Moisture transport in wood and wood-based panels a literature survey

Liu Tong

Moisture Transport in Wood

and Wood-based Panels —

A Literature Survey

Trätekn i kCentru m

MOISTURf TRANSPORT I N WOOD AND WOOD-BASED PANELS A l i t e r a t u r e survey TräteknikCentrum, Rapport P 8609056 Key words; diffusion free water moisture measurement moisture movement permeabi tity sorption Shockholm, November 1986

3.1.4 Bound water 3.1.3 Moment method

3.2 P e r m e a b i l i t y measurements 3.2.1 Water and non-polar l i q u i d s 5.2.2 Gases

0. SUMMARY 3 0. 1 Swedish summary - svensk sammanfattning 4

1. INTRODUCTION 3 1.1 Nomenclature 6 1.2 U n i t s 6 2. THEORETICAL BACKGROUND 7 2.1 D i f f u s i o n 8 2.1.1 Approach v/ith s o r p t i o n 9 2.1.1.1 A d s o r p t i o n and d e s o r p t i o n 9 2.1.1.2 E x t e r n a l r e s i s t a n c e i n s o r p t i o n 13 2.1.2 S t e a d y - s t a t e and dynamic d i f f u s i o n 14

2.1.3 Bound water and water vapor 15 2.1.4 Gas and vapor d i f f u s i o n 17 2.1.3 Non-isothermal m o i s t u r e d i f f u s i o n 18

2.1.6 S u c t i o n and p e n e t r a t i o n 21

2.2 P e r m e a b i l i t y 23 2.2.1 The expansion and s l i p flow o f gases 23

2.2.2 The i n f l u e n c e o f k i n e t i c energy and end e f f e c t s 24

2.2.3 S e r i e s c a p i l l a r y s t r u c t u r e i n wood 23

2.2.4 A c t i o n s o f f l u i d s on wood 23 2.3 A mathematical model as an example 26

3. MEASUREMENT TECHNIQUES 28 3.1 D i f f u s i v i t y measurements 28 3.1.1 Cup method 28 3.1.2 S o r p t i o n 28 3.1.3 Non-polar gases 29 30 30 3.1.6 Non-isothermal t r a n s p o r t 32 32 33 3.2.3 R e l a t i v e p e r m e a b i l i t y 33 3.2.4 Osmotic method 34 3.2.3 S u c t i o n and p e n e t r a t i o n 34 3.2.6 Pseudo-steady s t a t e method 35 3.2.7 Dynamic method 35 3.2.8 Computed tomography 36 3.3 Summary on measurement t e c h n i q u e s 36

4. INFLUENCING FACTORS 40

4.1 Density and species 40

4.2 Grain d i r e c t i o n 41 4.3 Temperature 41 4.4 Moisture content 42 4.5 Steaming 44 4.6 Freezing 45 4.7 M i c r o b i o l o g i c a l degradation 46 4.8 D r y i n g 46 4.9 Stress 47 4.10 Specimen t h i c k n e s s 48

5. PERMEABILITY AND DIFFUSIVITY OF WOOD BASED PANELS 50

5.1 Fundamental a n a l y s i s 50

5.2 Lehmann's work on p a r t i c l e b o a r d s and f i b e r b o a r d s 51

5.3 S c h u l t z ' and K e l l y ' s work on plywood 54

5.4 B r i s t o w ' s work on f i b e r b o a r d 56

5.5 D i f f u s i v i t y o f polymer composites 57

5.6 Comments on wood based panels 59

6. DATA ON DIFFUSIVITY AND PERMEABILITY 61

7. CONCLUSIONS 65

8. PROPOSAL FOR RESEARCH WORK ON WOOD-BASED PANELS 67

9. LITERATURE 69

This r e p o r t r e f e r s t o research grant 840970-6 from Swedish Council f o r B u i l d i n g Research t o Swedish I n s t i t u t e f o r Wood Technology Research.

Wood and wood-based panel.s f f iberhoardMi, port io loboards, plywoods) are hygroscopic m a t e r i a l s w i t h .1 complin-jtHd inner ' i t r u c t u r e . Their moi3ture content e x i s t s and moist m -^ transpuit. . ) i 1 m i i i three phases: as hound water, as vapor and as f r o e water. I h i s l i t e r a t u r e survey intends t o pay a t t e n t i o n mainly t o wood based ptrnt'ls, but dHMl-i a l s o w i t h the l i t e r a t u r - e on t l i e o r i e s and devices f o r irieas-ii i m j muisturb t i r i n s f j o r t i n wood, sinct? m o i s t u r e t r a n s p o r t i n wcod-l)asj;d panols lias tiej.-n s c a r c e l y s t u d i e d and tlie l i t e r a t u r e a v a i l a b l e i s q u i t e l i m i t e d .

M o i s t u r e moves i n wood i n the funius of d i f f u s i o n and t»ull)-flow (permeabi-l i t y ) . The d i f f u s i v i t y and permea(permeabi-lu(permeabi-liLy of wot)d or wood-(permeabi-liased pane(permeabi-ls are d i f f e r e n t f o r each moisture phase which i s d r i v e n by d i f f e r e n t f o r c e s

d u r i n g m o i s t u r e t r a n s p o r t . I n measuring tlie d i f f u s i v - i t y and p e r m e a b i l i t y of a m a t e r i a l , both s t e a d y - s t a t e and dynamic methods can be a p p l i e d . E i t h e r

l i q u i d s or gases can be used as t e s t i n g media, e.g. water, non-polar gases, a i r , n i t r o g e n and ethane e t c . With every technique or device the d i f f u s i -v i t y or p e r m e a b i l i t y of one or two m o i s t u r e phases i n a m a t e r i a l can be de-r i v e d and a combified u t i l i z a t i o n of s e v e de-r a l metluids can give d i f f u s i v i t y and p e r m e a b i l i t y of a l l t h r e e moisture phases. L.g. m o i s t u r e a d s o r p t i o n or d e s o r p t i o n of specimens can be a p p l i e d to determine the d i f f u s i v i t y of com-bined bound water and water vapor movement. With the technique of l i q u i d flow or gas f l o w , p e r m e a b i l i t y can be measured. The method w i t h non p o l a r gases i s s u i t a b l e f o r measuring the d i f f u s i v i t y of vapor through a i r - f i l l e d c a p i l l a r i e s .

D i f f u s i v i t y and p e r m e a b i l i t y of wood and wood-based panels are i n f l u e n c e d by s e v e r a l f a c t o r s , u s u a l l y i n c r e a s i n g w i t h temperature, m o i s t u r e content or r e l a t i v e humudity of t h e a i r , and d e c r e a s i n g w i t h den:,ity of specimens. Presteaming, f r e e z i n g or m i c r o b i o l o g i c a l d e g r a d a t i o n of wood m a t e r i a l a l l r e s u l t i n an increased p e r m e a b i l i t y .

Each type of wood-based panel has some p e c u l i a r i t i e s . I n f i b e r b o a r d s and p a r t i c l e b o a r d s m o i s t u r e i s t r a n s p o r t e d more as water vapor through i n t e r -p a r t i c l e c a -p i l l a r i e s and less as bound water. For -plywood b o i l i n g and p e e l i n g of wood i n i t s manufacturing process s o f t e n the m a t e r i a l , but glue l i n e s which j o i n t the veneer and p a r t i a l l y f i l l the lumens of wood can lead to a s t r o n g hinderance to vapor and f r e e water movement, causing a l a r g e r p r o p o r t i o n of bound water t r a n s p o r t . The d e n s i t y , amount and type of adhesive as w e l l as a d d i t i v e s , a f t e r - t r e a t m e n t and surface c o a t i n g are the s p e c i a l f a c t o r s which i n f l u e n c e the f ) e r m a b i l i t y and d i f f u s i v i t y of wood-based panels.

The i n t e n t i o n w i t l i t i n s survey i s t o form a basis f o r f u t u r e work on de-t e r m i n i n g de-the moisde-ture de-t r a n s p o r de-t in d i f f de-t ^ r e n de-t de-types of wood-based panels. A proposal f o r rosea roll work i s t l i e r e f o r e presented.

Trä och träbaserade s k i v o r är hygroskopiska m a t e r i a l med en komplicerad i n -re s t r u k t u r . Deras fuktinnehåll f i n n s i t r e o l i k a f a s e r , som bundet v a t t e n , som vattenånga och som f r i t t v a t t e n . Denna l i t t e r a t u r s t u d i e avser främst träbaserade s k i v o r , men behandlar också massivt trä, eftersom det f i n n s få s t u d i e r om f u k t t r a n s p o r t i träbaserade s k i v o r .

Fukt vandrar i trä och träbaserade m a t e r i a l genom d i f f u s i o n och massflöde ( p e r m e a b i l i t e t ) . Denna vandring sker på o l i k a sätt i de o l i k a f u k t f a s e r n a . O l i k a provmetoder kan också användas, där vätskor e l l e r gaser används som transportmedium. Därvid kan d i f f u s i o n e l l e r p e r m e a b i l i t e t för en e l l e r f l e -r a f a s e -r bestämmas. Kombination av o l i k a mätteknike-r kan ge de t -r e fase-rnas d i f f u s i v i t e t och p e r m e a b i l i t e t som är nödvändiga för en fullständig b i l d av f uktförloppen.

F u k t t r a n s p o r t e n påverkas av f l e r a o l i k a f a k t o r e r , t ex fuktinnehåll e l l e r l u f t e n s r e l a t i v a f u k t i g h e t , temperatur, d e n s i t e t , t j o c k l e k , t o r k n i n g och n e d b r y t n i n g .

