8712078
mpip(Q)rRTr
Liu Tong
Moisture Transport in Wood
and Wood-based Panels
A Pre-study of Sorption Methods
Trätek
L i u Tong, graduate s t u d e n t
MOISTURE TRANSPORT I N WOOD AND WOOD-BASED PANELS - A p r e - s t u d y o f s o r p t i o n m e t h o d s TräteknikCentrum, Rapport P 8712078 Keywords oomposite materials diffusion coefficient moisture movement pane Is sorption wood materials Stockholm December 1987
C O N T E N T Page SUMMARY 2 SVENSK SAMMANFATTNING 3 NOMENCLATURE 4 1. INTRODUCTION 6 2. THEORETICAL BACKGROUND 7
2.1 Moisture s o r p t i o n i n one dimension 7 2.2 M o i s t u r e s o r p t i o n i n t h r e e dimensions 9
3. EXPERIMENTAL U 3.1 Choice o f sample m a t e r i a l s 11
3.2 Choice o f s e a l a n t 13 3.3 D e t e r m i n a t i o n o f some a f f e c t i n g f a c t o r s 13
3.3.1 Temperature change o f samples i n s o r p t i o n 13
3.3.2 D i v e r s i t y o f t e s t r e s u l t s !-< 3.4 P r e p a r a t i o n o f samples 14 3.5 S o r p t i o n a l procedure 15 4. EXPERIMENTAL RESULTS 17 4.1 D i f f u s i v i t y o f t h e t e s t e d m a t e r i a l s 23 3. DISCUSSION 24 5.1 A v a i l a b i l i t y o f the s o r p t i o n methods 24 5.2 Surface r e s i s t a n c e 24 5.3 Comaprisons w i t h p r e v i o u s experiments 27 6. CONCLUSIONS 32 7. SUGGESTIONS FOR FUTURE STUDIES 33
SUMMARY
This i s a prestudy o f s o r p t i o n methods f o r measuring t h e moisture d i f f u -s i v i t y . E i g h t type-s o f wood-ba-sed panel-s and -spruce wood were mea-sured w i t h the s o r p t i o n method i n t h r e e r e l a t i v e h u m i d i t y ranges ( c l i m a t e s ) a t 20 °C. A t h r e e d i m e n s i o n a l s o r p t i o n method was a l s o t e s t e d w i t h one k i n d o f f i b e r -board. Problems such as e f f e c t i v e water vapor s e a l a n t , temperature change i n t h e s o r p t i o n process, s u r f a c e r e s i s t a n c e t o s o r p t i o n e t c t h a t might a f f e c t t h e e x p e r i m e n t a l r e s u l t s were i n v e s t i g a t e d .
The experimental r e s u l t s show t h a t t h e average moisture d i f f u s i v i t y i s ob-t a i n a b l e w i ob-t h a s o r p ob-t i o n ob-t e s ob-t . The ob-t h r e e - d i m e n s i o n a l s o r p ob-t i o n meob-thod g i v e s e s s e n t i a l l y t h e same r e s u l t s as t h e s o r p t i o n method. Density i s a very imp o r t a n t f a c t o r t h a t determines t h e moisture d i f f u s i v i t y o f woodbased imp r o -ducts .
Suggestions f o r f u t u r e s t u d i e s o f s o r p t i o n methods t o determine moisture d i f f u s i v i t y more p r e c i s e l y are made.
SVENSK SAMMANFATTNING
D i f f u s i v i t e t e n av f u k t i trä och tr'abaserade s k i v o r kan bestämmas genom s k sorptionsmätningar. Därvid mäts m a t e r i a l e n s viktändring som f u n k t i o n av t i -den v i d k o n d i t i o n e r i n g i o l i k a k l i m a t med bestämd l u f t f u k t i g h e t och tempe-r a t u tempe-r . Fötempe-r a t t sedan betempe-räkna d i f f u s i v i t e t e n f i n n s o l i k a t e o tempe-r e t i s k a an-greppssätt.
Det f i n n s också andra mätmetoder, som r e d o v i s a t s i en inledande l i t t e r a t u r -s t u d i e . Bland de-s-sa metoder v e r k a r -sorption-smetoden vara enkel a t t använda och e f t e r l i k n a r v e r k l i g h e t e n . Men d e t f i n n s några o k l a r h e t e r i tillämpning-en. Dessa har s t u d e r a t s i denna förstudie.
Förstudien k o n k r e t i s e r a r och p r e c i s e r a r d e t p r a k t i s k a tillvägagångssättet v i d sorptionsmätningar. Oli-ka t e o r e t i s k a beräkningssätt, a n t a l provkroppar, p r o v s t o r l e k , förseglingsmaterial m m har s t u d e r a t s .
R e s u l t a t e n v i s a r a t t sorptionsmetoden kan användas för a t t bestämma d i f f u -s i v i t e t e n -som f u n k t i o n av m a t e r i a l e t -s f u k t k v o t ( e l l e r av l u f t f u k t i g h e t e n v i d jämvikt). Noggrannheten i bestämningen beror på mätnoggrannheten och på t e o r e t i s k t beräkningssätt.
D i f f u s i v i t e t e n för några trabaserade s k i v o r har bestämts, både vinkelrätt mot skivans plan och p a r a l l e l l t , i e t t fåtal k l i m a t . S k i v d e n s i t e t e n är den parameter som verkar ha störst b e t y d e l s e , men s a m t l i g a data är t v p r e l i -minära .
För f o r t s a t t a s t u d i e r rekommenderas a t t mer avancerade beräkningsmetoder provas så a t t d i f f u s i v i t e t e n s fuktkvotsberoende kan bestämmas mer nogg r a n t . Dessa metoder kräver mer nonoggnoggranna mätdata än som f n f i n n s t i l l gängliga, övergångsmotståndet v i d p r o v y t a n måste dessutom studeras y t t e r l i -gare eftersom d e t kan ha s t o r b e t y d e l s e . S l u t l i g e n bör sorptionsmetoden jämföras med den s k koppmetoden som är mer e t a b l e r a d men mäter under d e l -v i s onormala b e t i n g e l s e r . På så sätt bör den lämpligaste metoden a t t be-stämma ångdiffusiviteten hos träbaserade m a t e r i a l kunna p r e c i s e r a s .
Nomenclature
a, b, c half sample thicknesses m
fl area
D moisture diffusivity based on moisture concen- m^/s
tration in the material
D* apparent diffusivity m^/s
t moisture fraction of sorption
E - (w^y - Wi)/(Wb - w j - (Uj^y - Ui)/(U|,-Ui)
E dimensionless average moisture concentration
or moisture content E - 1- E
E||, Ey, Ej the amount of E sorbed in x, y. z coordinate
^ directions in three dimensional sorption
g moisture flux kgAm^s)
L thickness of sample in diffusion direction m
sample length along air flow direction m
R gas constant J/mol*K
surface emissivity m/s
t time s
u moisture content, based on oven dry weight kg/kg
of a material
U), U2 the lower and higher moisture contents in a test kg/kg
V moisture concentration in the air kg/m^
V,, moisture concentrations on sample surface and kg/m^
in ambient air
U air velocity m/s
w moisture concentration in the tested materials. kg/m^
based on wet volume
w,, moisture concentrations on sample surface and kg/m^
in ambient air
Hf y, z space coordinates m
å critical length m
p
surface transfer coefficient of water vapor
m/s
p
density, the dry wight of a body divided by wet
volume
kg/m^
8
moisture diffusivity based on moisture
concen-tration in the air
water vapor diffusivity in the air
mVs
mVs
v
kinematic viscosoty of the air
mVs
0
relative humidity
subscript
ou
1
b
average value
iuitial value
boundary value
1. INTRODUCTION
I n the h y g r o s c o p i c a l range, namely, under the f i b e r s a t u r a t i o n p o i n t (FSP), m o i s t u r e i n wood and wood-based panels e x i s t s and moves as water vapor and bound water s i m u l t a n e o u s l y . The combined e f f e c t o f t h e movement o f these two water phases i s d e s c r i b e d as t h e e f f e c t i v e d i f f u s i v i t y ( d i f f u s i o n c o e f f i c i e n t , u s u a l l y r e f e r r e d t o as d i f f u s i v i t y f o r s i m p l i c i t y ) , since m o i s t u r e m i g r a t i o n i s a d i f f u s i o n process i n such a case. The two most com-mon techniques t o determine d i f f u s i v i t y i n s o l i d s are t h e cup method and the s o r p t i o n method. I n t h e s o r p t i o n method, the d i f f u s i v i t y i s determined when water vapor i s adsorbed i n t o o r desorbed from a m a t e r i a l : Set t h e samples t h a t have been i n moisture e q u i l i b r i u m i n a c e r t a i n c l i m a t e ( w i t h d e f i n i t e temperature and r e l a t i v e h u m i d i t y ) t o another predetermined c l i mate, measure t h e m o i s t u r e s o r p t i o n a l r a t e t i l l t h e samples reach e q u i -l i b r i u m a g a i n , and c a -l c u -l a t e t h e d i f f u s i v i t y o f the samp-les w i t h t h e sorp-t i o n a l r a sorp-t e , a c c o r d i n g sorp-t o some equasorp-tions d e r i v e d w i sorp-t h sorp-t h e law o f d i f f u s i o n , F i c k ' s law.
