Wood and Fiber Science, 37(2), 2005, pp. 242–257© 2005 by the Society of Wood Science and Technology

† Member SWST.

HEAT AND MASS TRANSFER IN WOOD COMPOSITE PANELS DURINGHOT PRESSING. PART II. MODELING VOID FORMATION AND MAT

PERMEABILITY

Chunping Dai†Senior Scientist and Group Leader

Changming YuVisiting Professor

and

Xiaoyan ZhouVisiting Associate Professor

Wood Composites GroupForintek Canada Corp.

2665 East MallVancouver, B.C.

Canada V6T 1W5

(Received June 2004)

abstract

Theoretical models have been developed to predict the porosity and permeability of wood strand matsduring consolidation. Based on the Poisson distribution of mat formation, the porosity model predicts theformation of both inside- and between-strand void volumes. It is proposed and predicted that the between-strand voids consist of voids between non-contact strand faces and voids around strand edges, with the for-mer dominating in the early stage of consolidation and the latter dominating in the latter stage ofconsolidation. The permeability model is developed based on the Carman-Kozeny theory for porous mate-rials. The model is compared and agrees with experimental results obtained from this study and from theliterature. The results show mat permeability is mainly controlled by voids between strands instead ofthose inside strands. Mat density has a primary effect and strand size has a secondary but very importanteffect on mat porosity and permeability especially in the later stage of consolidation. Strand thickness hasa stronger impact than strand width and length. Strand dimensions and mat permeability are shown to havesignificant effects on internal environmental conditions in wood composites during hot-pressing.

Keywords: Hot-pressing, wood composites, void volume, porosity, permeability, consolidation and modeling.

introduction

In the preceding paper of this series (Dai andYu 2004), a theoretical model was presented topredict mat environmental conditions based onthe physics principles of mass and energy con-servation, momentum of gas flow, thermody-namics, and resin curing kinetics. The matconditions such as temperature, moisture con-tent, and gas pressure were shown to be closely

linked to basic mat properties including thermalconductivity and permeability. One of theknowledge gaps identified was the lack of funda-mental understanding and experimental data ofmat permeability. The permeability is crucial tohot pressing of wood composites because it con-trols the convective heat and mass transfer fromsurfaces to core, and the ease with which internalvapor evaporates from the mat center to its edgesduring pressing and from core to surfaces duringpress opening. Specifically, the former controlsthe rate of core temperature rise and therefore

Dai et al.—HEAT AND MASS TRANSFER IN COMPOSITES. PART II. 243

resin curing rate, while the latter is a determiningfactor to minimize blows or blisters in finishedboards and pressing time.

The importance of mat permeability has alsobeen identified in other studies reported in a re-view by Bolton and Humphrey (1994). It washypothesized that mat permeability was linkedto the existence of voids between wood elementsinstead of those within them. Such a hypothesiswas rationalized by the fact that the permeabilityof a mat is usually much higher than that ofwood from which the mat is made. It was furtherspeculated that both void volume and permeabil-ity should be governed by the shape of the woodelements and mat densification. Unfortunately,the void volume and its relationship to perme-ability were not subsequently investigated orpublished.

Hata et al (1993) and von Haas (1998) wereamong the very few researchers who investigatedmat permeability using experimental approaches.Pre-pressed mats of resinated wood elementswere regarded as a continuum and tested for theirpermeability. While certain empirical models be-tween mat permeability, element geometry, andmat density were found based on the experimen-tal data, the models’ applications are limited bythe condition under which the experiments wereconducted. Particularly, the models cannot begeneralized to predict the permeability of matswith different element geometry. This can be-come a major drawback for any heat and masstransfer model considering that wood compositescan be made from a wide geometric mix of woodelements. A more generalized model of thepermeability-void volume-mat density wouldtherefore be highly desirable for analyzing the ef-fects of wood element geometry on hot-pressingbehavior and even product properties.

Indeed, the significance of understanding thevoids inside composite mats and final productsshould go beyond mat permeability and heat andmass transfer. From a material standpoint, voidvolume is one of the three major components ofwood composites, with the other two beingwood elements and resin additives. Thereforevoids ought to play a major role in defining boththe processing and the performance of wood

composites. While its importance has beenwidely acknowledged (e.g. Suchsland 1959;Humphrey and Bolton 1989; Zombori et al2003; Carvalho et al. 2003; Wu and Lee 2002),void volume in wood composites is poorly de-fined probably due to the lack of experimentaltechniques and partially due to the complex na-ture of the mat structure.