V a r j e s k i v t y p har v i s s a särdrag. I f i b e r s k i v o r ocli spånskivor sker f u k t -t r a n s p o r -t e n mer som va-t-tenånga och mindre som bunde-t v a -t -t e n . I plywood har t i l l v e r k n i n g s p r o c e s s e n mjukat upp m a t e r i a l e t hos träet, men l i m f o g a r n a agerar som späragerar för vattenånga och f r i t t v a t t e n . En s t o r d e l av f u k t t r a n s -p o r t e n i -plywood sker därför genom bundet v a t t e n . Andra f a k t o r e r är också b e t y d e l s e f u l l a för f u k t t r a n s p o r t e n i o l i k a s k i v o r , t ex l i m t y p , t i l l s a t s e r , y t b e h a n d l i n g .

S y f t e t med denna Översikt är a t t ge underlag för s t u d i e r av f u k t t r a n s p o r t i o l i k a s k i v t y p e r . F t t förslag t i l l program ges i s l u t e t av r a p p o r t e n .

The alm of t h i s survey i s fociis>^il (jn mo i r, 11 i f f ti-anspuit i n wood-based pa-n e l s , which may be a probleii. i pa-n b pa-n i h l i pa-n i ) fipjiI Lcat iopa-ns. New b u i l d i pa-n g

techniques w i t h t h i c k e r and lunrt:' t i g h t w a l l s become more dependent on a b e t t e r basic knowledge of Mu d i f f e r e n t b u i l d i n g components. I t i s espec i a l l y i m p o r t a n t t o know tlie im^'espechanisms f o r moisture t r a n s p o r t t o a v o i d l o -cal accumulation of moisture w i t h i n a b u i l d i n g c j m s t r u c t i o n (Sandberg 1973, Sherwood 1977, V e r a l l 1962, Nevander ar.d I linar^.jon 1981).

However, very few s t u d i e s are r e l a t e i J t u moisture trans|)ort i n wood-based panels. This survey w i l l t h e r e f o r e a l s o cover moisture t r a n s p o r t i n wood more g e n e r a l l y i n order t o get a background f o r f u t u r e work on wood-based panels. I t i s mainly l i m i t e d t o t h e o r i e s and methods f o r s t e a d y - s t a t e and i s o t h e r m a l t r a n s p o r t of m o i s t u r e , which i s the basis f o r p r e d i c t i n g and mo-d e l l i n g a l s o mo-dynamic ( u n s t e a mo-d y - s t a t e ) anmo-d non-isothermal moisture t r a n s p o r t behaviour t h a t occurs i n p r a c t i c e i n b u i l d i n g c o n s t r u c t i o n s . But these as-pects are not so developed y e t .

Wood-based panels have w i d e l y d i f f e r e n t p r o p e r t i e s depending on e.g. raw m a t e r i a l s , m a n u f a c t u r i n g process, a d d i t i v e s and adiiesives. The basic types are plywood, p a r t i c l e boards and f i b e r boards. P r o p e r t i e s l i k e v a r y i n g dens i t y , pore dens t r u c t u r e and dens u r f a c e q u a l i t y may probably i n f l u e n c e t h e i r a b i

-l i t y t o t r a n s p o r t m o i s t u r e . Basic handbooks (e.g. Nevander and F-lmarsson 1981) and reviews (e.g. Andersson J985) c o n t a i n l i t t l e i n f o r m a t i o n on mois-t u r e mois-t r a n s p o r mois-t i n wood and d i f f e r e n mois-t wood-based panels.

M o i s t u r e t r a n s p o r t i s u s u a l l y discussed i n terms of 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 ) and p e r m e a b i l i t y . Ihese p r o p e r t i e s have been e x t e n s i v e l y

s t u d i e d f o r wood s i n c e they i n f l u e n c e the impregnation of wood, timber d r y i n g e t c . New advances (Rosen 1985) and a textbook ( .iau 1984) are r e c e n t l y p u b l i s h e d . A l i t e r a t u r e study was a l s o made ( B e r t e l s e n 1982). A r i -gorous understanding of the f l o w p r o p e r t i e s of wood, however, has not been reached yet s i n c e wood i s a b i o l o g i c a l m a t e r i a l of v a r i a b l e s t r u c t u r e and the t r a n s p o r t mechanisms very c o m p l i c a t e d .

G e n e r a l l y i t i s recognized t h a t m o i s t u r e t r a n s p o r t through wood, which i s a hygroscopic m a t e r i a l , i n v o l v e s t h r e e mechanisms:

1) vapor movement through c e l l lumens and p i t c a v i t i e s ; 2) bound water movement through the c e l l w a l l s ;

3) f r e e water movement a l s o through c e l l lumens and p i f c a v i t i e s , but i n a l i q u i d form.

In p r e d i c t i n g o r a n a l y z i n g m o i s t u r e m i g r a t i o n through l i u i l d i n g w a l l s a knowledge of d i f f u s i v i t y and p e r m e a b i l i t y of each l a y e r (^ofistituent mater i a l s i s always e s s e n t i a l , w h i mater h can be .jeen e.g. i n n moiiel f o mater c a l c u l a -t i n g -the m o i s -t u r e -t r a n s p o r -t i n w.ills presen-ted by l»*nwalde ( 1982) and -the a r t i c l e by Q u i r o u e t t e (19H'0.

This survey reviews the theurt;! i i « I h a t - k g i oun i , ava i I - i h 1»-; iiir^asuring t e c h -niques and present knowleilge f'- r su'-'i an appr i m J i . ) ! • ^ I MI _{and v/ond-tia'5i:d}

A Specimen area p e r p e n d i c u l a r t o moisture f l o w

C Moisture c o n c e n t r a t i o n (kg moisture per m-' wet wood) D D i f f u s i v i t y

Db Bound water d i f f u s i v i t y Dv Water vapor d i f f u s i v i t y

Dt D i f f u s i v i t y i n the t r a n s v e r s e d i r e c t i o n of wood E E r a c t i o n a l moisture content change of a specimen

d u r i n g s o r p t i o n

Eh A c t i v a t i o n energy of bound water r Elux of moisture G S p e c i f i c g r a v i t y h R e l a t i v e h u m i d i t y K P e r m e a b i l i t y Ks S p e c i f i c p e r m e a b i l i t y L Specimen t h i c k n e s s i n the f l o w d i r e c t i o n

M Moisture content (kg moisture per kg dry wood) Mi I n i t i a l moisture c o n t e n t as s o r p t i o n s t a r t s Mm f i n a l moisture content as s o r p t i o n ceases Mt Moisture content at time t d u r i n g s o r p t i o n Mw Molecular weight of water

N Number of pores per u n i t area i n a specimen P Pressure AP Pressure d i f f e r e n c e P Average pressure m-^ kq/m^ m2/s m2/s m2/s m2/s J/mol kg/m2 m2/Pa s m2 m kg/kg kg/kg kg/kg kg/kg kg/mo1 Pa Pa Pa

Q Volume of f l u i d f l o w i n g through or i n t o a specimen R Gas c o n s t a n t

r Mean r a d i u s of pores i n specimen T Temperature t Time u P o r o s i t y X Distance r] V i s c o s i t y JLi Chemical p o t e n t i a l o- Surface t e n s i o n 8 Contact angle m-^ Pa mVmol. K m K s m Pa.s J/mol N/m rad

NOTE: Some nomenclature are e x p l a i n e d i n the i n t i m a t e c o n t e x t of the r e l e v a n t equations and u n l i s t e d here.

1.2 U n i t s

U n i t s i n t a b l e s and on a x i s of diagrams are i n some cases m u l t i p l i e d by a f a c t o r 10"^- This means t h a t the data i n e.g. a column of such a t a b l e s h a l l be d i v i d e d by lOn t o get the c o r r e c t order of magnitude.

As the c e l l u l a r wood f i b r e s are almost e n t i r e l y o r i e n t e d i n the l o n g i t u d i n a l d i r e c t i o n of t r e e stems and as the d i s t r i b u t i o n and s t r u c t u r e of d i f f e r e n t types of c e l l s are u s u a l l y somewhat d i f f e r e n t i n the r a d i a l and t a n g e n t i a l d i r e c t i o n s o f t r e e stems, wood possesses d i f f e r e n t t h e r m a l , moisture-con-d u c t i v e anmoisture-con-d mechanical p r o p e r t i e s i n l o n g i t u moisture-con-d i n a l , r a moisture-con-d i a l anmoisture-con-d t a n g e n t i a l d i r e c t i o n s . The r a d i a l and t a n g e n t i a l p r o p e r t i e s are o f t e n s i m i l a r and r e -f e r r e d to as t r a n s v e r s e p r o p e r t i e s .

Water e x i s t s i n wood i n three d i f f e r e n t forms: as water bound w i t h hydrogen bonds t o c e l l u l o s e m a t e r i a l s i n s i d e and on c e l l w a l l s and thus w i t h h i g h e r d e n s i t y than l i q u i d water; as f r e e water and as water vapor, which both occurs i n c e l l lumens and p i t pores. Below the f i b e r s a t u r a t i o n p o i n t

( u s u a l l y 30% m o i s t u r e c o n t e n t ) , which corresponds to e q u i l i b r i u m w i t h a i r a t 100 % r e l a t i v e h u m i d i t y , t h e r e are only bound water and water vapor i n wood. Free ( l i q u i d ) water comes about when the moisture c o n t e n t i s higher

than the f i b e r s a t u r a t i o n p o i n t .

I n tnoisture t r a n s p o r t bound water moves through the c e l l w a l l s d r i v e n by m o i s t u r e c o n c e n t r a t i o n d i f f e r e n c e below the f i b e r s a t u r a t i o n p o i n t , water vapor moves through c e l l lumens and p i t c a v i t i e s due t o p a r t i a l vapor p r e s sure d i f f e r e n c e below the f i b e r saturat"ioti p o i n t and f r e e water i s t r a n s -p o r t e d through c e l l lumens and -p i t c a v i t i e s above f i b e r s a t u r a t i o n -p o i n t by c a p i l l a r y pressure d i f f e r e n c e . Bound water and vapor movement i n wood i s regarded as a d i f f u s i o n process, w h i l e f r e e water flow i s a bulk flow de-s c r i b e d ade-s p e r m e a b i l i t y . They f o l l o w d i f f e r e n t lawde-s and move d i f f e r e n t l y i n wood s t r u c t u r e s .