However, some t h e o r e t i c a l and p r a c t i c a l procedures f o r the a p p l i c a t i o n o f s o r p t i o n methods f o r wood and wood products seemed t o be u n c e r t a i n and a c l a r i f i c a t i o n was needed i n a p r e - s t u d y which i s presented here.
2. THEORETICAL BACKGROUND
2.1 M o i s t u r e s o r p t i o n i n one dimension
As wood-based panels and wood are n o n - i s o t r o p i c , i t would be necessary t o determine d i f f u s i v i t y i n t h e i r t h r e e p r i n c i p a l d i r e c t i o n s i f moisture tran-s p o r t i n any d i r e c t i o n i tran-s t o be c a l c u l a t e d w i t h Pick'tran-s law:
— = V
dt
D, 0
0
0 0 D,
vw
where Dx, Dy, Dz a r e d i f f u s i v i t y " i n t h e t h r e e p r i n c i p a l d i r e c t i o n s , W moisture c o n c e n t r a t i o n and t time.(1)
I S
With t h e s o r p t i o n method, t h e s u r f a c e s o f r e c t a n g u l a r samples a r e g e n e r a l l y sealed except two o p p o s i t e ones, where s o r p t i o n w i l l take place unidimen-a i o n unidimen-a l l y . Under t h i s c o n d i t i o n , i f t h e d i f f u s i v i t y i s known t o be c o n s t unidimen-a n t , the s o r p t i o n a l f r a c t i o n a l moisture c o n t e n t É i n t h e samples can be analy-t i c a l l y expressed as f o l l o w s , which i s o b analy-t a i n e d by d i r e c analy-t s o l u analy-t i o n o f Pick's law w i t h v a r i a b l e s e p a r a t i o n under s o r p t i o n c o n d i t i o n s (Crank, 1975, p. 4 3 ) : n-1
1
(2n-iy
n\2n- \f
t P
a'
(2)where u i , u^, and UQV Qre t h e moisture c o n t e n t s i n t h e sample a t i n i t i a l , at f i n a l e g u i l i b r i u m and a t time t d u r i n g t h e s o r p t i o n process, w j , w^» and w^^ a r e moisture c o n c e n t r a t i o n s i n t h e sample a t t h e same time as U i , Urn and Ut. D i s t h e e f f e c t i v e d i f f u s i v i t y and a t h e h a l f sample t h i c k n e s s i n t h e s o r p t i o n d i r e c t i o n . I t should be noted t h a t i n a s o r p t i o n process t h e mois-t u r e c o n mois-t e n mois-t o r m o i s mois-t u r e c o n c e n mois-t r a mois-t i o n i s nomois-t u n i f o r m i n mois-t h e samples, u and w here a r e t h e mean values.
Another e x p r e s s i o n o f E which i s s p e c i a l l y s u i t e d f o r s h o r t s o r p t i o n time i s d e r i v e d by s o l v i n g Pick's law w i t h Laplace t r a n s f o r m a t i o n under s o r p t i o n c o n d i t i o n s (Crank, 1975, p. 4 8 ) :
4Dt 4r + 2y(-l)"ierfc na
(3) When É i s l a r g e r than 0.667, t h e f i r s t term i n Eq(2) can be taken t o r e p r e -sent t h e whole s e r i e s and t h e d i f f u s i v i t y can be expressed as:D= 4aJ
I d8
. « ^ 1 - É ) .
For C l e s s than 0.5, t h e summation term i n Eg(3) becomes n e g l i g i b l y small and Eq(3) reduces t o :
(5)
However when d i f f u s i v i t y changes w i t h moisture c o n c e n t r a t i o n , as i n t h e case o f m o i s t u r e d i f f u s i o n i n t h e wood m a t e r i a l , t h e d i f f u s i v i t y c a l c u l a t e d w i t h any o f t h e f o u r equations mentioned above w i l l vary w i t h s o r p t i o n t i m e . Crank (1975) d e s c r i b e d a method t o g a i n t h e exact d i f f u s i v i t y as a f u n c t i o n o f c o n c e n t r a t i o n w i t h a s e r i e s o f s o r p t i o n experiments: always s t a r t t h e s o r p t i o n from a c e r t a i n i n i t i a l c o n c e n t r a t i o n and t e r m i n a t e them at s u c c e s s i v e l y d i f f e r e n t f i n a l c o n c e n t r a t i o n s , and then w i t h numerical d i f f e r e n t i a t i o n d e r i v e concentrationdependent d i f f u s i v i t y from the r e l a -t i o n o f -t h e average d i f f u s i v i -t y o b -t a i n e d i n each s o r p -t i o n -t e s -t .
Techniques f o r d e t e r m i n i n g concentration-dependent d i f f u s i v i t y w i t h one s o r p t i o n t e s t have a l s o been i n v e s t i g a t e d by some o t h e r workers. Duda and Vrentes (1971) developed a method w i t h weighted r e s i d u a l approach, which i s s u c c e s s f u l e s p e c i a l l y i n t h e l a t e r stage o f s o r p t i o n due t o a very f l e x i b l e t r i a l e x p r e s s i o n o f t h e c o n c e n t r a t i o n p r o f i l e . Schoeber (1976) developed a method o f r e g u l a r regime a n a l y s i s i n the s o r p t i o n process. I n t h i s method, when a s o r p t i o n t e s t has proceeded f o r a c e r t a i n t i m e , t h e c o n c e n t r a t i o n -dependent d i f f u s i v i t y i s d e r i v a b l e by a n a l y s i n g t h e moisture c o n c e n t r a t i o n p r o f i l e which i s , a c c o r d i n g t o Schoeber, c h a r a c t e r i s t i c o n l y o f the t e s t e d m a t e r i a l i n such a s o r p t i o n a l stage, i . e . t h e stage o f r e g u l a r regime. For one s o r p t i o n process, Crank (1975, p. 239) s t a t e d t h a t he had proved the v a l i d i t y o f t h e f o l l o w i n g e q u a t i o n i n g i v i n g a reasonable approximation of t h e average d i f f u s i v i t y between t h e i n i t i a l and f i n a l c o n c e n t r a t i o n s :
I 2
D= 0.0492
( t ) i
2
where ( t ) l / 2 denotes t h e time taken when t h e f r a c t i o n a l moisture o f sorp-t i o n E i s equal sorp-t o 1/2. This expression i s a c sorp-t u a l l y d e r i v e d d i r e c sorp-t l y from Eq(5) by t a k i n g t h e value o f E as 0.5 and r e f e r r i n g t h e corresponding t as ( t ) l / 2 . I t would produce a r a t h e r accurate d i f f u s i v i t y when t h e d i f f u s i v i t y i s not c o n c e n t r a t i o n dependent. Otherwise i t can p r o v i d e an approximation t o the average o f t h e v a r y i n g d i f f u s i v i t y . Another a p p r o x i m a t i o n o f the average d i f f u s i v i t y (Crank, 1975, p. 245) i s g i v e n by:
(7)
where t h e term i n t h e b r a c k e t s should be taken a t t h e i n i t i a l s o r p t i o n stage (C i s l e s s than 0.6). I f t h e curve E versus t h e square r o o t o f t shows an a p p r o x i m a t e l y l i n e a r r e l a t i o n from E=0 up t o E=0.6 f o r a m a t e r i a l , then t h e average d i f f u s i v i t y o b t a i n e d w i t h Eq(6) and Eq(7) should be s i m i
-l a r (Crank, 1975, p. 2 4 6 ) . The e x p e r i m e n t a -l r e s u -l t s o f t h i s pre-study w i -l -l show t h a t such an approximate l i n e a r i t y holds t r u e f o r wood and wood-based panels. The exact d i f f u s i v i t y a t the f i n a l stage of the s o r p t i o n process i s o b t a i n a b l e w i t h (Crank, 1975, p. 246):
. 1 - E
(8)There are two disadvantages i n using Eq(8) ( F r e n d s d o r f f , 1964). I t g i v e s l e s s p r e c i s i o n than Eq(6) and ( 7 ) due t o a l a r g e r r e l a t i v e e r r o r of mea-sured p o i n t s near e q u i l i b r i u m . I t i s v a l i d o n l y when d i f f u s i v i t y i s not extremely concentration-dependent.
We see t h a t Eq(7) and ( 8 ) are o b t a i n e d from Eg(5) and (4) simply by making d e r i v a t i o n of f i n r e s p e c t t o t . I t i s i n t e r e s t i n g t o note t h a t by such a t r e a t m e n t t h e equations s u i t a b l e f o r constant d i f f u s i v i t y become a p p l i c a b l e f o r concentration-dependent ones.
A l l the above equations g i v e d i f f u s i v i t y based on moisture c o n c e n t r a t i o n i n the samples. Conversion w i t h t h e a i d o f s o r p t i o n isotherms w i l l be needed i f the d i f f u s i v i t y i s t o be expressed on the b a s i s of m o i s t u r e concentra-t i o n i n concentra-t h e a i r . The accuracy of such a r e c a l c u l a concentra-t i o n depends s concentra-t r o n g l y on the p r e c i s i o n o f the i s o t h e r m o f the sample m a t e r i a l .