The goal of this paper was to improve the fun-damental understanding of wood composite pro-cessing. The specific objectives were:● To develop a theoretical model to predict the

changes of void volume inside the mat as afunction of wood element size and mat densi-fication;

● To present a generalized model to predict themat permeability in terms of the void volumeand wood element size;

● To validate the permeability model by com-paring with experimental results; and

● To demonstrate the usefulness of the modelfor analyzing the effects of wood element sizeon hot-pressing process.

theoretcal modeling

Wood composites may be structurally classi-fied into two categories: veneer-based andstrand-based. The former represents productssuch as plywood and laminated veneer lumber(LVL), which are made from layers of veneer.Because of the continuity of veneer layers, thestructure and formation of voids in those prod-ucts are relatively straightforward and hence notinvestigated in this study.

In contrast, strand-based composites, whichbroadly represent such products as orientedstrandboard (OSB), parallel strand lumber (Par-allamTM), particleboard, and fiberboard, aremade from discontinuous wood elements, i.e.strands, particles, and fibers. The element dis-continuity and random forming process in-evitably induce voids between the elements. Infact, voids are the dominant volumetric fractionof a mat during forming. The void fraction thenexperiences a drastic change during mat consoli-dation. While most voids are removed during theinitial consolidation, a certain fraction of voids

244 WOOD AND FIBER SCIENCE, APRIL 2005, V. 37(2)

always exists even after excessive densification.It is therefore conceivable that the formation andremoval of voids are associated with strand dis-continuity, mat formation, and densification. Tomodel the void volume and further the perme-ability of mats, two general assumptions aremade concerning the element geometry and themat-forming process:

1) Original wood elements or strands in a matare assumed to be rectangular in shape. Theirdimensions are defined by length, width, andthickness.

2) Strands are formed following a random pro-cess in which their positions are randomlydistributed over the mat area. Note thatstrand orientation can be either random ororiented/partially oriented.

Random mat structure

Despite their more or less uniform appear-ance, strand mats are random in structure. Therandom mat structure is attributed to the natureof mat-forming processes which may at bestcontrol the local distributions of strand mass butnot the positions of individual strands. As a re-sult, the number of strand overlaps varies fromone location to another. To illustrate such struc-ture variations, we developed a computer simu-lation model using basic geometric theories (Daiand Steiner 1994b; Dai et al. 1996). Figure 1shows simulated distributions of strand overlapsin a randomly formed strand layer and in a multi-layered strand mat. The local strand overlapsvary from 0 to 5 in the single layer (Fig. 1a), andfrom 1 to 16 around the average of 10 strandoverlaps in the multi-layer mat (Fig. 1b). In the-ory, the relationship between the strand overlapsi and their average n is governed by a Poissondistribution (Dai and Steiner 1994b; Dai et al.1996). The probability of any given point in themat covered by i strands, p(i), is:

(1)

where: ai � sum of mat areas in which thestrand overlaps equal i [m2],

p ia

A

e n

ii

n i

( )!

–

= =

A � overall mat area [m2], andn � average number of strand overlaps.

Equation (1) establishes an important linkagebetween the random strand overlaps to their cor-responding mat areas. It allows for derivation ofsuch mat structural properties as strand bondedarea (Dai and Steiner 1993), horizontal densitydistribution (Dai and Steiner 1997), and voidvolume, which is to be analyzed in this paper.

The average strand overlap n is further de-fined by:

(2)

where: � � strand length [m],� � strand width [m], andNf � total number of strands in a mat.

Since mat density �m [kg/m3] is defined by:

(3)

where: � � strand thickness [m],ρs � original wood density of strands[kg/m3], andT � mat thickness [m], the averagestrand overlaps n can be further calcu-lated by combining Eqs. (2) and (3):

(4)

or simply:

(5)

where: Cr � compaction ratio or ρm /ρs, indicat-ing the degree of mat consolidation, andTr � thickness ratio or T/�.

Equations (1) and (5) suggest that the distribu-tion of strand overlaps in randomly formed matscan be fully described if the mat compactionratio and the thickness ratio are known. Thegreater the compaction ratio and the thicknessratio, the more uniform the mat (Dai and Steiner1997). The Poisson distribution is a mat struc-ture property, which is in fact independent ofstrand length, width, and mat size.

n C Tr r=

nTm

s

= ρρ τ

ρλωτρ

ms fN

TA=

nN

Af=

λω

Dai et al.—HEAT AND MASS TRANSFER IN COMPOSITES. PART II. 245

Fig. 1. Computer-simulated mat formation showing the variations of strand overlaps in: a). a single layer (average of oneoverlap), and b). a multi-layered mat (average of 10 strand overlaps).

246 WOOD AND FIBER SCIENCE, APRIL 2005, V. 37(2)

Void formation

Since wood is a cellular material, voids in astrand mat can exist both between strands and in-side strands. The between-strand porosity, �b, isdefined as the ratio of void volume betweenstrands over the total mat volume. The inside-strand porosity, �i, is defined as the ratio of voidvolume inside strands over the total mat volume.The total porosity in a mat, �t, is obviously equalto the sum of the two porosities, or:

(6)

Assume the cell-wall density, �c, is known(usually around 1500 kg/m3). The total matporosity can be calculated by:

(7)

Equation (7) implies that �t can be calculatedgiven that ρm is known (Eq.3). According to Eq.(6), �b or �i can be calculated if the other isknown. The following analyses will only focuson the derivation of between-strand porosity �b.

