Moisture transport in wood and wood-based panels comparison of the cup and sorption methods

Liu Tong

Moisture Transport in Wood and

Wood-based Panels - Comparison

of the Cup and Sorption Methods

Trätek

MOISTURE TRANSPORT I N WOOD AND WOOD BASED PANELS - C o m p a r i s o n o f t h e c u p a n d s o r p t i o n m e t h o d s Tr'ateknikCentrum Rapport I 8802014 Keywords diffusion coefficient moisture measurement moisture movement panel products sorption wood materials Stockholm A p r i l , 1988

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berskivor, spånskivor och plywood. Ett avtal om forskning och utveckling mellan industrin och Styrelsen för Teknisk Utveckling (STU) utgör grunden för verksamheten som utförs med egna, samverkande och externa resurser. Träteknik-Centrum har forskningsenheter, förutom i Stock-holm, även i Jönköping och Skellefteå.

The Swedish Institute for Wood Technology Re-search serves the five branches of the industry: saw-mills, manufacturing (joinery, wooden houses, fur-niture and other woodworking plants), fibre board, particle board and plywood. A research and deve-lopment agreement between the industry and the Swedish National Board for Technical Development (STU) forms the basis for the Institute's activities. The Institute utilises its own resources as well as those of its collaborators and other outside bodies. Apart from Stockholm, research units are also located in Jönköping and Skellefteå.

Page

SUMMARY ₃

SWEDISH SUMMARY - SVENSK SAMMANFATTNING 4

NOMENCLATURE ₅

1. INTRODUCTION ₇

2. THEORETICAL ASPECTS ₇

2.1 The cup method ₈

2.2 The s o r p t i o n method 9

2.3 The three-dimensional s o r p t i o n method ₁₁

2.4 _{Concentration-dependent d i f f u s i v i t y 13}

2.5 Regular regime a n a l y s i s ₁₈

3. _{EXPERIMENTAL 21}

3.1 M a t e r i a l s , methods and t e s t c l i m a t e s 21 3.2 Sample p r e p a r a t i o n and t e s t procedure 24 4. _{EXPERIMENTAL RESULTS: DIFFUSIVITY BASED ON MOISTURE 26}

CONCENTRATION IN THE AIR

4.1 Dry cups 26

4.2 Wet cups ₃₀

4.3 S o r p t i o n 33

4.4 Three-dimensional s o r p t i o n 37

4.5 Regular regime a n a l y s i s 40

5. COMPARISON AND DISCUSSIONS 41

5.1 Comparison o f t e s t methods 41

5.2 Discussion 46

5.2. 1 Dry cup and wet cup 46

5.2. 2 S o r p t i o n and three-dimensional s o r p t i o n 46

5.2.3 Adsorption and d e s o r p t i o n 46

5.2. 4 D i f f u s i v i t i e s o f t e s t e d m a t e r i a l s 46

5.2. 5 Cup and s o r p t i o n methods 47

5.2. 6 Surface r e s i s t a n c e 47

5.2. 7 The prospect o f r e g u l a r regime a n a l y s i s 48

6. CONCLUSIONS 49

7. APPENDICES 51

7.1 Appendix 1 - Conversion o f d i f f u s i v i t i e s on two bases 51 7.2 Appendix 2 - S o r p t i o n isotherms determined 53 7.3 Appendix 3 - D i f f u s i v i t i e s based on moisture c o n c e n t r a t i o n 56

i n the m a t e r i a l

7.3. 1 D i f f u s i v i t i e s o f t h e d r y cup method 56 7.3. 2 D i f f u s i v i t y o f t h e s o r p t i o n method 59

7.3. 3 Comparison 62

Four methods dry cup, wet cup, s o r p t i o n and t h r e e d i m e n s i o n a l s o r p t i o n -a r e i n v e s t i g -a t e d -and comp-ared v i -a experiments. S-amples prep-ared from f o u r m a t e r i a l s - f i b e r b o a r d , p a r t i c l e b o a r d , plywood and pine wood - are used i n the study. The experiment i s made i n a s e r i e s o f r e l a t i v e h u m i d i t i e s a t 20 'C.

The experimental r e s u l t s showed t h a t d r y cup and wet cup g i v e very s i m i l a r d i f f u s i v i t i e s . The d i f f u s i v i t i e s measured w i t h s o r p t i o n and three-dimensio-nal s o r p t i o n are a l s o n e a r l y t h e same. But t h e d i f f u s i v i t i e s from t h e cup method and s o r p t i o n method appear not r e a l l y i d e n t i c a l . At low r e l a t i v e hu-m i d i t y and 20 °C t h e d i f f u s i v i t i e s frohu-m cups are i n g e n e r a l s hu-m a l l e r than those from s o r p t i o n w h i l e a t h i g h r e l a t i v e h u m i d i t y they are l a r g e r than those from s o r p t i o n . This may be caused, a c c o r d i n g t o some p r e v i o u s i n v e s -t i g a -t i o n s i n l i -t e r a -t u r e , by s -t r e s s r e l a x a -t i o n o r i g i n a -t e d from -t h e s w e l l i n g or shrinkage i n t h e t r a n s i e n t d i f f u s i o n process o f s o r p t i o n , which does not e x i s t i n t h e s t e a d y - s t a t e moisture t r a n s p o r t o f t h e cup method. The cup method p r o v i d e s t h e r e a l d i f f u s i v i t y o f pure d i f f u s i o n w h i l e t h e s o r p t i o n method probably g i v e s t h e d i f f u s i v i t y o f t r a n s i e n t d i f f u s i o n process where s t r e s s r e l a x a t i o n occurs s i m u l t a n e o u s l y .