Eq(6) and Eq(7) are mainly a p p l i e d i n t h i s r e p o r t t o c a l c u l a t e t h e average d i f f u s i v i t y . Eq(8) was a l s o employed t o c a l c u l a t e the exact d i f f u s i v i t y of the f i n a l m o i s t u r e c o n c e n t r a t i o n , but the tendency f o r the q u a n t i t y
d l n ( l - C ) / d t t o approach a s t r a i g h t l i n e seemed not t o be apparent, so a s a t i s f a c t o r y r e s u l t was not o b t a i n e d and r e p o r t e d . This might be caused by the measurement p r e c i s i o n t h a t c o u l d not meet the h i g h requirement of t h i s e q u a t i o n , or t h a t m o i s t u r e d i f f u s i v i t y i n wood m a t e r i a l s i s very s t r o n g l y c o n c e n t r a t i o n dependent.
Methods o f Duda and Vrentes, 1971, or Schoeber, 1976, t o determine d i f f u -s i v i t y - c o n c e n t r a t i o n r e l a t i o n -s w i t h only one -s o r p t i o n proce-s-s were not t r i e d i n t h i s p r e - s t u d y e i t h e r . As the experiments are mostly made i n a c l i m a t e chamber, the r e s u l t s might not have enough p r e c i s i o n t o be able t o support those s o p h i s t i c a t e d a n a l y s i s , which would have a s t i l l higher r e -quirements f o r the measurements r e s u l t s than Eq(8).
2.2 M o i s t u r e s o r p t i o n i n t h r e e dimensions
The f r a c t i o n a l m o i s t u r e o f s o r p t i o n E i s i n some cases s u b s t i t u t e d by d i -mensionless average m o i s t u r e content E:
g V b - V i v _ U b - " i y _ ^ ^ (9)
Such an expression has the advantage of making v a r i a b l e s e p a r a t i o n con-v e n i e n t l y i n t h e case of t h r e e - d i m e n s i o n a l d i f f u s i o n . As the t e s t e d
10
r e c t a n g u l a r samples a r e not sealed i n t h e t h r e e - d i m e n s i o n a l s o r p t i o n experiment, E can be expressed as:
E^ExEyE.
(10) where Ex, Ey and Ez a r e t h e dimensionless average moisture c o n c e n t r a t i o n sorbed i n t o o r from the samples through the t h r e e s u r f a c e s p e r p e n d i c u l a r t o the X, Y and Z d i r e c t i o n s . We need t o prepare the samples i n such a way, as shown i n F i g u r e 1 , t h a t f o r panel samples the X, Y, Z c o o r d i n a t e s repec-t i v e l y c o i n c i d e w i repec-t h repec-the d i r e c repec-t i o n s p a r a l l e l repec-t o repec-the panel surfaces i n repec-t h e machine d i r e c t i o n ( d u r i n g panel manufacture) as w e l l as t h e t r a n s v e r s e machine d i r e c t i o n , and p e r p e n d i c u l a r t o the panel s u r f a c e s . For wood samples t h e X, Y, Z c o o r d i n a t e s can be arranged along the r a d i a l , tangen-t i a l and l o n g i tangen-t u d i n a l d i r e c tangen-t i o n s . I n botangen-th cases tangen-the d i f f u s i v i tangen-t y i n tangen-the X and Y d i r e c t i o n s are s i m i l a r and can be approximately assumed as equal. I f the samples a r e prepared t o have i d e n t i c a l dimensions i n t h e X and Y d i r e c -t i o n s , -t h e n :
(11)
F i g u r e 1.
Sample o f the three-dimensional s o r p t i o n method.
I f the samples had i n f i n i t i v e l e n g t h s i n the X and Y d i r e c t i o n s . Ex and Ey would t h e o r e t i c a l l y be u n i t y , as then t h e r e would be no moisture s o r p t i o n along the X and Y axes. I n t h i s case E=Ez. Assign the h a l f l e n g t h s o f t h e samples along t h e X, Y axes as a and b (a = b ) , along the Z a x i s as c. At a given s o r p t i o n t i m e , p l o t a curve o f E versus the r e c i p r o c a l o f the h a l f l e n g t h a, and e x t r a p o l a t e the curve t o l/a=0 t h a t would correspond t o
samples i n f i n i t e l y long i n t h e X and Y d i r e c t i o n s , as i n F i q u r e 2. A value o f E, expressed as E-max w i l l be found t h a t equals t o Ez:
?fiiax
(12) By connecting t h e E-max values a t each measurement time t , we can d e r i v e a E-max-t r e l a t i o n , and the average d i f f u s i v i t y i n the Z d i r e c t i o n i s then o b t a i n a b l e w i t h Eq(6) o r Eq(7) by s u b s t i t u t i o n o f (1-E-max) f o r C.
The d i f f u s i v i t y i n the X and Y d i r e c t i o n s can subsequently be d e r i v e d . This i s done by d e t e r m i n a t i o n o f an imaginary c r i t i c a l l e n g t h o f the samples i n the X and Y d i r e c t i o n s , say å, a t which t h e s o r p t i o n a l amount i n the Z d i -r e c t i o n i s i d e n t i c a l t o t h e s o -r p t i o n a l amount i n t h e X o -r Y d i -r e c t i o n .
11 Ez i s always equal t o E-max f o r samples o f t h e i n f i n i t i v e l e n g t h . At any g i v e n s o r p t i o n a l t i m e , E decreases as 1/a i n c r e a s e s , s i n c e a l a r g e r f r a c -t i o n o f mois-ture i s sorbed i n o r o u -t o f -t h e samples along X and Y axes. A-t the c r i t i c a l l e n g t h å, t h e value on t h e curve E i s equal t o :
E = E x E y E 2
= (E"^)^
(13)f i g u r e 2.
E x t r a p o l a t i o n curve o f E versus 1/a o f three-dimensio-n a l method.
S can be e v a l u a t e d by t h e above r e l a t i o n . The sample d i f f u s i v i t y i n the X
and Y d i r e c t i o n s can then be d e r i v e d w i t h t h e r e l a t i o n :
c )
xD,
(14) Dx o r Dy i s t h e average o f d i f f u s i v i t i e s i n t a n g e n t i a l and r a d i a l d i r e c t i o n s f o r s o l i d wood. Por wood based panels i t i s t h e average o f d i f f u s i -v i t i e s along machine d i r e c t i o n and across machine d i r e c t i o n , p e r p e n d i c u l a r t o panel s u r f a c e s . The t h r e e - d i m e n s i o n a l s o r p t i o n method was described and u t i l i s e d by Choong (1962). As no s e a l i n g i s necessary and s o r p t i o n takes l e s s t i m e , t h i s method i s b e l i e v e d t o be s i m p l e r t o handle and t i m e
-saving. But meanwhile, more samples a r e needed and t h e c a l c u l a t i o n i s more complex.
3. EXPERIMENTAL
The experiments a r e done w i t h both one-dimensional and three-dimensional s o r p t i o n . D i f f u s i v i t y i n a l l t h r e e p r i n c i p a l d i r e c t i o n s f o r e i g h t k i n d s o f panel m a t e r i a l s and one s o l i d wood, Swedish spruce, were measured.
3.1 Choice o f sample m a t e r i a l s I n order t o study t y , nine m a t e r i a l s f i b e r b o a r d s , t h r e e s o l i d wood, spruce d u c t s and wood. Th process) were a l s o three-dimensional t e s t e d m a t e r i a l s ,
the e f f e c t o f t h e composition and s t r u c t u r e on d i f f u s i v i -were t e s t e d w i t h t h e s o r p t i o n method: Pour k i n d s o f k i n d s o f p a r t i c l e b o a r d s , one k i n d each o f plywood and
The use o f s o l i d spruce i s f o r comparison o f panel p r o -ree k i n d s o f s p e c i a l samples made o f h a l f - h a r d board (wet
used t o i n v e s t i g a t e some f a c t o r s . The samples o f t h e s o r p t i o n method were made o n l y o f h a l f - h a r d board. The t h e i r d e n s i t y and sample s i z e s a r e l i s t e d i n Table 1 .
12
TABLE 1 . Tested m a t e r i a l s , d e n s i t y and sampl e s i z e s .
M a t e r i a l Density (kg/m^) Sample s i z e (mm)
( a b s o l u t e l y d r y ) Length Width Thickness ONE-DIMENSIONAL SORPTION FIBERBOARD 1. H a l f - h a r d board 690 120 100 12.1 (wet process) 2. I n s u l a t i o n board 210 I I M 12.9 3. MDF ( d r y process) 710 I I I I 9.8 4. Hard board 870 I I I I 6.2 PARTICLEBOARD 5. PF-glue p a r t i c l e b o a r d 670 I I I I 11.9 6. UF-glue " 610 I I I I 12.4 7. UMF-glue " 650 I I I I 12.1 PLYWOOD 8. PF-glue plywood 420 I I I I 12.0 SOLID WOOD 9. Spruce 420 100 82 6.9 SPECIAL 10. H a l f - h a r d board 700 120 100 8.2 ( s u r f a c e s m i l l e d ) 11. H a l f - h a r d board 690 I I I I 12.1 ( a b s o l u t e l y d r i e d ) 12. H a l f - h a r d board I I 60 I I 12.1 ( s m a l l l e n g t h ) THREE-DIMENSIONAL SORPTION A l l h a l f - h a r d board (wet process) 13. 690 240 240 12.1 14. I I 120 120 I I 15. I I 80 80 I I 16. I I 60 60 I I 17. I I 48 48 I I Notes:
1. M a t e r i a l s No.10, 1 1 , 12 a r e made, from t h e same boards as m a t e r i a l No.l. M a t e r i a l No.10 i s prepared by m i l l i n g o f f t h e s u r f a c e s o f t h e board by 2 mm on both s i d e s . The aim i s t o see the e f f e c t o f the densi-f i e d s u r densi-f a c e l a y e r s o densi-f wood-based panels on t h e i r d i densi-f densi-f u s i v i t y .