φ ρρt

m

c

= 1 –

φ φ φt b i= +

Voids between strands are first induced duringmat forming and can then be largely removedduring mat consolidation. Due to the randomvariations of strand overlaps, the manner inwhich voids are removed with increase in den-sity is highly nonuniform. Figure 2 shows aschematic of a model mat, which consists ofcolumns of overlapped strands. The number ofstrand overlaps in each column i and its corre-sponding column area ai vary, and are character-ized by the Poisson distribution (Eq.1). Duringthe early stage of mat consolidation, only thosecolumns of high strand overlaps are under com-pression. As the mat thickness T further de-creases, those columns will encounter greatercompression, whereas the columns of fewerstrands may realize lower compression and ac-cordingly some columns may have no compres-sion. It is intuitive that the compression willremove the voids between strands and thegreater the compression, the lower the void vol-ume. On the other hand, large voids must existbetween strands in the uncompressed columns.

To help model the void formation, we classifythe voids between strands into two types: non-

Fig. 2. Schematic of a model mat consisting of columns of overlapping strands characterized by a Poisson distribution(Eq. 1). Note that i � strand overlaps, imax, imin � maximum and minimum strand overlaps, ai, amax and amin � sum of the matareas containing respectively i, imax and imin strands, � � strand thickness, and T � mat thickness.

Dai et al.—HEAT AND MASS TRANSFER IN COMPOSITES. PART II. 247

contact voids and edge voids. The non-contactvoids exist due to lack of strand-to-strand con-tacts in the uncompressed columns, which sym-bolize the local mat areas with relatively lownumbers of strand overlaps (Fig. 3a). The edgevoids are induced by strand edges in the com-pressed columns, which represent the local matareas with high numbers of strand overlaps (Fig.3b). In our initial analysis (Dai and Steiner1993), we assumed that mats contain only thenon-contact voids. This may have led to under-estimation of the between-strand porosity. Modi-fications are made herein to include the voidsinduced by strand edges. This modification willallow for proper consideration of the effects ofstrand geometry, particularly the strand lengthand width.

Porosity model for non-contact voids.—For amat of thickness T, non-contact voids only existin those columns or mat areas with overlap num-ber i less than T/�. Therefore, the correspondingvoid volume equals (T-i�) ai and the porosity is(T-i�) ai /(TA). For all the columns with overlapnumber less than T/�, the porosity for non-contact voids �b.n is:

(8)

Substituting ai/A in Eq. (8) with Eq. (1) yields:

φ ζ ττ

b n ii

T

TAT i a,

/

–= ( )=∑1

0

(9)

where � � roughness coefficient. This is to takeinto account the existence of micro-voids be-tween contacts of nominally flat strand surfaces(Knudson et al 1999). Depending upon the sur-face roughness, � varies from 0.8 to1.0 withunity representing perfectly smooth strands.

Porosity model for edge voids.—In the com-pressed columns, triangular voids often existaround the strand edges (Fig. 3b). The size of thetriangular voids is likely controlled by the strandthickness � and lateral expansion of strands dueto compression. As they are compressed in thick-ness direction, the strands will expand in lengthand width directions. While it can be largelycontained by strand-to-strand surface contact,the lateral expansion encounters much less con-straint around the edges. Depending upon thecompression, the edge expansion coupled withbending deformation of the adjacent strands maypartially fill or completely eliminate the edgevoids (Fig. 3c). In a partially filled case, the voidvolume can be calculated by subtracting the areaof the parabolic expansion, Se,i [m2], from that ofthe triangle �ABC, St,i [m2], assuming theirdepths are the same (Fig. 4).

Let us first calculate the triangle area St,i. Asshown in Figs. 3b and 4, the baseline length of

φ ζ ττ

b n

n i

i

Te

TT i

n

i,

– /

–!

= ( )=∑

0

Fig. 3. Photograph pictures of strand mat cross-sections showing the void structure: a) non-contact voids, b) partiallyfilled edge voids, and c) completely filled edge voids.

248 WOOD AND FIBER SCIENCE, APRIL 2005, V. 37(2)

the triangles equals compressed strand thickness�i. Here the subscript i denotes the compressedstrand thickness in columns of i overlappingstrands. While it likely depends on the deflectionof crossing strands and mat densification, theheight of the triangle is assumed to be propor-tional to the baseline length (strand thickness).The triangle area, St,i, is then given by:

(10)

where: c� � an adjusted coefficient, which isfurther given by: c� � (�/�r)

0.5. Here �r is a ref-erence strand width for normalization (e.g.,0.025 m). This adjustment is made based on ourearly study, which showed that the distances be-tween strand crossings were correlated to thestrand width in the width direction (Dai andSteiner 1994a). In Eq. (10), the compressedstrand thickness is given by: �i � T/i.