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 t o some e x t e n t l a r g e r than t h e ones measured w i t h d e s o r p t i o n .

D i f f u s i v i t i e s f o r wood and wood based panels can be expressed on the bases of moisture c o n c e n t r a t i o n s , e i t h e r i n t h e a i r or i n t h e m a t e r i a l s . The d i f

-f u s i v i t i e s based on c o n c e n t r a t i o n i n t h e a i r are i n general about 10000 times l a r g e r i n order o f magnitude than t h e ones based on c o n c e n t r a t i o n i n the m a t e r i a l s . D i f f u s i v i t i e s on these two bases can be converted from one to another when t h e s o r p t i o n isotherm o f a m a t e r i a l i s known. I n t h e p r e -sent r e p o r t , d i f f u s i v i t i e s on both bases are c a l c u l a t e d . While t h e ones based on c o n c e n t r a t i o n i n t h e a i r are presented i n t h e main body o f t h e r e -p o r t , t h e ones based on c o n c e n t r a t i o n s i n t h e m a t e r i a l s are i n A-p-pendix 3. The experimental r e s u l t s are presented i n t a b l e s and graphs and i m p o r t a n t f a c t o r s a r e discussed i n d e t a i l .

The r e p o r t r e f e r s t o research g r a n t 860413-6 from Swedish Council f o r B u i l d i n g Research.

Två o l i k a t y p e r av provmetoder för a t t mäta d i f f u s i v i t e t e n av vattenånga i trä och träbaserade s k i v o r har s t u d e r a t s , nämligen kopp- och sorptionsmeto-den. Av vardera metoden har två o l i k a v a r i a n t e r använts, våt och t o r r kopp-metod samt en- och t r e d i m e n s i o n e l l s o r p t i o n . Som p r o v m a t e r i a l har använts t r e o l i k a s k i v o r ( f i b e r s k i v o r , spånskivor och plywood) samt massiv f u r u -s p l i n t . Experimenten har utfört-s v i d en r a d o l i k a r e l a t i v a l u f t f u k t i g h e t e r mellan 0.30 och 0.93 v i d 20"C.

De e x p e r i m e n t e l l a r e s u l t a t e n v i s a r a t t t o r r och våt koppmetod ger ungefär samma d i f f u s i v i t e t . Detsamma gäller för en- och t r e d i m e n s i o n e l l s o r p t i o n . Men sorptionsmetoderna ger lägre d i f f u s i v i t e t än koppmetoderna v i d låg r e -l a t i v -l u f t f u k t i g h e t och högre d i f f u s i v i t e t v i d hög -l u f t f u k t i g h e t . Detta be-r o be-r s a n n o l i k t på a t t metodebe-rna mätebe-r undebe-r o l i k a föbe-rhållanden. Koppmetoden mäter ren d i f f u s i v i t e t under stadigvarande b e t i n g e l s e r , medan s o r p t i o n ger d i f f u s i v i t e t som en övergångsprocess mellan o l i k a jämvikter så a t t andra fenomen, t ex spänningsrelaxation, uppträder s a m t i d i g t och påverkar r e s u l -t a -t e -t . Båda -typerna av d i f f u s i o n förekommer i p r a k -t i k e n .

Med sorptionsmetoden kan d i f f u s i v i t e t e n mätas både v i d a d s o r p t i o n och de-s o r p t i o n . Rede-sultaten v i de-s a r a t t a d de-s o r p t i o n ger något högre d i f f u de-s i v i t e t än d e s o r p t i o n . Det betyder t ex a t t d e t går snabbare a t t t o r k a trä än a t t f u k -t a upp d e -t i g e n .

D i f f u s i v i t e t e n ökar med r e l a t i v a l u f t f u k t i g h e t e n ( e l l e r m a t e r i a l e t s f u k t -innehåll). Det v e r k l i g a fuktberoendet kan beräknas med två o l i k a beräkningsmetoder, k a l l a d e N i l s s o n s och Stamms metoder. N i l s s o n s metod är t e o r e t i s k t mest k o r r e k t men kräver mätdata för e t t f l e r t a l o l i k a l u f t f u k t i g h e -t e r . Mä-tpunk-terna mås-te anpassas -t i l l en kurva, som sedan d e r i v e r a s för a -t -t få fram den v e r k l i g a d i f f u s i v i t e t e n v i d o l i k a l u f t f u k t i g h e t e r . Stamms metod är mera empirisk och ger e t t slags medelvärden. Den är användbar främst när man har få mätpunkter. De båda beräkningsmetoderna g e r i s t o r t s e t t samma

värden, men d i f f u s i v i t e t e n s fuktberoende är något o l i k a , särskilt när d i f f u s i v i t e t e n beräknas med l u f t f u k t i g h e t e n som bas.