2. M a t e r i a l No.11 i s d r i e d a t 103'C t o zero m o i s t u r e c o n t e n t b e f o r e t h e s o r p t i o n t e s t t o i n v e s t i g a t e t h e i n f l u e n c e o f p r e v i o u s d r y i n g on d i f f u s i v i t y .
3. M a t e r i a l No. 12 i s e x a c t l y i d e n t i c a l t o No.l except f o r i t s smaller l e n g t h , along which s o r p t i o n would take place. The aim i s t o see t h e e f f e c t o f e x t e r n a l r e s i s t e n c e o f s o r p t i o n on measured d i f f u s i v i t y . 4. UF, PF, and UMF a r e a b b r e v i a t i o n s o f glues: phenol-formaldehyde,
13 3.2 Choice o f s e a l a n t
To choose an e f f e c t i v e water v a p o r - t i g h t s e a l a n t f o r t h e specimens i n one-d i m e n s i o n a l s o r p t i o n , f i v e types o f s e a l i n g m a t e r i a l s were t e s t e one-d : ( 1 ) Epoxy r e s i n g l u e , ( 2 ) s i l i c o n e r e s i n g l u e , ( 3 ) neoprene g l u e , ( 4 ) a waterbased wood lacquer w i t h t h e trademark "Trälack" and ( 5 ) a v e g e t a b l e o i l -based glue w i t h t h e trademark "Tremco Utefog".
Each of t h e t e s t e d s e a l a n t s was spread on a l l t h e s u r f a c e s o f two hardboard samples which p r e v i o u s l y had been d r i e d t o zero m o i s t u r e c o n t e n t . When they had hardened or d r i e d , t h e sealed samples were s e t i n a c l i m a t e chamber w i t h a r e l a t i v e h u m i d i t y o f RH=0.80 and a temperature o f T=40'C, a r a t h e r severe c l i m a t e c o n d i t i o n , and weighed t w i c e a day. The weights o f a l l samples increased c o n s i d e r a b l y w i t h t i m e , so none o f these are good vapor-t i g h vapor-t s e a l a n vapor-t s . S e a l i n g w i vapor-t h vapor-two, vapor-t h r e e and f o u r l a y e r s o f neoprene, epoxy and s i l i c o n e g l u e s , each spread over t h e o t h e r , was t h e r e a f t e r t e s t e d but d i d not p r o v i d e much improvement.
Among t h e samples t e s t e d w i t h one l a y e r o f s e a l a n t , those sealed w i t h epoxy r e s i n and neoprene glues showed much l e s s weight i n c r e a s e than t h e o t h e r s . Then t h e combinations o f these two glues w i t h aluminium f o i l were t e s t e d . Two d r i e d hard board samples each were sealed w i t h aluminium f o i l adhered to t h e samples w i t h epoxy r e s i n or neoprene g l u e and t e s t e d i n t h e same c l i m a t e as above. These proved t o be remarkable v a p o r - t i g h t s e a l a n t s . I n f i v e days t h e average weight o f t h e samples sealed w i t h neoprene glue and aluminium f o i l changed j u s t from 36.82 g t o 36.80 g, i . e . l e s s than
0.06 %. The o t h e r two samples sealed w i t h epoxy r e s i n and aluminium f o i l i n c r e a s e d from 36.83 g t o 36.89 g, l e s s than 0.2 %. I n another t e s t , f o u r samples o v e n d r i e d t o zero % m o i s t u r e c o n t e n t were s c a l e d w i t h neoprene glue and aluminium f o i l and then put i n t o a c l i m a t e w i t h a RH o f 0.90 at 20°C f o r one month. The weight changes were l e s s than 0.4%. The changes are so s m a l l compared w i t h t h e weight i n c r e a s e o f t h e same samples unsealed t h a t i t i s n e g l i g b l e .
The s e a l a n t o f aluminium f o i l w i t h neoprene g l u e was chosen f o r t h e main experiments. Neoprene g l u e i s much t h i c k e r and does n o t seep i n t o t h e spe-cimens so much, a great advantage over epoxy r e s i n . Besides, i t does not harden so q u i c k l y when exposed t o a i r , t h i s g i v e s g r e a t convenience when many specimens need t o be s e a l e d .
3.3 D e t e r m i n a t i o n o f some a f f e c t i n g f a c t o r s
Some u n c e r t a i n f a c t o r s t h a t might i n f l u e n c e t h e e x p e r i m e n t a l r e s u l t s were i n v e s t i g a t e d b e f o r e t h e main experiments.
3.3.1 Temperature change o f samples i n s o r p t i o n
When water vapor i s adsorbed i n t o wood m a t e r i a l , s o r p t i o n energy, i n t h e form of s o r p t i o n heat, w i l l be r e l e a s e d which might i n c r e a s e t h e tempera-t u r e o f tempera-t h e samples and a l tempera-t e r tempera-t h e measured d i f f u s i v i tempera-t y , as tempera-t h e d i f f u s i v i tempera-t y of wood m a t e r i a l i s known t o be r a t h e r s t r o n g l y a f f e c t e d by temperature. On the o t h e r hand, the s o r p t i o n r a t e o f t h e wood m a t e r i a l a t room temperature or outdoor c o n d i t i o n s i s very s m a l l and t h e a i r c i r c u l a t i o n i n t h e s o r p t i o n
14
t e s t s t r o n g , so t h e temperature change would most p r o b a b l y never be l a r g e enough t o be i n f l u e n c i a l . To c l a r i f y t h i s problem, two samples, one h a l f -hard board and one -hardboard were d r i e d t o zero m o i s t u r e content before t e s t , which would p r o v i d e a r e l a t i v e l y l a r g e s o r p t i o n amount. A thermo-couple was f a s t e n e d w i t h a s m a l l g l u e tape t o t h e s u r f a c e o f t h e f i r s t sample, and an i d e n t i c a l thermocouple was a t t a c h e d w i t h two s t a p l e s t o t h e second sample. The samples were then put i n t o a c l i m a t e chamber w i t h the c l i m a t e o f RH=0.60 and T=20°C. Two o t h e r i d e n t i c a l thermocouples were hung i n t h e c l i m a t e chamber t o measure t h e a i r temperature as a r e f e r e n c e . The temperature was recorded c o n t i n u o u s l y . The s e n s i t i v i t y o f t h i s measurement system i s 0.5°C.
I n t h e days t h a t f o l l o w e d , n o t any s l i g h t e s t temperature d i f f e r e n c e was ob-served. So i t i s c l e a r t h a t t h e s m a l l amount o f s o r p t i o n heat r e l e a s e d does not b r i n g about an observable temperature change t o t h e samples i n the
s o r p t i o n method. Released s o r p t i o n heat i s thus a n e g l i g i b l e f a c t o r i n t h e s o r p t i o n and t h e t h r e e - d i m e n s i o n a l s o r p t i o n methods, a t l e a s t a t moderate r e l a t i v e h u m i d i t i e s and room temperature.
3.3.2 D i v e r s i t y o f t e s t r e s u l t s
I n order t o decide t h e proper number o f samples i n t h e s o r p t i o n method t o make t h e measured d i f f u s i v i t y r e p r e s e n t a t i v e o f a m a t e r i a l , an i n v e s t i g a -t i o n on -t h e d i v e r s i -t y o f -t e s -t r e s u l -t s was made b e f o r e -t h e main experimen-t. H a l f - h a r d board (wet process) was chosen f o r t h i s aim once more because o f i t s r e l a t i v e l y homogeneous s t r u c t u r e . Twenty-eight samples were sealed w i t h aluminium f o i l and neoprene glue i n such a way t h a t s o r p t i o n c o u l d take place o n l y i n t h e d i r e c t i o n p e r p e n d i c u l a r t o panel s u r f a c e s . Ten samples each were sealed f o r s o r p t i o n i n t h e two d i r e c t i o n s p a r a l l e l t o panel sur-f a c e , along machine d i r e c t i o n and t r a n s v e r s e machine d i r e c t i o n . A l l t h e samples were d r i e d t o zero moisture content a t 103°C before s e a l i n g , and a f t e r s e a l i n g once again. They were then cooled down i n a d e s i c c a t o r t o room temperature and s e t i n t o a c l i m a t e chamber w i t h RH=0.60, T=20°C. The purpose o f d r y i n g t h e samples was t o c r e a t e a l a r g e m o i s t u r e s o r p t i o n r a t e i n order t o i n t e n s i f y t h e d i v e r s i t y o f t h e measured d i f f u s i v i t y .
The t e s t r e s u l t s showed t h a t the v a r i a t i o n c o e f f i c i e n t s o f the measured d i f f u s i v i t i e s were 4.5 Ä, 5.2 % and 5.7 % f o r p e r p e n d i c u l a r t o panel surf a c e , p a r a l l e l t o panel s u r surf a c e i n machine d i r e c t i o n and across machine d i -r e c t i o n , -r e s p e c t i v e l y . They we-re thus l e s s than 6 %, So i t i s c e -r t a i n t h a t the t e s t r e s u l t s o f wood p r o d u c t s w i t h t h e s o r p t i o n method i s r e l a t i v e l y homogenous and t h e d i v e r s i t y low. Based on t h i s we used f i v e samples f o r each type o f m a t e r i a l i n the main experiments.