For a strand column with strand overlaps i, itscompression strain εi is given by:

(11)

The expansion in the strand width direction�� [m] is:

ε τ ττ τi

i T

i= =–

–1

Sc

t i i, = ω τ2

2

(12)

where � � Poisson ratio for the strand widthdirection (approximately 0.05, which is low dueto surface constraints).

The expansion area Se,i is:

(13)

where �� is given by Eq. (12).Combining Eqs. (10), (11), and (13), we get

the void area along the strand width Sω,i [m2]:

(14)

Note that a void exists only if Sω,i 0 (Fig.3b). If Sω,i � 0, a void is nonexistent (Fig. 3c).

Similarly, the void area along the strandlength Sλ,i [m2] is:

(15)

Sc T

i

T

i

T

i

c T

i

iλλ

λ

λ

µ

τλ

, –

–

=

≈

2

1

3

12

2

2

S S Sc T

i

T

i

T

i

i t i e iωω

ωµτ

ω

, , ,– –

–

= =

2

1

31

2

Se i i i i, = =2

3 2

1

3τ ω τ µ ε ωω

∆

∆ω µ ε ωω= i

Fig. 4. Schematic of a cross-section of strand overlaps and an edge void: a). overlaps between three strands with squaredarea of interest, and b). enlarged cross-section showing the dimensions of an edge void.

Dai et al.—HEAT AND MASS TRANSFER IN COMPOSITES. PART II. 249

where zero lateral expansion is assumed in thelength (grain) direction, or � � 0. Similar toEq. (10), the adjusted coefficient in the length di-rection is given by: c� � (�/�r)

0.5. Parameter �r isa reference strand length for normalization (e.g.,0.1 m).

For a single strand, its edge voids exist alongthe sides of length and width. While the cross-section areas of the voids are given by Eqs. (14)and (15), the depth of the voids should be deter-mined by the strand length and width. Accord-ingly, the volume of the voids is 2(S�,i � � S�,i �)[m3].

For all strands in the i overlap columns, thetotal volume of the edge voids is 2(S�,i � � S�,i�) Nf p(i). Since the edge voids only exist incolumns under compression or in which strandoverlap i is: ≥ T/� � 1, the porosity �b,e is thengiven by:

(16)

where: p(i) is the Poisson variable defined byEq. (1).

Combining with Eqs. (1) and (2), Eq. (16) canbe rewritten as:

(17)

Finally, the total porosity between strands �bincluding both the non-contact voids �b,n (Eq.9)and edge voids �b,e (Eq.17) can be readily ob-tained by:

(18)

Mat permeability

Classic model for porous media.—Permeabil-ity is a very important property of porous media,which cover a wide range of materials includingsoil, rock, and beds of natural or synthetic parti-cles and fibers. Therefore, the subject of perme-ability has been widely investigated and anenormous amount of knowledge has been accu-mulated (Dullien 1992). Among all the models

φ φ φb b n b e= +, ,

φω λω λ

τb e

ni i

i T

ie n

T

S S n

i,

–, ,

/ != +

= +

∞

∑2

1

φ λ ωω λτ

b ef

i ii T

N

TAS S p i, , ,

/

= +( ) ( )= +

∞

∑2

1

that have been developed, the Carman-Kozenymodel (Carman 1956 and Kozeny 1927) is prob-ably the most popular. Based on the analogy offlow through hydraulic channels, the genericform of the Carman-Kozeny equation for perme-ability kCK [m2] is:

(19)

where: � � porosity,S0 � specific surface area based onsolid’s volume [m-1], andk’� k0(Le /L)2, which is often referred toas Kozeny constant or tortuosity. Furtherk0 is a constant, and Le and L are the ef-fective microscopic flow length and themacroscopic flow length, respectively.

Note that the permeability as analyzed here is aproperty of macroscopic flow. According to Car-man (1956), the macroscopic flow is obtained byfluid particles actually traveling along a micro-scopic path length Le which is always longer thanthe shortest distance along the macroscopic di-rection L. The Kozeny constant k’ is a measure ofhow long the effective microscopic flow pathlength Le is compared to the macroscopic flowpath length L. Unfortunately, the value Le or Le /Lis seldom known. The best value for k’ to fit mostexperimental data on packed beds of spheres isequal to 5. Assume particles can be approximatedin shape by spheres. The specific surface area isthen given by:

(20)

and the common form of Carman-Kozeny forbeds of particles then becomes:

(21)

where: Dp � equivalent sphere diameter [m].

The Carman-Kozeny equation (Eq.21) hasbeen found particularly useful for most packedparticles or fibers (Dullien 1992). However, it

kD

CKp=

( )2 3

2180 1

φφ–

SD

D Dp

p p0

2

3 6

6= =π

π /

kk S

CK =( )

φφ

3

2021' –

250 WOOD AND FIBER SCIENCE, APRIL 2005, V. 37(2)

may not be valid for particles that deviate signif-icantly from the spherical shape or consolidatedmedia. Indeed, a consolidated mat of woodstrands deals with neither spherical particles nora loosely packed structure. Therefore, modifica-tions must be made before the Carman-Kozenymodel can be applied.