Fuktmängd som drivande k r a f t för d i f f u s s i o n kan u t t r y c k a s a n t i n g e n med l u f t f u k t i g h e t e l l e r med f u k t h a l t i trämaterialet som bas. L u f t f u k t i g h e t som bas används allmänt inom byggforskning och huvudresultaten i denna r a p p o r t presenteras på d e t t a sätt. F u k t h a l t e n i m a t e r i a l e t som bas används mest inom träforskning och dessa r e s u l t a t p r e s e n t e r a s i Appendix. Resultaten kan omräknas från den ena basen t i l l den andra med hjälp av s o r p t i o n s i s o t e r m e r som också bestämts. D i f f u s i v i t e t e n s s t o r l e k är ca 10.000 gånger större med l u f t f u k t i g h e t e n som bas. Det är därför mycket v i k t i g t a t t klargöra v i l k e n bas man avser. O k l a r h e t e r i d e t t a avseende h a r t i d i g a r e v a r i t v a n l i g a och förvirrande.

a, b,

c

fl,

B,E O

Dr

D*

É E

g

k

L

M Q R r Sh t

half sample tliicknesses in sorption and tliree

dimensional sorption metliods

constants in the equation of sorption isotherm

the criterion in the regular regime analysis

moisture diffusivity based on moisture

concen-tration in the material

constants in the exponential diffusivity

expre-ssions of Eq(14)

dimensionless diffusivity

a arbitrary diffusivity value

moisture fraction of sorption

£ = (w^v - Wi)/(Wb - w-J « (u^^ - Ui)/(Ub-Ui)

dimensionless average moisture concentration

or moisture content

the amount of E sorbed in x,y, z coordinate

directions in three dimensional sorption

moisture flux

flux parameter

constant in Eq( 14)

thickness of sample in diffusion direction

molecular weight of water

saturation water vapor pressure in the air

correlation coefficient of linear regression

gas constant

dimensionless space coordinate

Sherwood number

time

m

m^/s

m^/s

m^/s

kg/(m2s)

kg/m3

m

kg/mol

Pa

J/toolxK)

s

u^, U2 the lower and higher moisture contents in a test kg/kg

V moisture concentration in the air kg/m^

w moisture concentration in the tested materials, kg/m^

based on wet volume

H» y, 2 space coordinates

a critical length

m

m

p density, the dry wight of a body divided by wet kg/m^

volume

5 moisture diffusivity based on moisture concen- kg/m^

tration in the air

• relative humidity

•iiQ a relative humidity that is kept at constant value

during a series of test

•t a parameter defined in Eq(32)

T dimensionless time

subscript

au average value

initial value

D boundary value

Rbbreuiation

EMC equilibrium moisture content

FSP fiber saturation point

MC moisture content

RH relative humidity

I n wood and wood-based panels, moisture t r a n s p o r t i s a d i f f u s i o n process i n the hygroscopic moisture range. Knowledge o f d i f f u s i v i t y under such c o n d i -t i o n s i s a p r e r e q u i s i -t e f o r -t h e c a l c u l a -t i o n o f -t h e mois-ture -t r a n s p o r -t r a -t e i n any s p e c i f i c case. The cup method and s o r p t i o n method a r e t h e two most commonly used techniques i n chemical e n g i n e e r i n g and wood technology t o de-termine t h e d i f f u s i v i t y o f f l u i d s i n s o l i d s (Crank and Park, 1968, L i u Tong, 1986). These two methods are d i f f e r e n t i n s e v e r a l r e s p e c t s , among them the most i m p o r t a n t i s t h a t a steady d i f f u s i o n process i s employed i n the cup method w h i l e a t r a n s i e n t ( u n s t e a d y - s t a t e o r dynamic) s o r p t i o n process i s employed i n t h e s o r p t i o n method. I t has a l s o been r e p o r t e d (Comstock, 1963) t h a t d i f f u s i v i t i e s measured w i t h these two methods d e v i a t e to some e x t e n t .

The aim o f t h i s i n v e s t i g a t i o n i s t o study and compare t h e d i f f e r e n t aspects, p r i m a r i l y t h e measured d i f f u s i v i t y , o f these two methods. 2. THEORETICAL ASPECTS

Wood and wood based panels a r e a n i s o t r o p i c , and t h e i r moisture d i f f u s i v i t y are u s u a l l y c o n f i n e d t o u n i d i m e n s i o n a l . For a slab-formed body w i t h concen-t r a concen-t i o n - d e p e n d e n concen-t d i f f u s i v i concen-t y , concen-t h e equaconcen-tion o f u n i d i m e n s i o n a l d i f f u s i o n i s :

3w ^

j _ r aw)

at " 8x . ax ,

(1)

I n t h e above e q u a t i o n , t h e moisture 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 w can be replaced by t h e e q u i l i b r i u m moisture c o n c e n t r a t i o n i n t h e a i r v and t h e d i f f u s i v i t y £) by ^. This means t h a t t h e same moisture t r a n s p o r t process can be d e s c r i b e d by two d i f f e r e n t l y d e f i n e d c o n c e n t r a t i o n s and d i f f u s i v i -t i e s . These -two s e -t s o f q u a n -t i -t i e s can be conver-ted from one -t o ano-ther when t h e s o r p t i o n isotherm i s known, as w i l l be discussed i n Appendix 1 . Since t h e present study i s p r i m a r i l y made f o r t h e b u i l d i n g i n d u s t r y , d i f f u -s i v i t i e -s ba-sed on moi-sture c o n c e n t r a t i o n i n t h e a i r i -s o f main i n t e r e -s t here and a l l t h e measured d i f f u s i v i t i e s w i l l be presented on t h i s b a s i s . The d i f f u s i v i t i e s based on moisture 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 are given i n Appendix 3.