D i f f u s i o n i s the spontaneous movement of one m a t e r i a l i n another from a zone of h i g h e r c o n c e n t r a t i o n to a zone of lower c o n c e n t r a t i o n , u s u a l l y w i t h the system under a constant pressure. The r a t e of d i f f u s i o n s i s represented by 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 ) . P e r m e a b i l i t y ia a measure of the ease w i t h which a f l u i d flows through a porous m a t e r i a l m o t i v a t e d by a pressure d i f f e r e n c e . I f c o n c e n t r a t i o n and pressure d i f f e r e n c e s occur s i m u l -t a n e o u s l y , bo-th d i f f u s i o n and p e r m e a b i l i -t y c o n -t r i b u -t e -t o -the f l u i d move-ment. I t must be emphasized t h a t i n many s c i e n t i f i c areas d i f f u s i o n i s more g e n e r a l l y d e f i n e d , and sometimes encompasses the realm of [ j e r m e a b i l i t y . The laws d e s c r i b i n g d i f f u s i o n and p e r m e a b i l i t y are F i c k ' s laws and Darcy's law.

F i c k ' s f i r s t law ( f o r s t e a d y - s t a t e d i f f u s i o n ) :

F i c k ' s second law ( f o r dynamic d i f f u s i o n ) :

cable:

8 ^ 1 (4) P o i s e u i l l e ' s law can a c t u a l l y be regarded as Darcy's law expressed from the

s t a n d p o i n t of pore s t r u c t u r e . When i t i s combined w i t h Darcy's law, the mean r a d i u s of the c a p i l l a r i e s can be c a l c u l a t e d .

In l e s s hygroscopic m a t e r i a l s as most i n o r g a n i c porous b u i l d i n g m a t e r i a l s l i k e b r i c k s , porous concretes and rocks, t h e r e are a l s o t h r e e moisture phases, but the mobile bound water, known as evaporable water, e x i s t s only on the pore w a l l s and i s t h e r e f o r e much less than i n wood m a t e r i a l s and

un-important. Bound water movement i n such m a t e r i a l s can be d i s r e g a r d e d and the whole moisture t r a n s p o r t c o n s i s t s of water vapor and c a p i l l a r y con-densed l i q u i d water movement, which can u s u a l l y be d e p i c t e d by a s i n g l e d r i v i n g p o t e n t i a l ( A h l g r e n , 1972; Bazant, 1972; N i l s s o n , 1980). I n tliese b u i l d i n g m a t e r i a l s r e l a t i v e h u m i d i t y i n s i d e the m a t e r i a l or chemical potent i a l i s used i n s potent e a d of moispotenture c o n potent e n potent i n potenthe research of moispotenture d i f f u -s i o n becau-se i t i -s e a -s i e r t o mea-sure (Adam-son and Gaffner, 1972).

For wood and wood products moisture content i s e a s i e r t o measure than r e l a -t i v e h u m i d i -t y i n s i d e -the m a -t e r i a l s . However, mois-ture con-ten-t and r e l a -t i v e h u m i d i t y are l i n k e d through s o r p t i o n h y s t e r e s i s isotherms and can be con-v e r t e d from one t o another. Moisture content ( u s u a l l y k i l o g r a m of water per k i l o g r a m oven-dry wood) and moisture c o n c e n t r a t i o n ( k i l o g r a m of water per cubic meter of wet wood) can be considered as p r o p o r t i o n a l w i t h only neg-l e g i b neg-l e inaccuracy, they can be useti e q u i v a neg-l e n t neg-l y (but not e q u a neg-l neg-l y ) i n v a r i o u s expressions.

I n s y n t h e t i c non-porous polymers ( p l a s t i c s ) and t h e i r composits w i t h glass or g r a p h i t e f i b e r s , bound water alone moves.

The p a t t e r n of moisture movement i n wood m a t e r i a l s i s t h e r e f o r e more com-p l i c a t e d . A t t e n t i o n should be com-p a i d t o d i f f e r e n t moisture com-phases and how each of them i s a f f e c t e d by v a r i o u s v a r i a b l e s i n a n a l y z i n g moisture t r a n s -p o r t d u r i n g d i f f e r e n t c o n d i t i o n s . Such a n a l y s i s w i l l lay a sound basis f o r the comprehension of the o v e r a l l moisture movement t h a t alone i s s i g n i f i -cant and considered i n p r a c t i c e .

The laws presented above are only basic ones. I n p r a c t i c a l measurements and c a l c u l a t i o n s q u i t e d i f f e r e n t equations which are f u r t h e r developed are u s u a l l y a p p l i e d . A b r i e f p r e s e n t a t i o n i s given below:

2.1 D i f f u s i o n

E a r l y s t u d i e s of moisture d i f f u s i o n i n wood were done by l u t t l e (192';'); e t c . They s t u d i e d wood d i f f u s i v i t y d u r i n g d r y i n g by s o l v i n g F i c k ' s law ana-l y t i c a ana-l ana-l y i n d i f f e r e n t ways w i t h o u t n o t i c i n g t h a t wood d i f f u s i v i t y changeii w i t h moisture c o n t e n t and temperature, a negligence which was noun rc^j/1 fi-nished by o t h e r researchers, d i s t i n g u i s h a b l y by Stamm. D i f f u s i o n i-.-. tlic only mean of wood moisture t r a n s p o r t i n most p r a c t i c a l circumstances, an(i

cess. The reason can be seen i n t h e s e c t i o n S u c t i o n and P e n e t r a t i o n of t h i s survey, chapter 2.1.6.

2.1.1 Approach w i t h s o r p t i o n 2.1.1.1 A d s o r p t i o n and d e s o r p t i o n

I t might be Prager and Long (1951) who f i r s t v e r i f i e d t h e a p p l i c a b i l i t y o f s o r p t i o n process ( i n c l a d s o r p t i o n and d e s o r p t i o n ) of a gaseous f l u i d i n t o

or out o f a s o l i d f o r t h e measurement o f d i f f u s i v i t y . This method has gene-r a l l y been used by chemists on polymegene-rs, composite m a t e gene-r i a l s e t c (Kates and Long, 1953; Bagley and Long, 1955; Shen and S p r i n g e r , 1976; Bonniau and B u r n s e l l , 1981; e t c ) and on measuring wood d i f f u s i v i t y i n d i f f e r e n t man-n e r s . (Stamm, 1960a, b; Chooman-ng, 1963; Comstock, 1963; B i g g e r s t a f f , 1965; Choong 1965 and 1969; Prichananda 1966; Stamm 1967b; McNamara and H a r t , 1971; Koponen, 1984.)

The e q u a t i o n mostly used i n s o r p t i o n method i s known as Newmann's form of Pick's law;

D

/6 t (5)

where E = (M^-M^)/(M^-Mj^) i s t h e f r a c t i o n o f a o r p t i v e moisture g a i n ( o r l o s s ) a t time t . The e q u a t i o n i s a v a i l a b l e only when E i s l e s s than 0.66. L i s t h e t h i c k n e s s of t h e specimen a l o n g which u n i d i r e c t i o n a l d i f f u s i o n occurs.

Equation ( 5 ) i s d e r i v e d from t h e i n i t i a l l i n e a r p a r t o f t h e s o r p t i o n curve ( f i g u r e 1 ) .

f i g u r e 1. The curve of moisture gain o r l o s s o f a specimen d u r i n g moisture s o r p t i o n versus the square r o o t o f t i m e .

4t

The whole s o r p t i o n curve i s d e p i c t e d by an equation developed d i r e c t l y from Pick's law under s o r p t i o n a l c o n d i t i o n s :

For Ot/u*- > 0.05 the equation reduces t o

For E l e s s than 0.66 the s o r p t i o n i s r a t h e r a c c u r a t e l y d e s c r i b e d by Eq.(5). Some researchers a p p l i e d Eq.(7) f o r measuring d i f f u s i v i t y under the c o n d i -t i o n E l a r g e r -than 0.4, bu-t Eq.(5) have been much more popular owing -t o i -t s s i m p l i c i t y . I f Eq. (5) and Eq. ( 7 ) are a p p l i e d below and above E = 0.5 r e s p e c t i v e l y , t h e d i f f u s i v i t y d u r i n g t h e whole s o r p t i o n process can be d e t e r -mined.

Wood s o r p t i o n method has been used e i t h e r as a d s o r p t i o n by p l a c i n g s p e c i -mens of low moisture content i n high r e l a t i v e h u m i d i t y or as d e s o r p t i o n by d r y i n g specimens t o a lower moisture c o n t e n t . The r e l a t i v e h u m i d i t y and temperature of the ambient a i r must be constant and, most important of a l l , the moisture content of the specimen should not be above the f i b e r s a t u r a -t i o n p o i n -t . Then bound wa-ter and wa-ter vapor move s i m u l -t a n e o u s l y i n -t o or out of the specimens and the d i f f u s i v i t y measured belongs t o the combined bound water and vapor movement.

During the process of a d s o r p t i o n , some secondary l i n k a g e s i n wood m a t e r i a l break down, producing more s o r p t i v e s i t e s t h a t give wood m a t e r i a l a h i g h e r e q u i l i b r i u m moisture content i n d e s o r p t i o n than i n a d s o r p t i o n a t each r e l a t i v e h u m i d i t y , which i s known as h y s t e r e s i s e f f e c t . The e x t e n t of h y s t e r e -s i -s and the mean e q u i l i b r i u m moi-sture content decrea-se w i t h i n c r e a -s i n g tem-p e r a t u r e due t o decreased s o r tem-p t i v e s i t e s . The e q u i l i b r i u m a d s o r tem-p t i o n a l moisture content i s 0.84 time s m a l l e r than the corresponding e q u i l i b r i u m d e s o r p t i o n a l moisture c o n t e n t 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 i e s .