Model for strand mats.—To apply theCarman-Kozeny theory to wood composites, it isfirst hypothesized that the flow occurs only invoids between strands and the flow throughwood is negligible. Under this assumption, onlythe between-strand porosity �b (Eq. 18) shouldbe considered.

Secondly, the Carman-Kozeny model is modi-fied to account for the strand shape and the matconsolidation. Assume strands are rectangular inshape. Their specific surface area based on thesolid’s volume S1 [m-1] is:

(22)

For OSB strands, the length � and the width �are usually an order of magnitude greater thanthe thickness �. Equation (22) can therefore beapproximated by:

(23)

When a mat is consolidated, the strand thick-ness decreases. Due to the random variation, thethickness changes also vary. The effective strandthickness �e [m] at a given mat thickness or den-sity is given by:

(24)

Combining with Eq. (1), Eq. (24) becomes:

(25)

Similar to Eq. (23), the effective specificstrand surface area available for flow Se [m-1] is:

(26)See

= 2

τ

τ ττ

τ

en

i

i T

i

i

T

en

i

T

i

n

i= +

= +

∞

=∑∑–

/

/

! !10

τ ττ

τ

ei Ti

T

p iT

ip i= ( ) + ( )

= +

∞

=∑∑

/

/

10

S12≈τ

S1

22

1 1 1=+ +( ) = + +

λω λτ ωτλωτ τ ω λ

Finally, by combining Eq. (26) with Eq. (19),the modified Carman-Kozeny equation for pre-dicting permeability of wood composite mats k[m2] becomes:

(27)

where: c’ � tortuosity constant, which is deter-mined for best fit with experimentaldata. Since strand mats are layered instructure, the transverse permeability kTis different from the lateral permeabilitykL. The difference between kT and kL willlie in their corresponding values of theconstants c’T and c’L .

Thus, a fundamental model for mat perme-ability has been developed based on the classicCarman-Kozeny theory and the mat structure.This model has for the first time linked the matpermeability to such important parameters asmat porosity (mat densification) and strand di-mensions.

experimental tests

There were two basic objectives for conduct-ing the experimental tests: to validate the hy-pothesis that mat permeability is affected mainlyby between-strand porosity and to validate thepermeability model. The first objective wasachieved by comparing the permeability of matswith that of solid wood of which the mats werecomposed. To meet the second objective, perme-ability of mats of various strand dimensionswere tested and compared with the model pre-dictions.

Materials

To insure accurate results on the effects ofstrand dimensions, uniform strands were pre-pared. Aspen (Populus tremuloides) logs werefirst peeled using a rotary lathe into smooth ve-neer of intended thickness. The veneer was fur-ther dried and cut into rectangular strands ofuniform length and width. Five strand dimen-sions were chosen as shown in Table 1. The di-

kc

e b

b

=( )τ φ

φ

2 3

21' –

Dai et al.—HEAT AND MASS TRANSFER IN COMPOSITES. PART II. 251

mensional combinations enabled the effects ofall three strand-dimensions (thickness, width,and length) to be examined within the scope oftests. Strands were dried to 5% moisture contenton an oven-dry basis, blended with 2% (w/w)powdered phenol-formaldehyde resin and hand-formed to randomly oriented strand mats of 320mm by 320 mm. The mats were pressed to 10-mm thickness at three target densities: 500, 600,and 700kg/m3.

Special pressing methods were used to pro-duce homogeneous panel density to minimizethe effect of vertical density profile. The matswere pressed at low temperature 75°C until thesame temperature was is reached at the core.Then the platen temperature was further in-creased to 160°C and held at that temperatureuntil the core reached 125°C. The pressing timewas around 15 min. A total of nine boards weremade with three replicates for each target den-sity. Nine disc specimens of 60 mm in diameterwere cut from each board, which yielded a totalof 81 samples for the permeability tests.

To compare the permeability of strandboardwith solid wood, aspen lumber boards with aver-age density of 410 kg/m3 were pressed to 10 mmand two target densities: 600 and 700kg/ m3.After densification, a total of 42 disc specimensof 60 mm in diameter were then cut and sub-jected to the same permeability tests. Note thatonly the permeability along the panel thickness(radial) direction was measured.