From t h e d i f f u s i o n e q u a t i o n , t h e o r i e s and equations have been developed f o r the cup and s o r p t i o n methods. As a b e g i n n i n g , a b r i e f review o f them i s probably necessary.

2.1 The cup method

I n the cup method, the d i f f e r e n c e o f water vapor c o n c e n t r a t i o n o r r e l a t i v e h u m i d i t y i n s i d e a cup and o u t s i d e i t d r i v e s m o i s t u r e t o d i f f u s e through a sample t h a t i s sealed a i r - t i g h t l y on the cup. F i g u r e 1 . When the d i f f u s i o n has l a s t e d f o r a s u f f i c i e n t l y long t i m e and the steady s t a t e o f m o i s t u r e d i f f u s i o n i s approached, the r e l a t i o n o f f l u x and the d i f f u s i v i t y can be express as:

c^dv

g - - 0— - constant

dx

1

dv =6 v-vo

(2) av

Sav i s the average d i f f u s i v i t y . I t has been proven by many research workers before t h a t moisture d i f f u s i v i t y i n wood i s dependent on m o i s t u r e concen-t r a concen-t i o n . The average d i f f u s i v i concen-t y i s d e f i n e d as:

r

>av

=

5 dv

V - V Q . V O

(3)

The average d i f f u s i v i t y can be obtained from a s i n g l e experiment w i t h Eq(2) when the s t e a d y - s t a t e f l u x g i s measured by weighing the cup p e r i o d i c a l l y . The moisture c o n c e n t r a t i o n i n s i d e the cup can be kept constant by p l a c i n g e i t h e r a s a l t s o l u t i o n o r a d r y i n g agent i n i t . F i g u r e 1 . The former i s c a l l e d the wet cup and the l a t t e r the dry cup.

Test s e t f o r cup method A: Sample B: V a p o r - t i g h t s e a l i n g C: Cover o f cup, p l e x i g l a s s D: S i l i c o n e grease s e a l i n g E: Cup, g l a s s F: S a l t s o l u t i o n o r d r y i n g agent

vo, $0 : Water vapor concent-r a t i o n and concent-r e l a t i v e h u m i d i t y i n s i d e t h e cup

V, 4? : Those o u t s i d e the cup F i g u r e 1 . Test s e t f o r the cup method.

I n the s o r p t i o n method, o r more s t r i c t l y speaking, i n a u n i d i m e n s i o n a l s o r p t i o n method, a s l a b sample t h a t i s sealed v a p o r - t i g h t l y on f o u r edges i s c o n d i t i o n e d t o e q u i l i b r i u m i n a c l i m a t e w i t h d e f i n i t e moisture concen-t r a concen-t i o n o r r e l a concen-t i v e h u m i d i concen-t y . As concen-t h e concen-t e s concen-t s concen-t a r concen-t s concen-t h e sample i s suddenly placed i n another c l i m a t e , F i g u r e 2. Since t h e moisture c o n c e n t r a t i o n i n the m a t e r i a l s w i s used f o r c a l c u l a t i o n i n such a case, t h e i n i t i a l and boundary c o n d i t i o n s o f the d i f f u s i o n equation E q ( l ) i s :

Initial Condition : w « Wj -a < x < a, t« 0

BoundwyCondition: w-w^,^ x»±a. t>0

The u n i d i m e n s i o n a l t r a n s i e n t d i f f u s i o n r a t e o f t h e moisture s o r p t i o n i n t o or o u t o f t h e sample i n t h e measurement i s recorded by weighing t h e sample at r e g u l a r time i n t e r v a l s . When moisture e q u i l i b r i u m i s reached, t h e avera-ge d i f f u s i v i t y can be approximaly c a l c u l a t e d w i t h (Crank, 1975, P.239):

Dav - 0,0492-i^ ( 4 )

( t ) i

Here ( t ) l / 2 i s t h e time taken when t h e f r a c t i o n o f sorbed moisture c o n t e n t L i s equal t o 1/2. Eq(4) i s d e r i v e d from the 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 t h e case o f constant 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 -v a r i e s w i t h moisture c o n c e n t r a t i o n , i t can p r o -v i d e an approximation t o the average d i f f u s i v i t y . Crank (1975, P.242) showed i n a g r a p h i c form how much t h e 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(4) d e v i a t e d from the r e a l average d i f f u s i v i t y when the d i f f u s i v i t y had a l i n e a r o r e x p o n e n t i a l depen-dency on c o n c e n t r a t i o n . I f t h e approximate average d i f f u s i v i t i e s o f an ad-s o r p t i o n and a d e ad-s o r p t i o n procead-sad-s between two c l i m a t e ad-s are c a l c u l a t e d w i t h E q ( 4 ) , then t h e i r mean i s a much b e t t e r approximation o f t h e average d i f f u -s i v i t i e -s (Crank, 1975, P.244):

Eq(4) and ( 5 ) are employed f o r t h e s o r p t i o n and t h r e e - d i m e n s i o n a l s o r p t i o n met- hods i n t h i s i n v e s t i g a t i o n . D i f f u s i v i t i e s so c a l c u l a t e d are the ones based on moisture 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 . They need t o be converted i n t o t h e d i f f u s i v i t i e s based on moisture c o n c e n t r a t i o n i n the a i r w i t h s o r p t i o n isotherms.