3.4 P r e p a r a t i o n o f samples
Three k i n d s o f samples were prepared f o r each m a t e r i a l t o determine t h e i r d i f f u s i v i t y i n t h e t h r e e p r i n c i p a l d i r e c t i o n s . For every d i r e c t i o n f i v e samples were made. The l e n g t h s and w i d t h s o f a l l samples were sawn t o t h e s i z e s as l i s t e d i n Table 1 . Among them t h e h a l f - h a r d board samples were prepared i n such a way t h a t t h e sample l e n g t h s are i n t h e machine d i r e c t i o n and the w i d t h s i n t h e t r a n s v e r s e machine d i r e c t i o n . For t h e r e s t o f t h e pa-n e l m a t e r i a l s we d i d pa-n o t kpa-now t h e machipa-ne d i r e c t i o pa-n . But a l l samples were
15 taken from one l a r g e board so t h e sample l e n g t h s were a l l i n one d i r e c t i o n - e i t h e r along machine o r t r a n s v e r s e t h e machine d i r e c t i o n . The t h i c k n e s s of t h e panel samples was t h e o r i g i n a l t h i c k n e s s o f t h e m a t e r i a l s . The t h i n spruce wood samples were made from t h e same board o f spruce.
The samples o f t h e t h r e e - d i m e n s i o n a l s o r p t i o n method were prepared w i t h h a l f - h a r d board. The samples were i n f i v e s i z e s , as has been shown i n Table 1 . For each s i z e t h e r e a r e f i v e samples, t h e r e c i p r o c a l s o f t h e i r l e n g t h s were i n p r o p o r t i o n o f ;
1/240 : 1/120 : 1/80 : 1/60 : 1/48 = 1 : 2 : 3 : 4 : 5 This gave some convenience i n t h e d e t e r m i n a t i o n o f d i f f u s i v i t y .
A l l t h e samples were s e t i n a c l i m a t e o f RH=0.65, T=20°C i n a c l i m a t e room u n t i l they reached m o i s t u r e e q u i l i b r i u m . They were weighed t o t h e p r e c i s i o n of 0.01 g. Then they were a l l sealed c a r e f u l l y w i t h aluminium f o i l and neoprene glue on t h e predetermined s u r f a c e s , except f o r t h e samples o f t h r e e -dimensional s o r p t i o n , and s e t t o t h e same c l i m a t e u n t i l e q u i l i b r i u m was reached again. The samples were weighted once more, t h e weight o f t h e s e a l i n g s was equal t o t h e d i f f e r e n c e o f two weight measurements.
3.5 S o r p t i o n a l procedure
The d i f f u s i v i t y measurement w i t h t h e s o r p t i o n method i n t h e d i r e c t i o n per-p e n d i c u l a r t o t h e per-panel s u r f a c e and w i t h t h e t h r e e - d i m e n s i o n a l s o r per-p t i o n method was done i n a c l i m a t e chamber i n t h e l a b o r a t o r y o f t h e Wood
Technology Department. For these samples two c y c l e s o f measurements a t two c l i -mates were made:
(1) from RH=0.65 t o RH=0.80 T=20°C i n both c l i m a t e s (2) from RH=0.65 t o RH=0.30
As mentioned p r e v i o u s l y , t h e samples were c o n d i t i o n e d a t RH=0.65, T=20°C b e f o r e t h e s o r p t i o n experiment u n t i l t h e i r weights d i d n o t change w i t h time and m o i s t u r e e q u i l i b r i u m was reached. The samples were then p u t i n t h e c l i -mate chamber, which was s e t t o one o f t h e two f i n a l c l i m a t e s , each time t e r m i n a t e d o n l y when t h e weight change o f a l l samples was no longer ob-s e r v a b l e and e q u i l i b r a were aob-sob-sumed t o be reached. I n each c y c l e , t h e samples were p e r i o d i c a l l y taken o u t , weighed q u i c k l y and p u t back i n t o t h e chamber. The i n t e r v a l o f t h e measurement time was n o t r e g u l a r , i t was
s h o r t e r i n t h e f i r s t days as then t h e s o r p t i o n r a t e was l a r g e r . High a i r c i r c u l a t i o n (more than 3 m/s) was maintained i n t h e chamber by a f a n , and the f a n was t u r n e d o f f d u r i n g opening and weighing time t o reduce c l i m a t e changes.
The balance used has a p r e c i s i o n o f 0.01 g. The d u r a t i o n o f t h e weighing o p e r a t i o n was about 15 minutes, when a l l t h e samples were taken o u t o f t h e chamber and exposed t o t h e o u t s i d e a i r . This p e r i o d i c a l i n t e r r u p t i o n o f the s o r p t i o n process and exposure t o t h e room c l i m a t e i n e v i t a b l y caused some e r r o r .
Some t e s t s i n t h e same c l i m a t e chamber were a l s o made i n c l i m a t e s o f higher r e l a t i v e h u m i d i t y (RH=0.90), b u t i n t h e l a t e r stages o f s o r p t i o n t h e sample
16
w e i g h t s f l u c t u a t e d i n s t e a d o f changing monotonously which gave an im-p r e s s i o n t h a t e q u i l i b r i a were reached, so t h e t e s t s were ceased i n such a stage. I n l a t e r a n a l y s i s i t was found t h a t e q u i l i b r i a were a c t u a l l y not reached. This mistake was caused p a r t i a l l y by t h e g r e a t d i f f e r e n c e o f r e l a -t i v e h u m i d i -t y i n s i d e and o u -t s i d e -t h e c l i m a -t e chamber d u r i n g w i n -t e r -time when t h e r e l a t i v e h u m i d i t y i n t h e l a b o r a t o r y was r a t h e r low; p a r t i a l l y by l a c k o f experience o f such experiment. These t e s t r e s u l t s were d i s c a r t e d , but we learned something from t h e f a i l u r e .
D i f f u s i v i t y measurement o f t h e s o r p t i o n method i n t h e p a r a l l e l t o surface d i r e c t i o n was c a r r i e d o u t i n a c l i m a t e room i n t h e Swedish I n s t i t u t e f o r Wood Technology Research. Only one c y c l e w i t h RH from 0.65 t o 0.90, T=20'C was used. O r i g i n a l l y two c l i m a t e s had been planned (RH from 0.65 t o 0.90 and from 0.90 t o 0.65) b u t t o reach e q u i l i b r i u m i n t h e f i r s t r u n took an unexpected long t i m e , owing"to t h e t o o l a r g e l e n g t h and w i d t h o f t h e samples, so t h e second c y c l e was c a n c e l l e d . Smaller s i z e s should be used i n f u t u r e study. The measurements were made i n a s i m i l a r way as those per-formed i n t h e c l i m a t e chamber. The o n l y two d i f f e r e n c e s were t h a t t h e samples were weighed i n s i d e the c l i m a t e room, so the s o r p t i o n process was not d i s t u r b e d d u r i n g t h e measurements, and t h e r e s u l t s should t h e r e f o r e be
b e t t e r . The a i r c i r c u l a t i o n v e l o c i t y was s m a l l e r , approximately 1.4 m/s, which would presumably render a l a r g e r r e s i s t a n c e o f t h e boundary a i r
17 4. EXPERIMENTAL RESULTS
For t h e s o r p t i o n method, t h e f r a c t i o n a l moisture c o n t e n t versus time and m o i s t u r e c o n t e n t versus square r o o t o f time i n a s o r p t i o n c y c l e were c a l c u
-l a t e d and p -l o t t e d , two examp-les o f which a r e shown i n F i g u r e 3 and
F i g u r e 4. Average d i f f u s i v i t y o f t h e t e s t e d m a t e r i a l s i n each o f the t h r e e s o r p t i o n processes was c a l c u l a t e d w i t h E q ( 6 ) , by t h e ( t ) l / 2 values obtained from the s o r p t i o n curves. D i f f u s i v i t y was a l s o c a l c u l a t e d w i t h Eq(7) f o r comparison. Both s e t s o f data a r e l i s t e d i n Table 2, where the d i f f u s i v i t y o b t a i n e d w i t h Eq(7) are placed i n b r a c k e t s .
With the method o f t h e t h r e e d i m e n s i o n a l s o r p t i o n the samples reached e q u i -l i b r i a much f a s t e r than t h e samp-les o f the s o r p t i o n method. A t each mea-surement t i m e , a r e g r e s s i o n a l l i n e a r e q u a t i o n was d e r i v e d w i t h f a i r l y l a r g e c o r r e l a t i o n c o e f f i c i e n t s ( l a r g e r than 0.94) from t h e data o f dimensionless moisture c o n t e n t E and the r e c i p r o c a l o f sample l e n g t h s ( f i v e s i z e s ) . I n F i g u r e 3A, t h e f i r s t f i v e r e g r e s s i o n a l l i n e s f o r t h e t h r e e - d i m e n s i o n a l s o r p t i o n i n the c l i m a t e o f RH from 0.65 t o 0.80 a r e p l o t t e d . The i n t e r c e p t s of t h e l i n e s a r e t h e dimensionless moisture c o n t e n t E-max o f i n f i n i t e l y long samples, which was r e a d i l y o b t a i n a b l e from the r e g r e s s i o n a l equa-t i o n s . The slopes o f equa-t h e l i n e a r equaequa-tions i n F i g u r e 5A are n o equa-t equal. For an imaginary l i n e w i t h an i n t e r c e p t o f E=0.5, t h e slope was c a l c u l a t e d from the slopes o f two nearest l i n e s by t a k i n g weighted averages. Then the c r i -t i c a l l e n g -t h o f -the imaginary l i n e was c a l c u l a -t e d and -the d i f f u s i v i -t y i n the d i r e c t i o n p a r a l l e l t o the panel s u r f a c e s was o b t a i n e d w i t h Eq(14). The d i f f u s i v i t y measured w i t h the t h r e e - d i m e n s i o n a l s o r p t i o n was a l s o l i s t e d i n Table 2.