Owing t o the h y s t e r e s i s e f f e c t , the d i f f u s i v i t y measured w i t h a d s o r p t i o n i s s m a l l e r than d i f f u s i v i t y measured w i t h d e s o r p t i o n , but t h e i r p r o p o r t i o n s h o u l d be somehow d e f i n i t e . The average of a d s o r p t i o n a l and d e s o r p t i o n a l d i f f u s i v i t y can normally be used i n p r a c t i c e (Newns, 1956; Watt, 1960; Bramhall, 1971).

D i f f u s i v i t y of m o i s t u r e increases r e g u l a r l y w i t h an increase i n temperature or moisture content of wood. The e f f e c t i v e temperature of wood specimens d u r i n g s o r p t i o n i s not equal t o the ambient a i r due t o e v a p o r a t i o n heat taken away d u r i n g d e s o r p t i o n ( d r y i n g ) and condensation heat deposited i n specimens d u r i n g a d s o r p t i o n . But t h i s e f f e c t , u n l i k e i n the case of the v i o l a n t process of k i l n d r y i n g , i s small because of t h e slow r a t e of mois-t u r e s o r p mois-t i o n and has g e n e r a l l y been neglecmois-ted.

For the e f f e c t of moisture content change on d i f f u s i v i t y i n s o r p t i o n pro-cess, the s i t u a t i o n i s d i f f e r e n t . Eq.(5) i s a v a i l a b l e on the basis t h a t the s u r f a c e s of wood specimens come i n t o e q u i l i b r i u m w i t h ambient a i r imme-d i a t e l y , animme-d the moisture content i n the core has not changeimme-d a p p a r e n t l y .

McNamara and Hart (1971) proposed t h a t t h e more p r e c i s e mean d i f f u s i v i t y corresponding t o each s m a l l m o i s t u r e content range (Mt, Mt+ J^H) could be d e r i v e d by d i f f e r e n t i a t i n g Eq.(5):

The same d e d u c t i o n f o r Eq.(7) i s :

D = _ J ^ ^ ( 9 )

Eq.(8) and Eq.(9) can be a p p l i e d f o r E l e s s and l a r g e r than 0.5 respec-t i v e l y .

A t h e o r e t i c a l l y p r e c i s e c a l c u l a t i o n o f s o r p t i o n a l d i f f u s i v i t y can be de-r i v e d i n anothede-r mannede-r. The d i f f u s i v i t y measude-red accode-rding t o

Eq.(5) i s t h e mean value D i n t h e moisture content range (Mi, Mm). By d e f i -n i t i o -n , i t s r e l a t i o -n t o t h e exact d i f f u s i v i t y D i s

(10)

When we have known t h e change r a t e o f D t o Mm v i a some measurements, t h e exact d i f f u s i v i t y a t Mm w i l l be:

D(M^) — Dt f ^^'^i

Eq.(5) was d e r i v e d on t h e b a s i s o f constant sample t h i c k n e s s . Stamm (1956) s t u d i e d t h e d i f f u s i v i t y o f moisture i n cellophane and found t h a t i t s t h i c k -ness c o u l d vary over 100% between t h e s w o l l e n and oven-dry c o n d i t i o n s . He proved t h a t i n such a case, Eq.(5) s h o u l d be m o d i f i e d t o t a k e t h e t h i c k n e s s

v a r i a t i o n i n t o account as:

^ = / 6 " C^t

76"

where s i s t h e f r a c t i o n a l s w e l l i n g and Lo i s t h e i n i t i a l t h i c k n e s s .

The s w e l l i n g o f wood i s l e s s t h a n 13%, so i t s e f f e c t on d i f f u s i v i t y has not been accounted f o r . But f o r some wood—based panels, t h e t h i c k n e s s s w e l l i n g i s r e l a t i v e l y l a r g e i n a d s o r p t i o n and might have t o be considered.

I n another a p p l i c a t i o n o f s o r p t i o n method (Skaar, 1958; Koponen, 1984), t h e specimens a r e taken o u t from t h e s o r p t i o n chamber and sawn i n t o t h i n sheets p e r p e n d i c u l a r t o t h e m o i s t u r e d i f f u s i o n d i r e c t i o n ( a l l t h e o t h e r specimen s u r f a c e s a r e s e a l e d ) as shown i n f i g u r e 2. Each sheet i s weighed subse-q u e n t l y t o measure t h e m o i s t u r e d i s t r i b u t i o n . The moisture d i s t r i b u t i o n can a l s o be determined w i t h X-ray (tomography) or 7 -ray w i t h o u t d e s t r o y i n g t h e specimens.

f i g u r e 2. Sawn p a t t e r n of wood specimens i n s o r p t i o n method. A f t e r moisture content d i s t r i b u -t i o n i s measured by weighing, d i f f u s i v i t y can be c a l c u l a t e d a t any moisture c o n t e n t . (Koponen, 1984.)

As the moisture d i s t r i b u t i o n curve ( f i g u r e 3) changes from t j ^ t o t 2 (which can be o b t a i n e d by s o r p t i o n of two i d e n t i c a l specimens a t time t j ^ and t 2 r e s p e c t i v e l y ) t h e exact d i f f u s i v i t y a t the moisture content corresponding t o moisture c o n c e n t r a t i o n C can be d e r i v e d from t h e f o l l o w i n g equation which i s i n t e g r a t e d from Pick's second law.

(13) M a r t i n and Moschler (1970) presented a s i m i l a r approach f o r d i f f u s i v i t y c a l c u l a t i o n w i t h s o r p t i o n method.

f i g u r e 3. Moisture d i s t r i b u t i o n i n wood specimen d u r i n g adsorp-t i o n and d e s o r p adsorp-t i o n a adsorp-t adsorp-time adsorp-t j ^ and

2.1.1.2 E x t e r n a l r e s i s t a n c e i n s o r p t i o n

I n s o r p t i o n process, s u r f a c e s of t h e t e s t samples are assumed t o reach moisture e q u i l i b r i u m w i t h s u r r o u n d i n g a i r as soon as they have been placed i n a t e s t chamber and t h e r e i s no r e s i s t a n c e f o r moisture t r a n s p o r t i n the s u r f a c e s . But i n r e a l i t y , t h e r e does e x i s t r e s i s t a n c e on sample s u r f a c e which i s described w i t h s u r f a c e e m i s s i v i t y .

The d i f f u s i v i t y measured w i t h s o r p t i o n according t o E q . ( 5 ) , Eq.(7) and f i g u r e 1 should t h e r e f o r e be e n t i t l e d as apparent d i f f u s i v i t y because i t i s c o n t r i b u t e d from two r e s i s t a n c e s : t h e i n t e r n a l r e s i s t a n c e o r i g i n a t e d from the sample s t r u c t u r e i t s e l f , and t h e e x t e r n a l r e s i s t a n c e caused by the a i r boundary l a y e r adjacent t o t h e sample s u r f a c e . Ogura e t a l (1957) found t h a t f o r wood specimens o f Chamaecyparis Obtus, t h e e x t e r n a l r e s i s t a n c e i n s t i l l a i r i n l o n g i t u d i n a l d i r e c t i o n was e q u i v a l e n t t o t h e r e s i s t a n c e of 2.50 cm of specimen l e n g t h , and i n t r a n s v e r s e d i r e c t i o n t o 1.10 cm. E x t e r -nal r e s i s t a n c e i s represented by s u r f a c e e m i s s i v i t i e s , which i s d e f i n e d as

s =

where a i s the moisture f l u x f l o w i n g through t h e specimen s u r f a c e , Ca and Ce a r e moisture c o n c e n t r a t i o n s a t the s u r f a c e of specimen and of t h e am-b i e n t a i r r e s p e c t i v e l y . I f D i s t h e d i f f u s i v i t y o f t h e sample r e f l e c t i n g i n t e r n a l r e s i s t a n c e , 5 t h e s u r f a c e e m i s s i v i t y r e f l e c t i n g t h e e x t e r n a l r e s i s t a n c e , and D* t h e apparent d i f f u s i v i t y , t h e r e a r e r e l a t i o n s h i p s (Newmann's e q u a t i o n , 1931):

- ^ ^ - ^ - t - f - (13)

Here t g 5 i s h a l f s o r p t i o n a l time corresponding t o E = 0 . 5 i n E q . ( 5 ) and Eq.(7).*

D i f f u s i v i t y and s u r f a c e e m i s s i v i t y can e a s i l y be c a l c u l a t e d from the equa-t i o n s above i f s e v e r a l apparenequa-t d i f f u s i v i equa-t y D* or h a l f dry equa-time of equa-t h e same m a t e r i a l w i t h two d i f f e r e n t thicknesses are measured.

For s o r p t i o n method described by F i g u r e 2, F i g u r e 3, and Eq.(13), t h e mea-sured data f o r c a l c u l a t i n g d i f f u s i v i t y can r e a d i l y be u t i l i z e d t o d e r i v e s u r f a c e e m i s s i v i t y :

.^ÉLSÉSI.S^ (17)

E x t e r n a l r e s i s t a n c e i n wood a d s o r p t i o n and d e s o r p t i o n ( d r y i n g ) were also s t u d i e d by Choong e t a l (1969), Bazant (1972), and Rosen (1979). Rosen proved from wood d r y i n g t e s t s , t h a t s u r f a c e e m i s s i v i t y i s s t r o n g l y a f f e c t e d by a i r v e l o c i t y over t h e s u r f a c e up t o 3 m/s and t h e angle between a i r vel o c i t y and wood g r a i n . The r e vel a t i v e importance o f e x t e r n a vel r e s i s t a n c e i n -creases as sample t h i c k n e s s or a i r v e l o c i t y decrease. I n t h e case water s o r p t i o n process i s r e l a t i v e l y slow ( u n l i k e wood k i l n d r y i n g ) and t h e r e i s an a i r c i r c u l a t i o n i n t e s t chamber, the s u r f a c e e m i s s i v i t y has o f t e n been neglected and the measured apparent d i f f u s i v i t y regarded as t r u e d i f f u s i -v i t y .