^ , w i : R e l a t i v e humidity and moisture c o n c e n t r a t i o n , a t which

the sample has i n t h e i n i t i a l been t r e a t e d t o e q u i l i b r i u m b e f o r e s o r p t i o n . , wb: Those i n t h e s o r p t i o n process, boundary c o n d i t i o n . A: Samples B: V a p o r - t i g h t s e a l i n g on f o u r edges

2.3 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

S o r p t i o n t e s t s can a l s o be made w i t h an unsealed sample such t h a t s o r p t i o n occurs i n t h r e e d i r e c t i o n s s i m u l t a n e o u s l y (Choong, 1962). The advantage o f t h i s method over t h e u n i d i m e n s i o n a l method i s i t s f a s t speed i n approaching e q u i l i b r i u m , and thus i t s t i m e - s a v i n g f o r doing experiments.

The e q u a t i o n o f t h e 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 f o r a n i s o t r o p i c wood and wood products i s :

^!:^.i.f D — 1 + — f D — 1 + — f D — 1

at "

ax.

' ^ a i ,

ay. ^ay. az. ^az.

InitialCoxdition : w - W j . t-0

(6)

x - ± a

BomuiaiyCondition : w^Wt,^ y a ± b . t>0

z - ± c

D e f i n e a dimensionless average moisture c o n c e n t r a t i o n as:

g ^ W b - W ^ ^ U b - ^ ( 7 )

S u b s t i t u t e E and the average d i f f u s i v i t i e s i n each d i r e c t i o n i n t o Eq(6):

The s o l u t i o n o f t h i s t h r e e dimensional equation i s equal t o the product o f the t h r e e i n d i v i d u a l s o l u t i o n s o f u n i d i r e c t i o n a l d i f f u s i o n equations assuming t h a t t h e dimensionless average s o r p t i o n a l moisture c o n c e n t r a t i o n i n t h e t h r e e c o o r d i n a t e d i r e c t i o n s are uncoupled. This assumption has been proved t o be v a l i d (Choong, 1962):

E - E x E y E ^

The d i f f u s i v i t y o f wood and wood-based panels a r e s i m i l a r i n two d i r e c t i o n 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 wood, and i n the two d i r e c t i o n s p a r a l l e l t o the panel s u r f a c e f o r wood-based p a n e l s ) . We may regard them as equal. When a sample i s so prepared t h a t t h e l e n g t h s o f i t i n these two d i -r e c t i o n s a-re i d e n t i c a l ( F i g u -r e 3 ) , we w i l l have:

F i g u r e 3. Sample o f t h e three-dimensional s o r p t i o n method

I f the sample were i n f i n i t i v e l y long i n the X and Y d i r e c t i o n s . Ex and Ey would be u n i t y , then a value o f E, say E-max , would be equal t o Ez:

?inax

E-max a t d i f f e r e n t s o r p t i o n times can be d e r i v e d by e x t r a p o l a t i o n . Prepare s e v e r a l samples w i t h d i f f e r e n t l e n g t h s i n X and Y d i r e c t i o n s , p l o t t h e i r E

values versus the r e c i p r o c a l o f t h e i r l e n g t h s a t a c e r t a i n measurement t i m e , and a s t r a i g h t l i n e w i l l be o b t a i n e d . F i g u r e 4. E x t r a p o l a t e t h e l i n e to 1/a equal t o zero which corresponds t o a sample o f i n f i n i t i v e l e n g t h s along X and Y, then t h e value o f E-max w i l l be d e r i v e d .

A E

1

F i g u r e 4. Dimensionless moisture c o n t e n t E a t a c e r t a i n time d u r i n g sorp-t i o n versus sorp-t h e r e c i p r o c a l o f sorp-t h e l e n g sorp-t h 1/a f o r samples o f sorp-t h e three-dimensional s o r p t i o n .

The E-max values a t d i f f e r e n t times w i l l p r o v i d e i n f o r m a t i o n o f ( t ) l / 2 i n Eq(4). The average d i f f u s i v i t y i n t h e Z d i r e c t i o n can be c a l c u l a t e d w i t h t h i s time q u a n t i t y . Then t h e average d i f f u s i v i t y i n t h e X and Y d i r e c t i o n s can be e v a l u a t e d s i m p l y . The value o f Ez i s always equal t o E-max no matter how long t h e samples are along X and Y s i n c e E^, Ey and E 2 are n o t

coupled. From t h e l i n e t h a t corresponds t o a s o r p t i o n time ( t ) l / 2 ( i n o t h e r words E-max = 0.5), a p o i n t corresponding t o a c r i t i c a l sample l e n g t h along X and Y, denoted as å, can be found a t which Ex=Ey=Ez. Thus f o r a sample having the l e n g t h o f å, t h e E value i s :

E-ExEyE^-CE"''»'')^ ( 9 )

å can be e v a l u a t e d from t h e above r e l a t i o n . The average d i f f u s i v i t i e s i n the X and Y d i r e c t i o n s can then be c a l c u l a t e d from t h e r e l a t i o n :

Dxav-Dyav- - X^zav (^0)

.C ,

The disadvantage o f t h e t h r e e d i m e n s i o n a l method i s t h e complicated c a l c u -l a t i o n procedure i n v o -l v e d , and more samp-les than i n t h e u n i d i m e n s i o n a -l s o r p t i o n method have t o be prepared and measured.

