Bruttini, O.K. Crosser, A.I. Liapis, Freeze-drying of
34 (1979) 1203–1212.
pharmaceuticals in vials on trays: e?ects of drying chamber wall
[18] T. Metzger, E. Tsotsas, In?uence of pore size distribution on drying
temperature and tray side on lyophilization performance, Int. J. Heat
kinetics: a simple capillary model, Dry. Technol. 23 (2005) 1797–1809.
Mass Transfer 48 (2005) 1675–1687.
[19] L. Segura, P.G. Toledo, Pore-level modeling of isothermal drying of
[3] L.A. Campan˜one, V.O. Salvadori, R.H. Mascheroni, Food freezing
pore networks: e?ects of gravity and pore shape and size distributions
with simultaneous surface dehydration: approximate prediction of
on saturation and transport parameters, Chem. Eng. J. 111 (2005)
freezing time, Int. J. Heat Mass Transfer 48 (2005) 1205–1213.
237–252.
[4] J. Seyed-Yagoobi, H. Noboa, Drying of uncoated paper with gas-
[20] C.K. Sanket, F. Castaigne, Foaming and drying behaviour of ripe
?red infrared emitters – optimum emitters’ location within a paper
bananas, Lebensm-Wiss. Univ. Technol. 37 (2004) 517–525.
machine drying section, Dry. Technol. 21 (2003) 1897–1908.

---

Document Outline

• Effects of pore size distribution and pore-architecture assembly on drying characteristics of pore networks
  • Introduction
  • Network model
    • Diffusion in single pores
    • Mass balance in the network
    • Effective diffusivity
    • Pore size distribution
  • Results and discussion
    • Influence of pore size distribution width
    • Influence of type of pore size distribution
    • Effect of structure re-ordering on the drying kinetics
  • Conclusions
  • Acknowledgements
  • References

---