2.1.2 Steady-state and dynamic d i f f u s i o n

The s o r p t i o n process i n d e t e r m i n i n g d i f f u s i v i t y i s a dynamic (unsteady-s t a t e ) one, (unsteady-s i n c e moi(unsteady-sture content i n (unsteady-specimen(unsteady-s change(unsteady-s a l l t h e t i m e . A(unsteady-s a c o u n t e r p a r t t h e r e are s t e a d y - s t a t e methods t o measure d i f f u s i v i t y , the mostly used is-tKccup method (vapometer).

I n o r d i n a r y cup method, t h e atmospheres on t h e two s i d e s of specimen are c o n t r o l l e d and kept a t two d e f i n i t e r e l a t i v e h u m i d i t i e s , moisture

d i f f u s i o n r a t e and moisture content i n t h e specimens are s t a b l e . With a cup method, t h e measured d i f f u s i v i t y i s a mean value corresponding t o a mois-t u r e conmois-tenmois-t range i n mois-t h e specimen. The exacmois-t d i f f u s i v i mois-t y can be c a l c u l a mois-t e d w i t h E q . ( l l ) : By s e t t i n g t h e atmosphere a t constant r e l a t i v e humidity on one specimen s i d e and changing s u c c e s s i v e l y on t h e o t h e r s i d e i n a s e r i e s of measurements, t h e exact d i f f u s i v i t y can be d e r i v e d from average d i f f u s i -v i t y and i t s change r a t e w i t h moisture content on one specimen s u r f a c e . But i t can a l s o be obtained w i t h a somewhat more d i r e c t approach by measuring the f l u x change w i t h t h e successive moisture content change on one specimen s i d e (Bazant, 1972):

where M i s the s u r f a c e moisture content i n e q u i l i b r i u m w i t h t h e successively changing r e l a t i v e h u m i d i t y .

In t h e cup method t h e a i r space between t h e s u r f a c e s of t h e specimen and s a t u r a t e d s a l t s o l u t i o n a l s o r e s i s t s moisture d i f f u s i o n . Newns (1950) p r o -vided two means t o measure t h e r e s i s t a n c e : Keep t h e a i r space constant and measure t h e d i f f u s i v i t y o f one, two l a y e r s of i d e n t i c a l specimen respec-t i v e l y , or change respec-t h e d i s respec-t a n c e of respec-t h e a i r space berespec-tween respec-the s u r f a c e s of respec-t h e specimen and the s o l u t i o n w i t h one l a y e r of specimen. T v e i t (1966) and Siau

(1984, P.171) presented methods t o c a l c u l a t e t h e r e s i s t a n c e i n t h e cup d i -r e c t l y w i t h o u t change i n t h e t e s t s e t .

Cup method, l i k e s o r p t i o n method, has been e x t e n s i v e l y used by wood r e -searchers, f o r l i t e r a t u r e , see chapter 3.1.1. There are many v a r i a t i o n s o f cup methods. E.g. specimens can be placed between two channels through which a i r of two constant r e l a t i v e h u m i d i t i e s f l o w s (more s e n s i t i v e i f one i s s e t a t z e r o ) , o r one channel i s evacuated. I n t h e l a t t e r case, bulk flow and d i f f u s i o n occur s i m u l t a n e o u s l y . But i f the r e l a t i v e h u m i d i t y of a i r i n the channels changes w i t h time a t a c e r t a i n r a t e , t h e cup method w i l l be t u r n e d t o a dynamic one.

The advantage of the s t e a d y - s t a t e cup method i s t h a t the r e l a t i v e h u m i d i t y i n t h e t e s t can be c o n t r o l l e d t o change s u c c e s s i v e l y w i t h h i g h accuracy, thus o b t a i n i n g t h e p r e c i s e d i f f u s i v i t y - m o i s t u r e content r e l a t i o n w i t h great c e r t a i n t y . But the t e s t u s u a l l y takes a l o n g t i m e , o f t e n s e v e r a l months f o r one r u n , and thus i n c r e a s i n g t h e c o m p l e x i t y i n c o n t r o l l i n g the device w i t h necessary accuracy. The advantage of dynamic s o r p t i o n method i s t h a t i t takes much l e s s time, u s u a l l y one to t h r e e weeks f o r one r u n , and the de-v i c e as w e l l as t h e method i s s i m p l e r . The inaccuracy i n the measurement i s t h e r e f o r e a l s o s m a l l e r , a l t h o u g h t h e c a l c u l a t i o n i s more c o m p l i c a t e d . Near-ly a l l s t e a d y - s t a t e methods and device can a l s o be used f o r dynamic mea-surements^ i t can always save experiment time, but cause g r e a t e r complica-t i o n i n d i f f u s i v i complica-t y c a l c u l a complica-t i o n .

There i s some discrepancy i n t h e measured d i f f u s i v i t y w i t h s t e a d y - s t a t e and dynamic methods. I n t h e dynamic method, t h e moisture c o n t e n t of specimens a l t e r s w i t h t i m e , causing them t o s w e l l or s h r i n k . This can i n t e r f e r e t o some e x t e n t w i t h t h e pure m o i s t u r e d i f f u s i o n process. Stamm (1935, 1959) proved t h a t t h e s w e l l i n g and s h r i n k a g e of wood were about p r o p o r t i o n a l t o the m o i s t u r e c o n t e n t a l t e r a t i o n . Prichananda (1966) s t a t e d t h a t i n dynamic measurement d i f f u s i o n was n o t t h e o n l y mechanism i n v o l v e d . Stress r e l a x a -t i o n o r e v o l u -t i o n accompanying -the s w e l l i n g or shrinkage s -t r e s s a l s o played a p a r t , making t h e process d e v i a t e somewhat from Pick's law. The e f f e c t o f s t r e s s r e l a x a t i o n or e v o l u t i o n was l e s s a t low r e l a t i v e h u m i d i t y and h i g h temperature. Newns (1956), Downes (1958), and Watt (1960) found t h a t f o r c e l l u l o s e and wool, t h e a d s o r p t i o n of m o i s t u r e was a two stage process. I n i n i t i a l stage T i c k ' s law was obeyed, but i n t h e second stage t h e s o r p t i o n was n o n - F i c k i a n . They a t t r i b u t e d t h e non-Fickian behaviour t o t h e change i n the polymer i n t e r n a l s t r u c t u r e caused by t h e s w e l l i n g s t r e s s r e l a x a t i o n as the m o i s t u r e adsorbed i n t h e i n i t i a l stage e x e r t e d pressure and broke the secondary l i n k a g e . N e v e r t h e l e s s , f o r wood, t h e s t r u c t u r a l change seems t o be so s m a l l t h a t t h e second stage a d s o r p t i o n phenomenon have never been ob-served. Though t h e dynamic method i s i n f l u e n c e d by s t r e s s r e l a x a t i o n and t h e r e f o r e i s i n some discrepancy w i t h s t e a d y - s t a t e measurement, i t i s be-l i e v e d and proven t o obey F i c k ' s be-law i n generabe-l and have been e x t e n s i v e be-l y used by wood researchers w i t h s a t i s f a c t o r y r e s u l t s .

2.1.3 Bound water and water vapor

When the c e l l lumens and p i t pores o f wood have been f i l l e d w i t h metal (Stamm, 1959, 1960), p a r a f f i n (Yokota, 1959), o r r e s i n (Choong, 1969), va-por movement i s e l i m i n a t e d and t h e d i f f u s i v i t y measured belongs t o t h a t o f bound water.

Being i n d i f f e r e n t p h y s i c a l s t a t e s and movement manners, bound water and water vapor each have a d i f f u s i v i t y i n wood which changes i n d i f f e r e n t ways when temperature and m o i s t u r e c o n t e n t changes ( i t w i l l be discussed l a t e r ) , and which i s a f f e c t e d i n a q u i t e d i f f e r e n t way by t h e m i c r o s t r u c t u r e of v a r i o u s wood species. The d i f f u s i v i t y of bound wood depends mainly on wood d e n s i t y ( p o r o s i t y ) , d i f f e r e n t wood c e l l s t r u c t u r e s have only a l i t t l e i n -f l u e n c e , whereas -f o r t h e vapor d i -f -f u s i v i t y t h i s -f a c t o r has a very s t r o n g i n f l u e n c e . Bound water d i f f u s i v i t y dominates a t h i g h moisture content near the f i b e r s a t u r a t i o n p o i n t , w h i l e vapor d i f f u s i v i t y i s d e c i s i v e a t low moisture c o n t e n t s as w e l l as i n wood o f low d e n s i t y or a t h i g h tempera-t u r e s . Below 6% m o i s tempera-t u r e c o n tempera-t e n tempera-t bound watempera-ter n e a r l y ceases tempera-t o nwve. As

these two moisture phases always move s i m u l t a n e o u s l y , except when wood ma-t e r i a l s have d i r e c ma-t c o n ma-t a c ma-t w i ma-t h l i q u i d wama-ter, ma-t h e i r d i f f u s i v i ma-t y i s n o ma-t se-parated and the combined d i f f u s i v i t y i s r e f e r r e d t o ^ i moisture d i f f u s i v i t y . However, f o r a b e t t e r understanding, they should be s e p a r a t e l y analyzed and then considered combined a g a i n , as i n p r a c t i c a l use.