2.4 Concentration-dependent d i f f u s i v i t y

With t h e equations discussed p r e v i o u s l y , an average d i f f u s i v i t y i s ob-t a i n a b l e from one ob-t e s ob-t w i ob-t h e i ob-t h e r ob-t h e cup or s o r p ob-t i o n or ob-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. The t r u e o r concentration-dependent d i f f u s i v i t y can then be c a l c u l a t e d w i t h s e v e r a l average d i f f u s i v i t i e s from a s e r i e s o f t e s t s , when i n t h e t e s t i n g processes one c l i m a t e i s kept a t a constant value vo and another one v changes s u c c e s s i v e l y i n each t e s t . The average d i f f u s i -v i t y i n each t e s t i s :

6 a v - — ^ 6dv

V - V O J V Q

As the average d i f f u s i v i t y changes w i t h t h e upper boundary o f t h e i n t e g r a l

V t h a t v a r i e s i n each t e s t w h i l e t h e lower boundary vo i s a c o n s t a n t , i t i s

a f u n c t i o n o f v. D i f f e r e n t i a t i o n o f t h e average d i f f u s i v i t y w i t h respect t o

V w i l l r e s u l t i n t r u e d i f f u s i v i t y as a f u n c t i o n o f moisture c o n c e n t r a t i o n .

,.<i[a..x(v-vo)i_ dS^ (H)

dv *^ ^ dv

I t i s obvious t h a t i n order t o d e r i v e t h e t r u e d i f f u s i v i t y w i t h t h e above e q u a t i o n , t h e r e l a t i o n between t h e measured average d i f f u s i v i t y values and the c o r r e s p o n d i n g v a r i a b l e m o i s t u r e c o n c e n t r a t i o n v need t o be c o r r e l a t e d by c u r v e - f i t t i n g f i r s t . F i g u r e 5.

I n E q ( l l ) , t h e values o f t h e v a r i a b l e m o i s t u r e c o n c e n t r a t i o n v must vary i n the range which i s e i t h e r l a r g e r o r s m a l l e r than t h e constant moisture con-c e n t r a t i o n vo. I f V v a r i e s i n a range t h a t con-crosses vo, then t h e v values should be d i v i d e d a t t h e p o i n t vo i n t o two p a r t s , and E q ( l l ) can subse-q u e n t l y be a p p l i e d t o e i t h e r p a r t i n c a l c u l a t i n g t h e t r u e d i f f u s i v i t y .

J(Nilsson)

F i g u r e 5. Average d i f f u s i v i t i e s ( d o t s ) measured i n a s e r i e s o f t e s t s p l o t t e d versus t h e v a r y i n g r e l a t i v e h u m i d i t y and f i t t e d t o a c u r v e . The t r u e d i f f u s i v i t y ( d a r k l i n e ) from N i l s s o n ' s method i s d e r i v e d by t h e d i f f e r e n t i a t i o n o f t h a t curve. The d o t t e d l i n e i s the t r u 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 Stamm's method.

I n Sweden t h i s technique was f i r s t u t i l i s e d by N i l s s o n (1980), so i t w i l l be r e f e r r e d t o as N i l s s o n ' s method. For t h e cup method, t h i s means t h a t t h e moisture c o n c e n t r a t i o n i n s i d e t h e cup i s kept a t a constant value ( v o ) w h i l e t h e moisture c o n c e n t r a t i o n o u t s i d e changes s u c c e s s i v e l y i n each

t e s t . For s o r p t i o n and t h r e e - d i m e n s i o n a l s o r p t i o n t e s t s , t h e samples a r e always p r e c o n d i t i o n e d t o e q u i l i b r i u m i n a d e f i n i t e c l i m a t e (vo) and then set t o c l i m a t e s t h a t s u c c e s s i v e l y vary w i t h each new t e s t f o r s o r p t i o n t o take p l a c e .

For t h e cup method E q ( l l ) i s sometimes w r i t t e n i n another form. With t h e successive change o f c l i m a t e o u t s i d e t h e cup i n each t e s t o f t h e t e s t se-r i e s , t h e s t e a d y - s t a t e f l u x g a l s o changes c o se-r se-r e s p o n d i n g l y . g = 6 av V - V Q (12) g X L " 6 a v X ( V - V o ) S u b s t i t u t i o n o f Eq(12) i n t o E q ( l l ) r e s u l t s : dv dv (13)

The concentrationdependent d i f f u s i v i t y can then be deduced from d i f f e r e n -t i a -t i o n o f -t h e g - V c u r v e .