In F i g u r e 3B two (l-Emax)-t curves o f such i n f i n i t e l y long samples were p l o t t e d t o g e t h e r w i t h the E-t curves o f h a l f - h a r d board (wet process) t e s t e d w i t h t h e s o r p t i o n method i n the same c l i m a t e . I t can be seen t h a t the curves f i t each o t h e r almost p e r f e c t l y .
The d i f f u s i v i t y values c a l c u l a t e d w i t h Eq(6) ad (7) i n Table 2 a r e based on the m o i s t u r e c o n c e n t r a t i o n i n t h e t e s t e d m a t e r i a l s . When they are converted i n t o the d i f f u s i v i t y based on the moisture c o n c e n t r a t i o n i n the a i r by t h e r e l a t i o n :
dv
8 = D ^
(15)t h e i r order o f magnitude a r e about 10,000 times l a r g e r . Here J and D are the moisture d i f f u s i v i t y based on m o i s t u r e c o n c e n t r a t i o n i n the a i r and i n the t e s t e d m a t e r i a l s , r e s p e c t i v e l y .
The converted d i f f u s i v i t i e s a r e presented i n Table 3. As the s o r p t i o n i s o -therms o f the sample m a t e r i a l s were n o t known, t h e s o r p t i o n iso-therms o f T v e i t (1966) and Kollmann (1975) f o r the same m a t e r i a l s were used. Some e r r o r would a r i s e as these isotherms might n o t f i t the m a t e r i a l s t e s t e d en-t i r e l y , b u en-t such e r r o r would probably n o en-t be so l a r g e as en-t o a f f e c en-t en-t h e r i g h t order o f magnitude.
18
A
PF-glue particleboard
4b 80 120 léo 200 240 200 3^0 300 400 440 480 520 5é0 6Ö0 640 6é0 7^0 700 800 S o r p t i o n Time Hour RH: 0.65 -> 0.30. T - 20 •€ : 0.65 -> 0.»0. T - 20 •€B
Spruce plywood (PF-glue)
Ö 40 80 120 160 2Ö0 240 280 320 360 4Ö0 440 4Ö0 520 560 6Ö0 6^0 eéo 7é0 760 edo
S o r p t i o n Time Hour
r i g u r e 3. Curves o f t h e f r a c t i o n a l moisture o f s o r p t i o n i n r e l a t i o n t o s o r p t i o n t i m e . S o r p t i o n d i r e c t i o n : P e r p e n d i c u l a r t o panel sur-faces.
19 1 .9 i ! A a **
c
5
.7 ca o e ••i •8 .5 .4 .3 .2 .1PF-glue particleboard
I B T i 5 2 5 2 H ~ BB 4 0 ^Square Root o f S o r p t i o n Tine eqr (HOUR)
1 .9 .8 .7 .6 .5 .4 .3 .2 .1 0 F i g u r e 4. c
5
c 3 mSpruce plywood(PF"-glue)
3 iB 20 2B 15 §5 4 5 ~ ~4b Square Root o f S o r p t i o n Tine eqr (HOUR)Curves o f t h e f r a c t i o n a l m o i s t u r e o f s o r p t i o n versus t h e square r o o t o f t h e s o r p t i o n time.
20
TABLE 2. Average d i f f u s i v i t y based on m o i s t u r e c o n c e n t r a t i o n i n t h e m a t e r i a l s ( u n i t 10~iO m2/s).
Outside b r a c k e t s : c a l c u l a t e d w i t h E q ( 6 ) . I n s i d e b r a c k e t s : c a l c u l a t e d w i t h Eq(7).
S o r p t i o n d i r e c t i o n : P e r p e n d i c u 1 a r P a r a l l e l
Test c o n d i t i o n : Climate chamber Climate room Climate room
Climate: 0.65-0.80 0.65-0.30 0.65-0.90 0.65-0, .90
ONE DIMENSIONAL Width Length
SORPTION d i r e c t i o n d i r e c t i o n FIBERBOARD 1. H a l f - h a r d board 0.34 0.72 0.43 3.3 4.0 wet process (0.48) (0.64) (0.56) ( 3 . 8 ) (4.8) 2. I n s u l a t i o n board 1.60 2.70 18 20 (1.80) (2.10) (19) (23) 3. MDF ( d r y process) 0.19 0.60 3.1 3.4 (0.22) (0.56) (3.7) (4.0) 4. Hardboard 0.08 0.28 3.2 3.0 (0.11) (0.22) (4.0) (3.5) PARTICLEBOARD 5. PF-glue p a r t i c l e - 0.14 0.30 3.4 4.8 board (0.20) (0.31) (2.4) (6.3) 6. UF-glue p a r t i c l e - 0.88 1.7 3.0 3.8 board (1.00) (1.3) (3.0) (5.2) 7. UMF-glue p a r t i c l e - 1.0 board (1,2) PLYWOOD 8. PF-glue plywood 0.24 0.76 3.8 4.5 (0.40) (0.76) (4.1) (7.6) SOLID WOOD 9. Spruce 0.38 0.88 8.8 (0.52) (0.76) (10) l o n g . SPECIAL 10. H a l f - h a r d board 0.30 0.64 s u r f a c e s m i l l e d (0.40) (0.56) 11. H a l f - h a r d board 0.38 0.80 a b s o l u t e l y d r i e d (0.52) (0.64) 12. H a l f - h a r d board 2.7 s m a l l l e n g t h (2.9) THREE DIMENSIONAL SORPTION H a l f - h a r d board 0.34 0.76 (0.48) (0.64) 1.10 (1.60) 1.6 (1.3) p a r a l l e l II Notes: 1. P a r a l l e l and p e r p e n d i c u l a r imply t h e s o r p t i o n d i r e c t i o n i n r e l a t i o n t o the panel s u r f a c e s .
2. For spruce, t h e value i n column 5 i s t h e l o n g i t u d i n a l one, a l l t h e r e s t are t r a n s v e r s e ( r a d i a l o r t a n g e n t i a l ) .
21 TABLE 3. Average d i f f u s i v i t y based on m o i s t u r e c o n c e n t r a t i o n i n the a i r
( u n i t 10-6 m2/s).
S o r p t i o n d i r e c t i o n : P e r p e n d i c u 1 a r P a r a l l e l
Test c o n d i t i o n : Climate chamber Climate room Climate room
C l i m a t e : 0.65-0.80 0.65-0.30 0.65-0.90 0.65-0, .90
ONE DIMENSIONAL Width Length
SORPTION d i r e c t i o n d i r e c t i o n FIBERBOARD 1. H a l f - h a r d board 0.21 0.29 0.38 1.7 2.2 wet process (0.30) (0.25) (0.67) ( 2 . 0 ) (2.6) 2. I n s u l a t i o n board 1.0 1.4 11 14 (1.-3) (1.2) (12) (16) 3. MDF ( d r y process) 0.12 0.23 1.6 1.8 (0.14) (0.22) (1.9) (2.1) 4. Hardboard 0.10 0.21 2.8 2.6 (0.12) (0.16) (3.6) (2.9) PARTICLEBOARD 5. PF-glue p a r t i c l e - 0.16 0.22 5.2 7.7 board (0.21) (0.22) (3.9) (9.9) 6. UF-glue p a r t i c l e - 0.87 1.1 4.4 5.6 board (0.95) (0.92) (4.0) (7.2) 7. UMF-glue plywood 0.15 (7.2) (0.17) PLYWOOD 8. PF-glue plywood 0.27 0.60 4.8 5.3 (0.45) (0.60) (4.8) (8.8) SOLID WOOD 9. Spruce 0.15 0.24 l o n g . 9.2 (0.20) (0.16) l o n g . (10) l o n g . SPECIAL 10. H a l f - h a r d board 0.19 0.26 s u r f a c e s m i l l e d (0.26) (0.23) 11. H a l f - h a r d board 0.24 0.31 a b s o l u t e l y d r i e d (0.32) (0.26) 12. H a l f - h a r d board 1.4 small l e n g t h (1.5) THREE DIMENSIONAL SORPTION H a l f - h a r d board 0.21 0.29 (0.30) (0.25) 0.72 0.44 p a r a l l e l (1.0) (0.37) II Notes: Same as i n Table 2.
Each d i f f u s i v i t y value i s r e c a l c u l a t e d from the c o r r e s p o n d i n g data i n Table 2.
22
4.5 i 5.8 é
Reciproctl of half sample length
- .6
8
0.65 -> 0.«0. 0.65 -> 0.30 Tltfee Dia. Sorpcioa: Curve 1.