Stamm (1946, 1960) and Choong (1965), analogized the c a l c u l a t i o n o f e l e c -t r i c c o n d u c -t i v i -t y when a n a l y z i n g -the -t r a n s p o r -t o f bound wa-ter and wa-ter va-por and r a i s e d a model f o r t h e c a l c u l a t i o n o f t h e combined d i f f u s i v i t y , on the base t h a t both bound water d i f f u s i v i t y and vapor d i f f u s i v i t y were a l -ready known ( f i g u r e 4 ) . C e n t inuou» Bound W o t » r M o v e m e n t 7—rr-r P A T H N o . 4 P A T H No. 3 P A T H No 2 PATH No 1 • ' ' / / • M o v e m e n t •> / C e l l C o v i t y R5 p V l M e m b r o n e WQII R J P i t C h o m b e r R3 P i t P o r e R i C r o » » W a l l R4 F i g u r e 4. Diagrammatic sketches showing t h e movement paths through the c e l l s t r u c t u r e o f softwood (Choong, 1965)

C o n t i n u o u s C e l l W o n R(,

To c a l c u l a t e t h e combined d i f f u s i v i t y i n e i t h e r l o n g i t u d i n a l o r t r a n s v e r s e d i r e c t i o n s from t h i s model, a group of average g e o m e t r i c a l f i g u r e s d e s c r i -b i n g t h e v a r i o u s c a p i l l a r i c s t r u c t u r e s o f wood c e l l s , t h e -bound water d i f f u s i v i t y and vapor d i f f u s i v i t y i n t h e l o n g i t u d i n a l o r t a n g e n t i a l d i r e c -t i o n were -t o be s u b s -t i -t u -t e d i n Eq.(19). S-tamm proved -t h a -t -t h e model predic-ted moisture d i f f u s i o n i n wood d r y i n g f a i r l y good.

- f

(19)

Bound water d i f f u s i v i t y i s g e n e r a l l y found t o f o l l o w t h e A r r h e n i u s ' equa-t i o n .

(20)

whereof t h e a c t i v a t i o n energy Eb i s a f u n c t i o n o f moisture c o n t e n t . The l o n g i t u d i n a l bound water d i f f u s i v i t y i s two t o t h r e e times t h e t r a n s -verse bound water d i f f u s i v i t y (Stamm, 1960). An average value o f 2.5 can be used.

Water vapor d i f f u s i v i t y i n t h e c e l l lumens o f wood i s i n f e r r e d t o be (Stamm, 1946; Choong, 1965; Siau, 1971):

where G i s s p e c i f i c g r a v i t y o f moist c e l l - w a l l substance, /O i s d e n s i t y o f water, Po i s s a t u r a t e d vapor pressure and Da i s water vapor d i f f u s i v i t y i n bulk a i r t h a t has been proven t o be:

(22) Tarkow and Stamm (1960) s a i d t h a t water vapor d i f f u s i o n through t h e p i t membrane pores was r e s t r i c t e d and i t s d i f f u s i v i t y was about 1/40 t h a t o f f r e e water vapor d i f f u s i v i t y o b t a i n e d w i t h Eq.(21). P e t t y (1973) l a t e r mo-d i f i e mo-d t h e f i g u r e anmo-d provemo-d a c c o r mo-d i n g t o more a c c u r a t e measurements t h a t the d i f f u s i v i t y r a t i o n was 1/3.

2.1.4 Gas and vapor d i f f u s i o n

Non-polar gases as carbon d i o x i d e , n i t r o g e n and ethane do n o t form chemical bonds w i t h wood substance and move i n t h e same c a p i l l a r y path as water va-por as they d i f f u s e through wood and wood composites. I t i s v e r i f i e d by Tarkow and Stamm (1960, a, b ) , Evers (1965) and B e a l l and Wang (1974) t h a t the d i f f u s i v i t y r a t i o o f a non-polar gas t o water vapor i n bulk a i r i s equal t o t h e d i f f u s i v i t y r a t i o o f them i n a i r f i l l e d c a p i l l a r i e s o f wood. Vapor d i f f u s i v i t y i n wood was measured a c c o r d i n g t o t h i s assumption and t h e r e s u l t s o b t a i n e d were s a t i s f a c t o r y . Tarkow and Stamm (1960, b) proved t h a t at low m o i s t u r e c o n t e n t s , m o i s t u r e movement i n wood was e s s e n t i a l l y water vapor movement and i t was t h e r e f o r e p r e d i c t a b l e from t h e d i f f u s i v i t y o f non-polar gas. With i n c r e a s i n g m o i s t u r e c o n t e n t t h e bound water d i f f u s i o n becomes i n c r e a s i n g l y i m p o r t a n t and combined d i f f u s i o n i n c r e a s e d .

But p r a c t i c a l l y t h e r e should be some d i f f e r e n c e between non-polar gases and p o l a r water vapor as t o t h e i r i n t e r a c t i o n w i t h wood c e l l w a l l s . For vapor d i f f u s i o n though wood, t h e r e a r e two r e t a r d a n t f o r c e s : mechanical b l o c k i n g by t h e t o r t u o u s c a p i l l a r i e s , and r e s i s t a n c e due t o p r o x i m i t y of t h e p o l a r water molecules t o t h e c a p i l l a r y w a l l s whereupon c l u s t e r s o f p o l a r hyd-r o x y l s ahyd-re phyd-resent (Cady, 1935). The second hyd-r e t a hyd-r d a n t f o hyd-r c e does not e x i s t f o r non-polar gas molecules. This should l e a d t o some d e v i a t i o n between t h e t r u e vapor d i f f u s i v i t y and t h a t p r e d i c t e d w i t h non-polar gas d i f f u s i o n . I t might, however, be t o o s m a l l t o have been d e t e c t e d by Tarkow, Evers, e t c . Gas d i f f u s i v i t y through wood can a l s o be c a l c u l a t e d w i t h t h e analogy o f e l e c t r i c c i r c u i t i f t h e geometry o f t h e c a p i l l a r y s t r u c t u r e i s known

(Stamm, 1946). When t h e mean f r e e path o f gas i s of t h e same s i z e order as the diameters o f t h e p i t membrane pores, t h e d i f f u s i o n through t h e pores i s c o n t r i b u t e d by t h e mutual gaseous d i f f u s i o n and Knudsen d i f f u s i o n . I n d r i e d s o f t wood a r a t h e r l a r g e p r o p o r t i o n o f t h e t r a i c h e i d s , mainly i n latewood, i s a s p i r a t e d and n o t c o n d u c t i v e . With these two c o n s i d e r a t i o n s and a more advanced knowledge o f wood c e l l m i c r o s t r u c t u r e . P e t t y (1973) m o d i f i e d Stamm's model (1946) f o r gas d i f f u s i v i t y c a l c u l a t i o n i n softwood.

2.1.5 Non-isothermal moisture d i f f u s i o n

I t has been found f o r a l o n g time ( J o s t , 1952, P.521; Crank, 1975, P.353) t h a t besides c o n c e n t r a t i o n d i f f e r e n c e , temperature d i f f e r e n c e also causes m o i s t u r e d i f f u s i o n i n non-isothermal moisture circumstances. This has been r e f e r r e d t o as thermal d i f f u s i o n or Soret e f f e c t . E r i c k s o n et a l (1981) and Siau and Babiak (1983) showed i n experiments t h a t moisture i n wood boards was d r i v e n by both moisture content g r a d i e n t and temperature g r a d i e n t and under some c o n d i t i o n s m o i s t u r e even moved a g a i n s t moisture content g r a d i e n t and down the temperature g r a d i e n t .

Moisture t r a n s p o r t and heat t r a n s p o r t under non-isothermal c o n d i t i o n s are coupled. Lebedev (1961) and Luikov (1975) s t a t e d t h a t i f the thermal p r o -p e r t i e s ( s -p e c i f i c heat a, thermogradient c o e f f i c i e n t f ) and t r a n s f e r

c o e f f i c i e n t s ( m o i s t u r e d i f f u s i v i t y , thermal d i f f u s i v i t y Dh) were assumed t o be independent of p o s i t i o n s i n a porous s o l i d , the coupled r e l a t i o n i n the temperature below 100"C c o u l d be expressed as

-^=0-^^ t O - f ^ (23)

c ^ y ^ q

^oc

The second terms i n Eq.(24) accounts f o r the moisture e v a p o r a t i o n i n the s o l i d evolved w i t h the temperature f i e l d change, e i s moisture evaporations c o e f f i c i e n t , s i s the e v a p o r a t i o n heat of l i q u i d water. These two equations can be used i n any m o i s t u r e content range, so D i n Eq.(23) s h o u l d be the combined expression of moisture d i f f u s i v i t y and l i q u i d water t r a n s p o r t cons t a n t (consee S u c t i o n and P e n e t r a t i o n , chapter 2.1.6), adopting each i n c o r r e -spondance t o the moisture content l e v e l .

I n h i g h moisture content range D would remain constant when the temperature i s c o n s t a n t . At r e l a t i v e l y low m o i s t u r e c o n t e n t , D decreases w i t h decrea-s i n g moidecrea-sture c o n t e n t , t i l l moidecrea-sture movement changedecrea-s from l i q u i d flow t o vapor and bound water d i f f u s i o n . The thermogradient c o e f f i c i e n t f decreases w i t h i n c r e a s i n g temperature.

I n the case of wet s o l i d d r y i n g , whui^ the temperature i s above 100"C, i n -tense moisture e v a p o r a t i o n w i l l occur and excessive vapor pressure g r a d i e n t becomes the main d r i v i n g f o r c e i n a d d i t i o n t o moisture c o n c e n t r a t i o n gra-d i e n t angra-d temperature g r a gra-d i e n t , then Eq.(23) angra-d Eq.(24) each ought to be added w i t h a term on the r i g h t s i d e r e p r e s e n t i n g the c o n t r i b u t i o n of ex-cessive vapor pressure on moisture and heat t r a n s p o r t , and the moisture f l u x i s :

F = Fc i - P t i - F p

^äc^^fär ^opä^ ^^^^

where p i s the excessive vapor pressure i n the porous s o l i d and Dp molar vapor t r a n s p o r t c o e f f i c i e n t .

The coupled moisture and heat t r a n s p o r t at non-isothermal circumstances i s much more c o m p l i c a t e d than i s o t h e r m a l moisture t r a n s p o r t . Many problems are s t i l l u n c e r t a i n and unsolved i n t h i s f i e l d . Crank (1975) s t u d i e d vapor d i f f u s i o n , heat d i f f u s i o n and some o t h e r s p e c i a l problems, s e t up t h e i r e q u a t i o n s , and f u r t h e r discussed t h e i r a n a l y t i c a l s o l u t i o n s . Luikov (1966, 1980) a l s o i n v e s t i g a t e d a g r e a t deal i n t h i s f i e l d t h e o r e t i c a l l y .