However, a few p o i n t s from experiments can be connected smoothly by s e v e r a l d i s t i n c t curves and t h e d i f f e r e n t i a t i o n o f these curves, as i s r e q u i r e d i n N i l s s o n ' s method, may d i f f e r t o some e x t e n t . Therefore a problem appears here as t o which curve i s t h e most proper one. As a f i r s t choice polynomial c o r r e l a t i o n i s a p p l i e d t o t h e data from t h e present study. I t has appeared t h a t i n some i m p o r t a n t cases such d i f f u s i v i t y curves have a p e c u l i a r shape.

While t h e same p o i n t s a r e c o r r e l a t e d w i t h e x p o n e n t i a l d i f f u s i v i t y exp r e s s i o n s l i k e Eq(14), t h e curves aexpexpear t o be s i m i l a r t o exp r e v i o u s s t u -d i e s o f some o t h e r researchers (e.g. B e r t e i s e n , 1984, an-d Svensson, 1987) and a r e consequently much more acceptable. F i g u r e 6.

200 4* > S 120 O 60 <:/jberboard(pprp) "ipineciangj Hdatlvt Hualdlty in

Figur 6. D i f f u s i v i t i e s from t h e s o r p t i o n method o f t h e present study c a l c u l a t e d by Stamm's method ( p o i n t s ) f i t t e d w i t h f o u r t h o r d e r p o l y -nomial ( d o t t e d ) and e x p o n e n t i a l ( d a r k ) curves.

For s o l i d wood, t h e c o r r e c t n e s s o f t h e e x p o n e n t i a l dependency o f d i f f u s i v i -t y on -t h e mois-ture c o n c e n -t r a -t i o n i n wood has been found and proved by seve-r a l seve-reseaseve-rch woseve-rkeseve-rs b e f o seve-r e , e.g. Simpson (1974). Rosen (1976) made such c o n c l u s i o n s a f t e r having summarized t h e preceding i n v e s t i g a t i o n s e x t e n s i v e -l y and made some experiment h i m s e -l f . B e r t e i s e n (1984) has shown t h e n e a r -l y e x p o n e n t i a l dependency o f t h e d i f f u s i v i t y on t h e moisture c o n c e n t r a t i o n i n the a i r f o r Scandinavian spruce. These two f i n d i n g s a r e c o n s i s t e n t because the d i f f u s i v i t i e s on these two bases a r e r e l a t e d v i a s o r p t i o n isotherms, which i s a sigmoid monotonously i n c r e a s i n g f u n c t i o n f o r wood. F i g u r e 15 i n Appendix.

Since wood-based panels c o n s i s t almost p u r e l y o f wood m a t e r i a l , t h e r e i s enough reason t o consider such e x p o n e n t i a l dependency being g e n e r a l l y t r u e a l s o f o r t h e panels. The d i f f u s i v i t i e s w i l l then be i n t h e form o f :

'av

— f

V - V o ' V o

dv

k ( v - v o )

(14)

Here do. Do, k and p a r e c o n s t a n t s t o be determined by experiment. From t h i s e q u a t i o n , t h e average d i f f u s i v i t y measured i n a t e s t can be expressed as:

With some a l g e b r a i c treatment o f Eq(15), we g e t :

l n f 6 a v X ( v - v „ ) 4 e " " ' l - l " f T l + '^>^^ ' ' ' '

From t h e measured average d i f f u s i v i t i e s i n a s e r i e s o f t e s t s , t h e values o f the c o n s t a n t s do and k can be determined w i t h Eq(16) by i t e r a t i v e r e g r e s -s i o n o f l e a -s t -square. The procedure i -s : Set t h e term do*exp(k*vo)/l< i n

the l e f t hand s i d e o f Eq(16) a t a f i r s t i n i t i a l l y estimated and, t h e r e -a f t e r , preceding v -a l u e , -and then from t h e me-asured s e v e r -a l p o i n t s ( v , cl-av) c a l c u l a t e t h e r e g r e s s i o n a l l i n e a r l i n e w i t h l e a s t square between ln(<(av*(v - vo) + (/b*exp(k*vo)/k) and v. The i n t e r c e p t and slope o f t h e l i n e w i l l be

ln(</o/k) and k.

Since Eq(16), l i k e E q ( l l ) , i s deduced from t h e i n t e g r a t i o n expression o f the average d i f f u s i v i t y , a r e s t r i c t i o n t o t h e i t e r a t i v e r e g r e s s i o n mentioned above i s t h a t a l l t h e v a r i a b l e moisture c o n c e n t r a t i o n v values are l a r -ger or s m a l l e r than t h e constant moisture c o n c e n t r a t i o n vo. I f vo l i e s among s e v e r a l v values they must be d i v i d e d i n t o two p a r t s a t vo, and t h e i t e r a - t i v e r e g r e s s i o n can then be a p p l i e d f o r e i t h e r p a r t .

To c a l c u l a t e t r u e d i f f u s i v i t y w i t h N i l s s o n ' s method t h e e x p e r i m e n t a l l y mea-sured ( ( a v , v ) p o i n t s should n o t be t o o few and should n o t d i s t r i b u t e i n a too narrow i n t e r v a l because i t i n v o l v e s t h e d i f f e r e n t i a t i o n o f t h e f i t t e d curves. Otherwise t h e p r e c i s i o n o f t h e c a l c u l a t e d d i f f u s i v i t i e s w i l l most probably be very low.