O m Dm. SorpciM ; CurveJ, Curve2 Curved
o 30 6b 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600
S o r p t i o n Time Hour
F i g u r e 5. Test curves o f t h e t h r e e - d i m e n s i o n a l method w i t h h a l f - h a r d f i b e r b o a r d samples.
Above; F i r s t f i v e r e g r e s s i o n a l l i n e s o f 1^ vs 1/a r e l a t i o n s i n c l i m a t e RH=0.65 t o 0.80, T=20°C.
Below: Comparison o f t h e f r a c t i o n a l m o i s t u r e o f s o r p t i o n i n ré-l a t i o n t o s o r p t i o n time o f t h e s o r p t i o n method and the t h r e e - d i m e n s i o n a l method.
23 4.1 D i f f u s i v i t y of the t e s t e d m a t e r i a l s
As f o r t h e measured d i f f u s i v i t y of the m a t e r i a l s t e s t e d , some general r e -marks are made:
For a l l t h e wood-based panels the d i f f u s i v i t y i n the p e r p e n d i c u l a r t o panel s u r f a c e d i r e c t i o n i s about 5 t o 25 times l a r g e r than t h a t i n the p a r a l l e l t o s u r f a c e d i r e c t i o n . D i f f u s i v i t y i s g e n e r a l l y l a r g e r f o r panels of low d e n s i t y .
The most apparent f e a t u r e o f f i b e r b o a r d s i s t h a t t h e i r d i f f u s i v i t y depends s t r o n g l y and c h i e f l y on t h e i r d e n s i t y . Hardboard showed an e x t r a o r d i n a r i l y low d i f f u s i v i t y i n the p e r p e n d i c u l a r t o s u r f a c e d i r e c t i o n . The reason might be t h a t when the d e n s i t y increases above a c e r t a i n l e v e l t h e r e would be almost no gaps between f i b e r s , so t h a t m o i s t u r e d i f f u s i o n has t o take place e n t i r e l y through the compressed wood c e l l s .
The t e s t e d PF-glue p a r t i c l e b o a r d showed a lower d i f f u s i v i t y even though i t s d e n s i t y i s a b i t l a r g e r than t h e UF-glue panels. This may have something t o do w i t h the f a c t t h a t PF-glue i s g e n e r a l l y more m o i s t u r e r e s i s t a n t than UF-g l u e .
The plywood used i n t h i s experiment i s made from PF-glue and spruce wood. The d e n s i t y of the t e s t e d plywood i s a b i t l a r g e r than the spruce. I t s d i f -f u s i v i t y i n the p e r p e n d i c u l a r t o s u r -f a c e d i r e c t i o n , which corresponds t o the r a d i a l d i r e c t i o n of the wood, d i f f e r s not very much from t h a t of spruce i n the t r a n s v e r s e d i r e c t i o n . This conforms t o Lehmann's reasoning (1972) t h a t glue f i l m between p l y s are not c o n t i n u o u s , and i t s c o n t r i b u t i o n i n r e -ducing the d i f f u s i v i t y i s not e s p e c i a l l y l a r g e as i t would be i f the f i l m were c o n t i n u o u s .
Spruce wood i n the t r a n s v e r s e d i r e c t i o n seems not t o p r o v i d e an a p p a r e n t l y lower d i f f u s i v i t y than wood-based panels except f o r i n s u l a t i o n board, even though i t s b i o l o g i c a l s t r u c t u r e has not been d i s o r d e d as i n panel mate-r i a l s . I n the l o n g i t u d i n a l d i mate-r e c t i o n i t s d i f f u s i v i t y i s l a mate-r g e s t , non-sumate-r- non-sur-passed by any panel except i n s u l a t i o n board.
For a l l the panel m a t e r i a l s , t h e d i f f u s i v i t y i n the two p a r a l l e l t o s u r f a c e d i r e c t i o n s showed a f a i r l y s m a l l d i f f e r e n c e ( t h e data i n the l a s t two co-lumns of Table 2 ) . An unexpected r e s u l t i s t h a t the d e n s i t y of h a l f - h a r d board w i t h i t s s u r f a c e m i l l e d ( m a t e r i a l No. 10) i s l a r g e r than t h a t o f the u n m i l l e d board ( m a t e r i a l No. 1 ) . G e n e r a l l y the d e n s i t y of panels decreases from s u r f a c e t o middle l a y e r . The u n u s u a l l y h i g h d e n s i t y of the m i l l e d pa-nel (Table 1) might e x p l a i n i t s lower d i f f u s i v i t y . The h a l f - h a r d board t h a t was d r i e d t o zero m o i s t u r e c o n t e n t (No. 11) b e f o r e the s o r p t i o n t e s t showed a d i f f u s i v i t y which d i f f e r s l i t t l e from the same board u n d r i e d ( N o . l ) . D r y i n g does t h e r e f o r e not seem t o a l t e r the d i f f u s i v i t y of the panel pro-ducts a p p a r e n t l y , p r o b a b l y because they have a l r e a d y been hot-pressed du-r i n g manufactudu-re.
The average d i f f u s i v i t y measured i n the c l i m a t e RH=0.65 t o 0.30 i s about t w i c e as l a r g e as t h a t i n the c l i m a t e RH=0.65 t o 0.80. This i s c o n t r a d i c t o -ry t o the g e n e r a l concept t h a t d i f f u s i v i t y i n t h e wood m a t e r i a l increases w i t h the m o i s t u r e c o n c e n t r a t i o n . But i t conforms w i t h the known f a c t f o r wood t h a t d i f f u s i v i t y o b t a i n e d w i t h d e s o r p t i o n i s l a r g e r than t h a t w i t h ad-s o r p t i o n . So i t might be e x p l a i n e d aad-s t h a t the l a t t e r e f f e c t dominatead-s i n t h i s case.
24
5. DISCUSSION
I t i s well-known t h a t the moisture d i f f u s i v i t y i n wood m a t e r i a l i s concent r a concent i o n d e p e n d e n concent . D l f f u s i v i concent i e s i n an a d s o r p concent i o n o r d e s o r p concent i o n process a l so appears t o be d i f f e r e n t t o some e x t e n t . These phenomena l a y some l i m i t a -t i o n s -t o our a n a l y s i s o f e x p e r i m e n -t a l r e s u l -t s as we have o n l y l i m i -t e d da-ta from the t h r e e s o r p t i o n c y c l e s a t d i f f e r e n t r e l a t i v e h u m i d i t y l e v e l s . But some u s e f u l i n f o r m a t i o n about the s o r p t i o n method i s s t i l l obtained w i t h the experiment. I t a l s o p r o v i d e d some data f o r a r e l a t i v e l y l a r g e number of t y p i c a l panel m a t e r i a l s .
5.1 A v a i l a b i l i t y o f the s o r p t i o n methods
The approximate average d i f f u s i v i t y c a l c u l a t e d w i t h Eq(6) and Eq(7) are r a t h e r s i m i l a r . As i n the a p p l i c a t i o n of these two equations, d i f f e r e n t data from the experiment were f e d , t h i s s i m i l a r r e s u l t i m p l i e s t h a t the c a l c u l a t e d d i f f u s i v i t y i s b a s i c a l l y c o r r e c t . The d i f f u s i v i t y i n Table 2 can t h e r e f o r e be accepted as the approximate average d i f f u s i v i t y w i t h the
e f f e c t o f s u r f a c e r e s i s t a n c e unseparated i n the t e s t e d c l i m a t e s . This i n t u r n proved the a v a i l a b i l i t y of Eq(6) and ( 7 ) i n the s o r p t i o n method i n g i v i n g the average d i f f u s i v i t y . From t h i s s t a r t i n g p o i n t , d i f f u -s i v i t y - c o n c e n t r a t i o n r e l a t i o n -s can be d e r i v e d when a -s e r i e -s o f -s o r p t i o n ex-periments w i t h s u c c e s s i v e l y changing c l i m a t e s i s a p p l i e d .
The t h r e e - d i m e n s i o n a l s o r p t i o n method y i e l d s the same d i f f u s i v i t y as the s o r p t i o n method. This i s remarkable s i n c e i n t h i s method a d i f f e r e n t c a l c u -l a t i o n procedure i s emp-loyed. From F i g u r e 5B we can see t h a t the E! curves o b t a i n e d w i t h these two methods n e a r l y o v e r l a p i n a l l the ranges where such curves can be drawn w i t h the t h r e e - d i m e n s i o n a l method. As E approaches 1, the r e g r e s s i o n a l l i n e a r e q u a t i o n o f the t h r e e - d i m e n s i o n a l method i s no longer o b t a i n a b l e as then the E d i f f e r e n c e between samples of d i f f e r e n t s i z e s vanishes. So the t curves (equal t o (l-Emax)-t curves) of t h i s method are not complete. But we can say t h a t the t h r e e - d i m e n s i o n a l s o r p t i o n method g i v e s the same average m o i s t u r e d i f f u s i v i t y as the one-dimensional s o r p t i o n method.
5.2 Surface r e s i s t a n c e
The s u r f a c e r e s i s t a n c e from the boundary l a y e r on the sample s u r f a c e i n the a d s o r p t i o n and d e s o r p t i o n processes may cause some e r r o r i n measured d i f f u -s i v i t y . We apply f i r -s t l y the boundary l a y e r t h e o r y and then Newman'-s equa-t i o n i n equa-t h i s case equa-t o analyse equa-the e r r o r caused by equa-the s u r f a c e r e s i s equa-t a n c e i n measured d i f f u s i v i t y .