Procedures

A special device was developed to allow air toflow through the disc specimens and the pressuredrop and air flow rate to be measured. According

to the principle of the apparatus shown in Fig.5,the permeability was calculated as following:

(28)

where: k = permeability [m2];µ = viscosity of fluid [Pa.s], (for air atroom temperature µ = 1.846 × 10–5

Pa • S);L = length in flow direction ,thicknessof specimen [m];F = cross-sectional area of the specimen[m2];Q = volumetric flow rate at pressure P2[m3/s];∆P � pressure differential � P1 – P2[Pa]; P = (P1 + P2) /2 arithmetic average pres-sure [Pa];P1 � given air pressure [Pa]P2 � pressure at which Q was mea-sured [Pa].

results and discussion

Predicted porosity variations during matconsolidation

Porosity in wood composites is in generalhighly correlated to product density. While den-sity is easy to measure, porosity is very difficultto quantify especially considering the fact thatvoids exist both within cellular wood structureand between wood elements. Modeling offers

kL Q P

F P P= ⋅ ⋅ ⋅

⋅ ⋅µ 2

∆

Table 1. Strand dimensions used for the permeabilitytests.

Test No. Length (mm) Width (mm) Thickness (mm)

1 50.8 25.4 0.752 101.6 25.4 0.753 152.4 25.4 0.754 50.8 6.3 0.755 50.8 6.3 1.05

Fig. 5. Schematic of the permeability testing apparatus.

252 WOOD AND FIBER SCIENCE, APRIL 2005, V. 37(2)

one way to shed insight into the void structurenot only in the final product but also during themanufacturing process.

Porosity and density relationship.—Figure 6depicts the predicted porosity variations in a matduring consolidation. While the total porosity �tlinearly decreases with mat density, the porosityvariations inside strands �i and between strands�b are noticeably different both in terms of thetrend and the magnitude. After forming, a mat ofstrands is usually very porous due to the exis-tence of voids between strands. These voids,however, can be rapidly eliminated during theearly stage of consolidation, as evidenced by asharp decrease of the between-strand porositywith increase in mat density in Fig. 6. Duringthis stage, the inside-strand porosity increasesmainly because the relative volumetric changeof the mat with mat density is much greater thanthat of voids inside strands. In fact, the inside-strand void volume cannot realize a significantdecrease until most of the voids between strandsare eliminated. The breaking point seems tooccur around or shortly after a mat density of400 kg/m3 or the original wood density.

Further consolidation leads to a very slow de-crease in porosity between strands and a rela-tively rapid decrease in porosity inside strands.While reduction of voids between strands is nec-essary to create strand-to-strand contact forbonding (Dai and Steiner 1993), decrease ofvoids inside strands inevitably leads to densifi-

cation of wood substance, which ideally shouldbe avoided to maximize volumetric recovery ofwood. As shown in Fig. 6, the decrease in poros-ity after 400 kg/m3 mat density comes directly atthe expense of wood volumetric loss. Currently,most of the strand-type wood composites includ-ing particleboard and oriented strandboard re-quire that mat density be around 600 to 800kg/m3. At such high densities, not only are thefinal products significantly heavier than solidwood, but also 40 to 50% of wood volume is lost(Fig. 6). This volumetric loss is substantiallyhigh compared to less than 10% loss for veneer-based products. The high loss stems from thediscontinuity of strands and the random mat for-mation. This result suggests the importance ofstrand preparation and mat formation to produc-ing lower density products.

Non-contact voids vs edge voids.—The voidsexist between strands in a mat due to the lack ofstrand contacts and/or the existence of strandedges. Figure 7 reveals that the non-contactvoids dominate during the early stage of matconsolidation. As the mat is further consolidated,localized contacts between strands are devel-oped, resulting in the elimination of large voids.As the voids between strand faces are elimi-nated, small voids around strand edges start toemerge and eventually dominate in the finalporous network. The elimination of the edgevoids appears to be difficult (Fig. 7) and in-evitably leads to the loss in wood recovery(Fig.6). On the other hand, a small amount of the

Fig. 6. Typical variations of total porosity �t, inside-strand porosity�i, between-strand porosity �b and volumet-ric loss of wood during mat consolidation.

Fig. 7. Typical variations of between-strand porosity�b, non-contact porosity �b, n and edge porosity �b, e duringmat consolidation.

Dai et al.—HEAT AND MASS TRANSFER IN COMPOSITES. PART II. 253

voids may not be detrimental at all since theycan offer passages for gas to flow through themats during pressing and air/vapor to permeatethrough the boards in service – an attribute be-coming increasingly important to the durabilityof the building envelop (e.g., Bumbaru et al.1988).

Effects of strand dimensions on between-strand porosity.—Figures 8 a, b, and c show, re-spectively, the effects of strand length, width,and thickness on the porosity between strands.For both strand length and width, the porositydecreases as the strand dimensions increasemainly because of the edge effects. The relation-ships are nonlinear with porosity being moresensitive to changes in length and width when

the dimensions are small. The porosity changeslittle when strands become really long or wide.