Skaar and Siau (1981) and Siau (1983 a, b) w i t h coworkers t r i e d from

another approach: M o i s t u r e movement i n i s o t h e r m a l c o n d i t i o n s was assumed to be m o t i v a t e d e i t h e r by g r a d i e n t of a c t i v a t e d moisture molecules i n wood M* or by g r a d i e n t of chemical p o t e n t i a l xi alone, but both of the v a r i a b l e s M* and -u i n c o r p o r a t e d moisture content and temperature i n t h e i r e x p r e s s i o n :

Bb .

M = 0,0077 7' +6 J6 T-^ZåO-f RTLnh (27)

M o i s t u r e t r a n s p o r t can be expressed and c a l c u l a t e d from:

^ — ^ ^ ^ ^ (29)

where D^* and can be converted i n t o moisture d i f f u s i v i t y .

Siau and Babiak (1983) and Siau and J i n (1985) l a t e r experimented w i t h both the assumed d r i v i n g f o r c e s M* and A J , but t h e i r p r e d i c t i o n s were i n e x a c t . S t a n i s h (1986) r e c e n t l y f u r t h e r developed the concept of chemical p o t e n t i a l as d r i v i n g f o r c e .

I t might be w o r t h m e n t i o n i n g here t h a t Bramhall (1976 a, 1976 b, 1977, 1978, 1979) proposed t h a t the t r a n s p o r t of a l l the t h r e e moisture phases i n wood should be considered t o be d r i v e n by pressure d i f f e r e n c e s alone b o t h a t i s o t h e r m a l and n o n - i s o t h e r m a l c o n d i t i o n s . He remarked t h a t moisture t r a n s p o r t m o t i v a t e d by m o i s t u r e c o n c e n t r a t i o n d i f f e r e n c e and temperature d i f f e r e n c e a l l c o u l d be u n i f o r m l y regarded and expressed as being caused by pressure d i f f e r e n c e i n wood. From such a s t a n d p o i n t he regarded P i c k ' s law t h a t took m o i s t u r e c o n c e n t r a t i o n d i f f e r e n c e as d r i v i n g f o r c e as i n c o r r e c t , a p p l i c a b l e only a t i s o t h e r m a l c o n d i t i o n s . He s a i d t h a t when moisture con-c e n t r a t i o n was used as the d r i v i n g f o r con-c e as i n Picon-ck's law, the d i f f u s i v i t y of wood changed tremendously w i t h change i n moisture content or tempera-t u r e , butempera-t tempera-t h e d i f f u s i v i tempera-t y would notempera-t a l tempera-t e r i f pressure was used as tempera-t h e

d r i v i n g f o r c e . M o i s t u r e c o n c e n t r a t i o n d i f f e r e n c e alone c o u l d not e x p l a i n nonisothermal moisture t r a n s p o r t , but pressure d i f f e r e n c e c o u l d . The r e l a

-t i o n o f p a r -t i a l vapor pressure, -tempera-ture, and mois-ture con-ten-t c o u l d be expressed, a c c o r d i n g t o Bramhall (1979), as:

(30) where a and b were l i n e a r and q u a d r a t i c f u n c t i o n s o f temperature respec-t i v e l y , d was a c o n s respec-t a n respec-t .

Babbit (1950, 1951, 1956) s t a t e d t h a t j u s t as water vapor d i f f u s i o n was d r i v e n by t h e g r a d i e n t o f p a r t i a l vapor pressure, bound water should be d r i v e n by t h e g r a d i e n t o f a "spreading pressure", s i n c e t h e adsorbed mole-c u l e s on s o l i d s u r f a mole-c e mole-c o u l d he mole-considered as a two-dimensional gas. The mathematical expression o f spreading pressure c o u l d be i n f e r r e d from proper m o i s t u r e a d s o r p t i o n model, which would be a p p l i c a b l e f o r both i s o t h e r m a l and non-isothermal bound water d i f f u s i o n . Skaar (1982) and Nelson (1986) f u r t h e r developed t h e expression o f spreading pressure.

The i d e a l s of Bramhall, Babbit and Nelson r e g a r d i n g pressure or spreading pressure as t h e genuine d i v i n g f o r c e come from a n a l y s i s and d e d u c t i o n . Ex-p e r i m e n t a l v e r i f i c a t i o n s are s t i l l l a c k i n g today exceEx-pt Skaar's t e s t (1982) w i t h spreading pressure, which u n f o r t u n a t e l y gave poor coincidence w i t h h i s t e s t r e s u l t s .

Although Bramhall's remark t h a t d i f f u s i v i t y would not change w i t h moisture content i f pressure should be used as d r i v i n g f o r c e conforms w i t h some ex-periments made by o t h e r s , (e.g. S t i l l w e l l 1926, P.4), i t v i o l a t e s w i t h o t h e r t e s t r e s u l t s i n o t h e r cases (e.g. T v e i t , 1966).

The attempt o f Siau, Skaar, and Nelson e t c . t o take chemical p o t e n t i a l , mo-t i v a mo-t e d moismo-ture conmo-tenmo-t o r spreading pressure as mo-t h e only d r i v i n g pomo-ten- poten-t i a l f o r bound wapoten-ter d i f f u s i o n , and f u r poten-t h e r f o r combined moispoten-ture d i f f u s i o n i n non-isothermal c o n d i t i o n s and Bramhall's proposal o f u t i l i z i n g pressure as t h e only d r i v i n g f o r c e f o r a l l moisture phases would g r e a t l y s i m p l i f y , i f e v e n t u a l l y s u c c e s s f u l , t h e a n a l y s i s and probably a l s o t h e c a l c u l a t i o n o f n o n i s o t h e r m a l moisture t r a n s p o r t . The m o t i v a t i n g f o r c e s o f moisture t r a n s -p o r t i n i s o t h e r m a l c o n d i t i o n s are a c t u a l l y two: moisture content g r a d i e n t and temperature g r a d i e n t , which can be r e p l a c e d i n a n a l y s i s by some two o t h e r r e l e v a n t parameters. A n a l y z i n g and c a l c u l a t i n g made w i t h t h e two f o r -ces s e p a r a t e l y a r e t h e r e f o r e normal and n a t u r a l as Sandberg (1973) and N i l s s o n (1980) d i d i n b u i l d i n g m a t e r i a l s . I f t h e attempts o f Siau, Skaar, Nelson, and Bramhall should e v e n t u a l l y be proven t o be r e a l l y s u c c e s s f u l i n i n c o r p o r a t i n g two working parameters i n t o one i n a d e f i n i t e manner i n t h e f u t u r e , i t would c o n t r i b u t e a l o t t o t h e comprehension o f non-isothermal m o i s t u r e movement.

I n t h e i n v e s t i g a t i o n o f t h e coupled moisture and heat t r a n s p o r t i n wood and wood composites under non-isothermal c o n d i t i o n s , i t i s i m p e r a t i v e t o have the knowledge o f thermal p r o p e r t i e s l i k e t h e thermal c o n d u c t i v i t y and t h e r -mal d i f f u s i v i t y o f t h e m a t e r i a l s . The d e f i n i t i o n o f these two c o e f f i c i e n t s come from t h e basic law o f heat c o n d u c t i v i t y , F o u r i e r ' s laws, which are analogous w i t h F i c k ' s laws m a t h e m a t i c a l l y .

Wood and wood composites a r e good heat i n s u l a t o r s , they possess low thermal c o n d u c t i v i t y due t o t h e e f f e c t i v e r e s i s t a n c e t o heat f l o w o f t h e a i r t r a p

-ped I n c e l l c a v i t i e s and i n t e r - c e l l u l a r spaces. The thermal c o n d u c t i v i t y p a r a l l e l t o the g r a i n have been found t o range from 2.25 t o 2.75 of the va-l u e p e r p e n d i c u va-l a r t o the g r a i n d i r e c t i o n of wood.

Siau (1971) s e t a model based on i d e a l i z e d wood c e l l s t r u c t u r e and analo-gized heat c o n d u c t i o n I n wood t o e l e c t r i c conduction. With the model, dry wood thermal c o n d u c t i v i t y was c a l c u l a t e d a p p l y i n g wood d e n s i t y of the spe-cimens and a i r thermal c o n d u c t i v i t y . Siau showed t h a t the model r e s u l t e d i n good agreement w i t h e x p e r i m e n t a l data. This proved t h a t heat t r a n s p o r t i n wood i s a much s i m p l e r phenomenon than moisture t r a n s p o r t .

The thermal p r o p e r t i e s of wood as s p e c i f i c heat and thermal c o n d u c t i v i t y , thermal d i f f u s i v i t y were also found t o be i n simple l i n e a r r e l a t i o n s w i t h wood d e n s i t y and m o i s t u r e c o n t e n t (Rowley, 1933, Maclean, 1941).

2.1.6 S u c t i o n and p e n e t r a t i o n

In a d d i t i o n t o water s o r p t i o n , water s u c t i o n ( o r a b s o r p t i o n ) has also been u t i l i z e d t o measure moisture t r a n s p o r t i n wood, though t o a l e s s e r e x t e n t . Here some c o n f u s i o n was easy t o a r i s e when a few researchers ( T u t t l e , 1925) designated the measured values as d i f f u s i v i t y , since i n water s u c t i o n f r e e l i q u i d water movement I s i n v o l v e d t h a t i s not a d i f f u s i o n process.

Rosen (1974 a, b) c o r r e c t l y s a i d t h a t i n s u c t i o n process when a piece of wood was immersed i n water, bound water, water vapor, as w e l l as f r e e water

( t h a t i s Immediately i n c o r p o r a t e d i n t o the c e l l w a l l ) moved i n the wood be-low the f i b e r s a t u r a t i o n p o i n t , and t h a t moisture t r a n s p o r t c o n s i s t e d of combined bound water and vapor d i f f u s i o n . As moisture c o n t e n t reached the f i b e r s a t u r a t i o n p o i n t , f r e e water movement became the only moving moisture phase, bound water and water vapor ceased t o move.