According t o t h e o r i e s i n t h i s f i e l d s u r f a c e r e s i s t a n c e can e i t h e r be de-s c r i b e d by de-s u r f a c e t r a n de-s f e r c o e f f i c i e n t o f water vapor 8 (Minede-s and Maddox, 1985) or by s u r f a c e e m i s s i v i t y Se (Choong and Skaar, 1972; Rosen, 1979):
8 = P ( v , - V , ) = S e ( W , - W j (16) where g i s the moisture f l u x through boundary l a y e r . Vs and Ws are the s u r
-face moisture c o n c e n t r a t i o n s and Va and Wa are the moisture c o n c e n t r a t i o n i n the b u l k a i r . B and Se are r e l a t e d v i a s o r p t i o n i s o t h e r m :
25
Se =
P
V , - V (17)This r e l a t i o n enables us t o c a l c u l a t e Se from B. Then by u t i l i z i n g Newman's r e l a t i o n (Choong and Skaar, 1972), which i s o r i g i n a l l y a p p r o x i -mated from t h e a n a l y t i c a l s o l u t i o n o f t h e d i f f u s i o n equation f o r constant d i f f u s i v i t y under t h e c o n d i t i o n o f given s u r f a c e r e s i s t a n c e :
± _ 1 ^'^
D S , a (18)
i t w i l l be p o s s i b l e t o c a l c u l a t e d i s s u s i v i t y D from The measured apparent d i f f u s i v i t y D*. According t o t h e boundary l a y e r t h e o r y , t h e s u r f a c e c o e f f i -c i e n t o f water vapor t r a n s f e r B i n laminar f l o w regime i s equal (Hines and Maddox, 1985, p. 185) t o :
8. ,
. yp= 0.664
(19)where a i s water vapor d i f f u s i v i t y i n b u l k a i r . L f i s t h e sample l e n g t h along a i r f l o w d i r e c t i o n and k i n e m a t i c v i s c o s i t y o f t h e a i r . U i s t h e a i r v e l o c i t y . boundary layer
/Cux
W « . V a W0. Vfl F i g u r e 6. Boundary l a y e r on t h e sur-face o f t h e sample and t h e d i f f e r e n c e o f moisture c o n c e n t r a t i o n between t h etwo s i d e s o f t h e l a y e r .
I t should p r o b a b l y be s t r e s s e d t h a t t h e above e q u a t i o n i s v a l i d o n l y f o r laminar f l o w o f t h e a i r over t h e sample s u r f a c e . I t has been shown ( L i u Tong, 1988) t h a t f o r t h e samples o f t h e s o r p t i o n method, t h e a i r f l o w over them a r e always l a m i n a r .
Here we take spruce as an example t o e v a l u a t e t h e s u r f a c e r e s i s t a n c e and i t s e f f e c t on t h e measured d i f f u s i v i t y w i t h t h e above equations.
The sample l e n g t h i n a i r f l o w d i r e c t i o n i s 100 mm, a i r v e l o c i t y i s
1.4 m/s. Apply Simpson's (1971) s o r p t i o n i s o t h e r m t o c a l c u l a t e t h e q u a n t i t y dVs/dWs i n Eq(17). The c a l c u l a t i o n procedure (from l e f t t o r i g h t ) and r e -s u l t -s a r e given a-s f o l l o w -s .
RH o f a i r i n 6 dVs/dWs Se D* D
s o r p t i o n (10-2 X m/s) ( x l O - * ) (10-6 m/s) (10-10 m2/s) (10-10 m2/s)
0.80 1.35 1.30 1.76 0.380 0.386
26
From the c a l c u l a t i o n s above we can see t h a t the d i f f e r e n c e of the apparent d i f f u s i v i t i e s D* which c o n t a i n the e f f e c t o f s u r f a c e r e s i s t a n c e and the d i f f u s i v i t i e s D are very s m a l l . I f the boundary l a y e r t h e o r y i s c o r r e c t i n t h i s case, then t h i s can be i n t e r p r e t e d as t h a t the s u r f a c e r e s i s t a n c e i s so small compared w i t h the i n t e r n a l d i f f u s i o n a l r e s i s t a n c e i n the s o r p t i o n process t h a t i t i s p r a c t i c a l l y n e g l i g i b l e , as long as s u f f i c i e n t a i r c i r c u -l a t i o n i s m a i n t a i n e d .
However, i n a r e c e n t l y p u b l i s h e d paper ( A v r a m i d i s and Siau, 1987) e n t i r e l y d i f f e r e n t c o n c l u s i o n s were gained w i t h respect t o s u r f a c e r e s i s t a n c e under e x p e r i m e n t a l c o n d i t i o n s s i m i l a r t o the ones i n t h i s pre-study. Avramidis and Siau found t h a t the average d i f f u s i v i t y measured w i t h s o r p t i o n method increases when sample t h i c k n e s s o f the same m a t e r i a l increases. For example f o r Western w h i t e p i n e they measured r a d i a l d i f f u s i v i t i e s o f 0.352 x lO'J-O, 0.407 X 10-10 and 0.609 x 10-^0 „hen sample t h i c k n e s s e s are 5, 10 and 20 mm, r e s p e c t i v e l y , a t 0.063 moisture c o n t e n t and 30 'C under the a i r ve-l o c i t y of 2.5 m/s. F o ve-l ve-l o w i n g the arguments o f Choong and Skaar (1972), they regarded t h i s d i f f e r e n c e as being p u r e l y caused by s u r f a c e r e s i s t a n c e and reasoned t h a t the t h i c k e r samples must have been a f f e c t e d l e s s by the s u r -face r e s i s t a n c e than the t h i n n e r ones which made the t h i c k e r samples have l a r g e r apparent d i f f u s i v i t y . They regarded t h a t by using Newman's equation a l o n e , i t would be p o s s i b l e t o c a l c u l a t e the t r u e d i f f u s i v i t y from the apparent d i f f u s i v i t y o f s e v e r a l samples having d i f f e r e n t t h i c k n e s s . Guided by such argument, they c a l c u l a t e d the t r u e d i f f u s i v i t y of
0.927 X lO'lO fT)2/8 from the above quoted apparent d i f f u s i v i t y of Western
w h i t e p i n e and concluded t h a t the s u r f a c e r e s i s t a n c e s i s not n e g l i g a b l e but very i n f l u e n t i a l .
Here we are c o n f r o n t e d w i t h a troublesome problem: i s s u r f a c e r e s i s t a n c e i n f l u e n t i a l or n e g l i g i b l e i n the s o r p t i o n method? Should we accept the r e -s u l t -s of boundary l a y e r t h e o r y or Newman'-s equation? Thi-s complicated problem cannot be solved d e f i n i t i v e l y here because i t i s impossible t o do w i t h o u t some profound i n v e s t i g a t i o n . But i t i s f e l t u s e f u l t o make some reasoning i n order t o s e t some l i g h t on the p r e s e n t l y u n s o l v a b l e problem. I n the boundary l a y e r t h e o r y , the modern mass t r a n s f e r t h e o r y i s a p p l i e d t o c a l c u l a t e the r e s i s t a n c e of vapor movement through the f l o w i n g a i r l a y e r a d j a c e n t t o the sample s u r f a c e . No c o n s i d e r a t i o n i s taken t o the t r a n s i e n t m o i s t u r e d i f f u s i o n i n s i d e the sample i t s e l f . When Newman's equation i s used i n the way as Avramidis and Siau (1987), the s u r f a c e r e s i s t a n c e i s not con-s i d e r e d d i r e c t l y from the boundary a i r l a y e r , but i n d i r e c t l y from the d i f f u s i v i t y change of the sample. However, i t i s commonly known t h a t the appearance and v a r i a t i o n of moisture g r a d i e n t i n a sample i n e v i t a b l y cause s t r e s s e s . As s t r e s s e s a l t e r the molecular c o n f i g u a r a t i o n of sample mate-r i a l , they w i l l a l s o i n f l u e n c e the d i f f u s i o n . So i n a t mate-r a n s i e n t d i f f u s i o n process, d i f f u s i o n and s t r e s s v a r i a t i o n s are coupled, some k i n d of i n t e r -a c t i o n must e x i s t between them which m-akes the d i f f u s i v i t y d i f f e r t o some e x t e n t from a pure d i f f u s i o n case. This i s known as the e f f e c t of s t r e s s r e l a x a t i o n on d i f f u s i v i t y (Crank, 1953, Comstock, 1962). This e f f e c t w i l l be discussed more i n next s e c t i o n . The drawback i n a p p l y i n g Newman's equat i o n alone equat o c a l c u l a equat e s u r f a c e r e s i s equat a n c e i s equat h a equat equathe e f f e c equat of s equat r e s s r e -l a x a t i o n o f d i f f u s i o n i s m i s t a k i n g -l y a t t r i b u t e d t o s u r f a c e r e s i s t a n c e t h a t has n o t h i n g t o do w i t h the sample i t s e l f , which may produce c o n s i d e r a b l e e r r o r . Therefore the c o r r e c t n e s s of d i r e c t l y u t i l i z i n g Newman's equation t o c a l c u l a t e s u r f a c e r e s i s t a n c e i s very much q u e s t i o n a b l e , and so are the r e -s u l t -s of Avramidi-s' and Siau'-s paper.