In contrast, the relationship between porosityand strand thickness is almost linear and highlypositive. The void volume always increases withan increase in strand thickness. According to themodel, both non-contact voids and edge voidsare highly dependent upon strand thickness (Eqs.9–17). For this reason, strand thickness has thestrongest impact on porosity among all strand di-mensions. Strand width also has greater effectthan length. These results suggest that one wayto manufacture low-porosity products is to usethin and large strands.

Permeability model validations and predictions

Comparing permeability between wood andmat.—A key assumption for this model is thatthe mat permeability is due to the voids betweenstrands instead of those inside strands. Figure 9compares the vertical permeability through matthickness and the transverse (perpendicular-to-grain) permeability of wood. Over the typicaldensity range of mat consolidation, both the matpermeability and the wood permeability de-crease in a logarithmically linear manner as seenby the regression lines in Fig.9. The wood per-meability is consistently lower by an order ofmagnitude. This result implies that the flowthrough wood may indeed contribute very little

Fig. 8. Effects of strand dimensions on the between-strand porosity: a). Effect of strand length (width: 25.4 mmand thickness: 0.76 mm), b). Effect of strand width (length:101.6 mm and thickness: 0.76 mm), and c). Effect of strandthickness (length: 101.6 mm and width: 25.4 mm).

Fig. 9. Logarithmic plot comparing the vertical perme-ability of aspen OSB boards with the perpendicular-to-grainpermeability of aspen wood at various densifications.

254 WOOD AND FIBER SCIENCE, APRIL 2005, V. 37(2)

to the overall permeability of a mat. It thereforeconfirms that the flow inside a mat mainly oc-curs through the voids between strands as op-posed to those inside strands.

Model validation.—Because of our equipmentlimitations, it was difficult to perform the perme-ability tests without incurring significant errorson mats with density below 450 kg/m3. As a firstvalidation, we used the data from von Haas(1998), who tested density as low as 300 kg/m3.Figure 10 compares the model predictions withthe experimental data with a remarkably closeagreement. Here the tortuosity constant used tofit the experimental data c’T is 500 (Eq. 27).

To further validate the model, Fig. 11 comparesthe permeability of mats made of different stranddimensions. The experimental data show consid-erable variations, which seems consistent withwhat was reported in the literature (e.g., Boltonand Humphrey 1994). In addition to the naturalcauses of wood, the permeability variations arelikely due to the variations in mat/panel structureand the edge effects of relatively small testingspecimens. The mat structural variations cancause variations of both porosity �b and tortuosityc’ (Eq. 27). As far as the edge effect, larger speci-men size may yield more consistent results, espe-cially for strandboards. Despite the variations, thetrends between the permeability and the strand di-mensions seem well predicted by the model.

Relationships between mat permeability andstrand dimensions.—Figures 12a, b, and c depictthree predicted family curves of mat permeability

with respect to strand length, strand width, andstrand thickness, respectively. For strand lengthand width, the larger the dimensions, the lowerthe permeability. However, the degree with whichpermeability changes decreases as the dimensionsincrease. In other words, permeability is moresensitive to small strands than large strands. Thisresult stems from the influence of strand dimen-sions on between-strand porosity through theiredge effects (Fig. 8a and b). Furthermore, strandlength and width have diminished effects on per-meability at lower density range. During the earlystage of consolidation, the mat is highly porousand its porosity structure is governed by the largegaps between strand surfaces instead of the smallvoids around strand edges. As a result, the matpermeability is very high and should be mainlycontrolled by mat density.

Fig. 10. Logarithmic plots comparing mat vertical per-meability between the model prediction and experimentaldata (Strand length: 30.60 mm, width: 5.10 mm and thick-ness: 0.62 mm, and cT’�500).

Fig. 11. Logarithmic plots comparing mat vertical per-meability between the model prediction and experimentaldata: a). Effect of strand length, b). Effect of strand width,and c). Effect of strand thickness (See Table 1 for otherstrand dimensions, and cT’�500)

Dai et al.—HEAT AND MASS TRANSFER IN COMPOSITES. PART II. 255

Besides mat density, strand thickness is an-other dominant factor in determining mat perme-ability. As shown in Fig. 12c, increasing strandthickness significantly increases mat permeabil-ity, even at lower mat density. The strong thick-ness effect is due to its effects on both thebetween-strand porosity (Fig. 8c) and the strandspecific surface area (Eq. 26). It is also interest-ing to note that similar to strand length andwidth, strand thickness has a greater effect onmat permeability as strands get thinner.

Effects of strand dimensions on hot pressing

Figure 13 shows an example of how strand di-mensions can affect hot-pressing by depicting

the variations of core temperature, gas pressure,and moisture content in mats of strands with dif-ferent thickness during pressing. The results arebased on predictions using the heat and masstransfer model developed in the preceding paper(Dai and Yu 2004) and the permeability modeldescribed in this paper. It is apparent that strandthickness has a significant impact on all threepressing parameters, particularly the maximumcore temperature, the maximum gas pressure,and the final core moisture content. The highermaximum core temperature, higher gas pressure,and higher final core moisture content are all at-tributed to the thinner strands and hence the

Fig. 12. Logarithmic plots showing the relationshipsbetween mat vertical permeability and strand dimensions(cT’�500): a). Effect of strand length (Width: 25.4 mm andthickness: 0.76 mm), b). Effect of strand width (Length:101.6 mm and thickness: 0.76 mm), and c) Effect of strandthickness (Length: 101.6 mm and width: 25.4 mm).