Thus m o i s t u r e movement i s d r i v e n by d i f f e r e n t f o r c e s and i s i n d i f f e r e n t phases i n s u c t i o n d u r i n g two d i s t i n c t stages. Below the f i b e r s a t u r a t i o n p o i n t , i t i s the same as s o r p t i o n and Eq.(5) and Eq.(7) c o u l d be used. Spolek and Plumb (1981) showed t h a t above the f i b e r s a t u r a t i o n p o i n t , f r e e water movement was caused by l i q u i d phase pressure d i f f e r e n c e o r i g i n a t e d from the c a p i l l a r y pressure of c e l l lumens and p i t pores, which was even-t u a l l y r e l a even-t e d even-t o even-the waeven-ter s a even-t u r a even-t i o n grade and f u r even-t h e r even-t o f r e e waeven-ter con-t e n con-t g r a d i e n con-t . This was a l s o s con-t a con-t e d and proven by Berger and Pel (1973). I n such case, l i k e bound water below f i b e r s a t u r a t i o n p o i n t , f r e e water t r a n s -p o r t should be regarded t o be caused by f r e e water content d i f f e r e n c e . The parameter d e n o t i n g f r e e water c o n d u c t i v i t y was defined by Rosen (1974, a, b) as f r e e water t r a n s p o r t c o n s t a n t . Free water t r a n s p o r t c o n s t a n t i s d i f f e r e n t from the combined d i f f u s i v i t y of bound water and vapor though i t c o u l d be c a l c u l a t e d from Eq.(5) or Eq.(7) i f f r e e water c o n t e n t change i s accounted o n l y . Therefore, i t appears t h a t moisture d i f f u s i o n and bulk flow i n wood c o u l d be c o h e r e n t l y d e s c r i b e d w i t h i d e n t i c a l equations, w i t h Pick's law, a l t h o u g h the l a t t e r i s not a d i f f u s i o n process and the f r e e water t r a n s p o r t c o n s t a n t i s more a d i r e c t e x p r e s s i o n of p e r m e a b i l i t y r a t h e r than d i f f u s i v i t y .

Free water movement d u r i n g wood d r y i n g above the f i b e r s a t u r a t i o n p o i n t i s the c o u n t e r p a r t t o f r e e water s u c t i o n and t h e i r f r e e water t r a n s p o r t con-s t a n t con-should be very con-s i m i l a r . Free water t r a n con-s p o r t c o n con-s t a n t , according to

Spolek's deduction i s p r o p o r t i o n a l t o wood p e r m e a b i l i t y and i s t h e r e f o r e a simple expression of i t . Skaar (1958) s t a t e d t h a t above f i b e r s a t u r a t i o n p o i n t , f r e e water t r a n s p o r t constant i s a p p a r e n t l y s m a l l e r than moisture d i f f u s i v i t y below f i b e r s a t u r a t i o n p o i n t . Choong (1972) and Yao (1966) con-f i r m e d t h i s statement w i t h t h e i r experimental r e s u l t s .

Yao (1966) s t a t e d t h a t f r e e water t r a n s p o r t constant, l i k e bound water d i f -f u s i v i t y , changed e x p o n e n t i a l l y w i t h the r e c i p r o c a l o-f temperature accor-ding t o Eq.(12). But t h i s bears no t h e o r e t i c a l base and has obtained no f u r t h e r testimony from o t h e r researches. L i k e p e r m e a b i l i t y , f r e e water t r a n s p o r t constant i s s t r o n g l y i n f l u e n c e d by the m i c r o c a p i l l a r y s t r u c t u r e of wood and wood composites. This e x p l a i n s why some wood species take much longer time than others of s i m i l a r d e n s i t y i n d r y i n g .

Closely r e l a t e d w i t h s u c t i o n i s p e n e t r a t i o n , which has been i n v e s t i g a t e d by wood workers f o r wood treatments t o render i t w i t h s p e c i a l l y s u p e r i o r p r o -p e r t i e s . P e t t y (1985) s t u d i e d the -p e n e t r a t i o n of a non--polar l i q u i d i n t o wood. His work proved t h a t i f the c o n t a i n e r h o l d i n g the specimens was eva-cuated p r i o r to t e s t , the p e n e t r a t i o n d i s t a n c e s and the a b s o r p t i o n amount V c o u l d be a c c u r a t e l y p r e d i c t e d by Darcy's law;

3 = (31)

Thus the p e n e t r a t i o n and a b s o r p t i o n i n vacuum p e n e t r a t i o n process i s p r o -p o r t i o n a l t o the square r o o t of time t and the -p e r m e a b i l i t y of s-pecimens K. Petty f u r t h e r showed t h a t w i t h vacuum p e n e t r a t i o n , the two p a r a l l e l ca-p i l l a r y s t r u c t u r e of d i f f e r e n t s i z e order i n the t a n g e n t i a l d i r e c t i o n of the f i v e c o n i f e r wood he t e s t e d c o u l d be revealed and t h e i r p e r m e a b i o l i t y mean r a d i i a s c e r t a i n e d .

For p e n e t r a t i o n of non-vacuum processes Washburn (1921) deduced t h a t f o r porous s o l i d s w i t h pores of small i n t e r n a l surfaces the p e n e t r a t i o n o f l i q u i d was also p r o p o r t i o n a l to the square r o o t of time when c a p i l l a r y f o r c e and some e x t e r n a l pressure f u n c t i o n e d as d r i v i n g f o r c e s . This was ex-pressed as Lucas-Washburn equation. Back (1965 a, b, 1966) i n v e s t i g a t e d the p e n e t r a t i o n of water i n t o i n s u l a t i o n boards, paper, and f i b e r b u i l d i n g boards w i t h t h i s equation and proposed a method to t e s t the water r e s i -stance of i n s u l a t i o n board. Österberg and Back (1960), Morgan and Purslow

(1973) and Stamm (1973) s t a t e d t h a t the Lucas-Washburn equation was not obeyed d u r i n g p e n e t r a t i o n i n the i n i t i a l i n s t a n t , the p r a c t i c a l p e n e t r a t i o n and a d s o r p t i o n were proven being:

5 bo

^ = V. -t K. / T o ~ c o ^ ( ^

where Kj^ and K2 were constants. So and Vo were p o s i t i v e or negative con-s t a n t con-s depending on w e t t i n g procecon-scon-s. For water and wood, they are p o con-s i t i v e r e p r e s e n t i n g an i n i t i a l r a p i d uptake of water.

Eg.(33), Eq.(34) are i n t i m a t e l y r e l a t e d t o Eq.(31) and Eq.(32), the pene-t r a pene-t i o n of non-vacuum process oughpene-t a l s o pene-t o be f u n c pene-t i o n s of wood permeabi-l i t y . Therefore, p e n e t r a t i o n , e s p e c i a permeabi-l permeabi-l y vacuum p e n e t r a t i o n can be u s e f u permeabi-l i n i n v e s t i g a t i n g p e r m e a b i l i t y .

2.2 P e r m e a b i l i t y

P e r m e a b i l i t y ( b u l k f l o w ) has been I n v e s t i g a t e d f o r v a r i o u s types of porous media l i k e rocks, sands, s o i l , p o r c l a i n and wood e t c i n many d i f f e r e n t areas i n order to c l a r i f y how f l u i d s t r a n s f e r i n these m a t e r i a l s (Whitney, Ingmanson and Han, 1955; Scheidegger 1957; Wiest 1969; Siau 1972). For wood and wood—based panels, as f o r other porous s o l i d s , p e r m e a b i l i t y has been measured w i t h e i t h e r l i q u i d s or gases by e x e r t i n g a pressure d i f f e r e n c e t o d r i v e a f l u i d t o move through them. The pressure d i f f e r e n c e c o u l d be kept constant as i n s t e a d y - s t a t e methods or changing w i t h time as i n dynamic or u n s t e a d y - s t a t e methods. As p e r m e a b i l i t y i s g e n e r a l l y i n v e r s e l y p r o p o r t i o n a l t o the v i s c o s i t y of f l u i d (both gases and l i q u i d s ) , i t can be m u l t i p l i e d by the v i s c o s i t y of the f l o w i n g f l u i d , g i v i n g the s p e c i f i c p e r m e a b i l i t y which i s not a f f e c t e d by the measuring f l u i d but a p r o p e r t y of the porous s t r u c -t u r e of -the medium:

K5 = Kq

I t should be n o t i c e d t h a t i n some a r t i c l e s s p e c i f i c p e r m e a b i l i t y i s named as p e r m e a b i l i t y whereas p e r m e a b i l i t y i s c a l l e d apparent p e r m e a b i l i t y . I t i s because the a u t h o r s i n c o r p o r a t e d the v i s c o s i t y of f l u i d s i n Darcy's law. With s t e a d y - s t a t e methods, which have been much more commonly used than dynamic methods, Darcy's law i n Eq.(3) i s d i r e c t l y a p p l i c a b l e f o r l i q u i d s . For gases as t e s t media, however, some m o d i f i c a t i o n s of Darcy's law must be made.

2.2.1 The expansion and s l i p flow of gases

As gases are u t i l i z e d t o measure p e r m e a b i l i t y , t h e i r c o m p r e s s i b i l i t y have t o be taken i n t o c o n s i d e r a t i o n and Darcy's law f o r gaseous p e r m e a b i l i t y Kg i s changed t o :

Q = K f - ^ |

where P i s the mean a b s o l u t e pressure w i t h i n the specimen and P i s the pressure a t which the f l o w volume Q i s measured.

When the mean f r e e path of a gas molecule approaches the s i z e of t h e

openings through which flow occurs as the p i t membrane pores of wood c e l l s , a t r a n s i t i o n from viscous f l o w t o molecular f l o w ( s l i p f l o w ) occurs (Babbit 1951; Comstock, 1967; Siau, 1984, p. 85-88). Pure s l i p flow i s described by