Fig. 13. An example of predicted effect of strand di-mensions (strand thickness with length fixed at 100 mm andwidth 25 mm) on heat and mass transfer in strand mats dur-ing hot pressing: a). Effect on core temperature, b). Effect oncore gas pressure and c). Effect on core moisture content.

256 WOOD AND FIBER SCIENCE, APRIL 2005, V. 37(2)

lower permeability (both transverse permeabilityand lateral permeability).

Likewise, the effects of strand length andwidth can also be predicted. Due to their effectson permeability, longer or wider strands willlead to higher maximum core temperature,higher core gas pressure, and higher core mois-ture content. It is worth noting that high core gaspressure often causes problems of “blows” or de-laminations. To minimize the “blows,” one mayneed to use lower moisture strands and/or pro-long the decompression time when makingboards with strands of large dimensions.

summary and conclusions

Theoretical models are developed for the firsttime to mathematically characterize the porosityand permeability of wood strand-based compos-ite mats. To facilitate the model development, astrand mat is conceptually visualized as a systemof overlapping strand columns. Assuming ran-dom mat formation, the strand overlaps in thecolumns follow a Poisson distribution with itsaverage determined by the product of com-paction ratio (mat density over strand density)and thickness ratio (mat thickness over strandthickness). Since wood is a porous material, thevoid volume inside a mat is composed of voidsinside strands and voids between strands. Whilethe total mat porosity is readily given by knowndensity of cell wall, the porosity between strandsin a consolidated mat needs to be calculated bytaking into account the random variations ofstrand overlaps and the effects of strand edges.The between-strand void volume is classifiedinto, and calculated by, non-contact voids andedge voids. Besides the Poisson strand overlapvariation, other factors such as strand surfaceroughness and lateral strand expansion are alsoconsidered.

According to the model predictions, the totalmat porosity linearly decreases with mat density,whereas the between- and inside-strand porosi-ties change in highly nonlinear but distinctly dif-ferent manners. The results shed importantinsights into the development of strand-to-strandcontact and the loss of wood volume during the

course of mat consolidation. The model also pre-dicts the different manners in which mat porosi-ties are affected by strand length, width, andthickness, with the thickness being most signifi-cant followed by the width and the length.

With the prior knowledge of mat porosities,the Carman-Kozeny theory for porous materialis applied to model the permeability of woodstrand composites. Under the assumption thatgas flow inside a mat occurs only betweenstrands, the model takes into account thebetween-strand porosity and the strand specificsurface area. Experimental tests are conducted tovalidate the permeability model. The results re-veal that permeability of solid wood is an orderof magnitude lower than that of strand mats atthe same density. Reasonably good agreementsare found between the model predictions and theexperimental results. The model predicts differ-ent relationships between the mat permeability,the mat density, and the strand dimensions.

Through the model, the variations of coretemperature and gas pressure inside a mat duringhot-pressing can be successfully linked to the ef-fects of mat permeability, porosity and strand di-mensions. This study may provide a theoreticalbasis for systematic analyses of the processingand properties of wood composites, particularlystrand-based products.

acknowledgment

The authors would like to thank Forintek’s in-dustry members, Natural Resources Canada(Canadian Forest Service), and the Provinces ofBritish Columbia, Alberta, Saskatchewan, Mani-toba, Quebec, Nova Scotia, New Brunswick, andNewfoundland, and Labrador for their guidanceand financial support for this research.

references

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Bumbaru, D., R. Jutras, and A. Patenaude. 1988. Airpermeance of building materials. Canada Mortgage andHousing Corp. Technical Report. 12 pp.

Dai et al.—HEAT AND MASS TRANSFER IN COMPOSITES. PART II. 257

APPENDIX: ERRATA FOR PART 1

Editorial errors were noticed with Equations 4 and 8f in part 1 of this publication series (Dai andYu 2004). The correct equations should be:Equation 4:

or (4)

Equation 8f:

(8f)

k k k

k k k

k k k

mat x sx g

mat y sy g

mat z sz g

,

,

,

–

–

–

= ( ) +

= ( ) +

= ( ) +

1

1

1

ε ε

ε ε

ε ε

∂∂

=∂

∂∂

∂∂

∂ερτ

ρ ρ ρν ν ν ν˙ – – –Eu

x

u

y

u

zevapxg yg zg

∂∂

+∂

∂+

∂∂

+∂

∂=ερ

τρ ρ ρν ν ν νu

x

u

y

u

zExg yg zg

evap˙

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