I n a d d i t i o n t o Nilsson's method t h e r e i s another approach s u i t a b l e f o r wood and wood p r o d u c t s , e n t i t l e d as Stamm's method here, which does n o t r e q u i r e so many p o i n t s t o t h e measured data, though i t i s a l s o l e s s reasonable t h e -o r e t i c a l l y than N i l s s -o n ' s meth-od. Acc-ording t -o Stamm ( S i a u , 1984, P.154), f o r both t h e s o r p t i o n and cup methods t h e measured average d i f f u s i v i t y w i l l be a p p r o x i m a t e l y equal t o t r u e d i f f u s i v i t y when t h e average d i f f u s i v i t y measured between two c l i m a t e s i s assigned t o a m o i s t u r e c o n t e n t u t h a t i s at t h e t w o - t h i r d s o f t h e i n t e r v a l o f t h e e q u i l i b r i u m lower ( u l ) and h i g h e r (u2) m o i s t u r e c o n t e n t s :

2

U = U , + - ( U 2 - U i ) ( 1 7 ) This approach has been j u s t i f i e d from t h e reasoning t h a t , f o r t h e s o r p t i o n

t e s t , t h e measured d i f f u s i v i t y i s an average one t h a t corresponds t o t h e moisture content u which i s t h e expression o f a time average f o r moisture content between t h e i n i t i a l MC (M^ here) and t h e boundary MC (M2 here) t h a t v a r i e s p a r a b o l i c a l l y w i t h time. For t h e cup method, t h e s t e a d y - s t a t e MC d i s t r i b u t i o n i n s i d e t h e sample i s a curve r a t h e r than a s t r a i g h t l i n e s i n c e the d i f f u s i v i t y i s concentration-dependent. Stamm has approximated t h e MC d i s t r i b u t i o n t o a p a r a b o l i c curve and deduced t h a t t h e space average MC between MC on t h e two s u r f a c e s o f t h e sample ( u i and u2 here) can be c a l c u -l a t e d w i t h Eq(17).

Stamm's method i s commonly used i n wood technology. With t h i s method a t r u e d i f f u s i v i t y value i s d i r e c t l y c a l c u l a t e d from a measured average d i f f u s i v i

-t y w i -t h no need f o r d i f f e r e n -t i a -t i o n . This makes -t h i s me-thod f r e e from -t h e requirement t o t h e number and d i s t r i b u t i o n o f t h e measured average d i f f u s i -v i t y .

These a r e t h e advantage o f Stamm's method over N i l s s o n * s . Stamm's method, however, i s e s s e n t i a l l y an e m p i r i c a l one w i t h o u t f i r m t h e o r e t i c a l b a s i s w h i l e N i l s s o n ' s method i s c o r r e c t from t h e t h e o r e t i c a l p o i n t o f view. But when t h e i n t e r v a l between u l and u2 i n Eq(17) i s n o t l a r g e , Stamm's method can n o t be f a r from c o r r e c t n e s s . Moreover, s i n c e i t i s l e s s s e n s i t i v e t o the measured data number and d i s t r i b u t i o n , t h i s method may be used t o check whether t h e r e s u l t s o b t a i n e d w i t h N i l s s o n ' s method c o n t a i n t o o much e r r o r or n o t . I f they do, then Stamm's method would d e f i n i t e l y g i v e b e t t e r r e -s u l t -s and -should con-sequently be u-sed alone.

Thus, w i t h Stamm's method when t h e average d i f f u s i v i t y has been c a l c u l a t e d from Eq(2) or E q ( 5 ) , i t can be regarded as t h e t r u e d i f f u s i v i t y D a t a moisture c o n t e n t from Eq(17). This moisture c o n t e n t corresponds t o a r e l a -t i v e h u m i d i -t y o b -t a i n a b l e from -t h e s o r p -t i o n iso-therm o f -t h e -t e s -t e d m a -t e r i a l . Since t h e moisture d i f f u s i v i t y i s regarded t o be e x p o n e n t i a l l y dependent on RH o r MC as expressed i n Eq(14), t h e r e i s a r e l a t i o n :

ln5-In6o + kv

(18)

InD-lnDo + pw

Erom s e v e r a l t r u e d i f f u s i v i t y and moisture c o n c e n t r a t i o n values o b t a i n e d w i t h Stamm's method i n a s e r i e s o f t e s t s , a l i n e a r r e g r e s s i o n between I n o and V can be made a l s o w i t h l e a s t square. By doing so, t h e constants oo and k i n t h e d i f f u s i v i t y expression can be determined.

Stamm's method i s n o t regarded t o be v a l i d f o r c a l c u l a t i n g t h e l o n g i t u d i n a l d i f f u s i v i t i e s o f s o l i d wood ( S i a u , 1984, P.154), so i t w i l l n o t be u t i l i z e d i n t h i s r e p o r t i n such cases.

I n t h e p r e s e n t i n v e s t i g a t i o n , N i l s s o n ' s method i s employed f o r t h e measured data from t h e d r y cups and wet cups. Whereas t h e t r u e d i f f u s i v i t i e s from the d r y cups seem t o be good, t h e ones from t h e wet cups appear t o be much worse. This i s because t h e c o n s t a n t moisture c o n c e n t r a t i o n vo ( c o r r e s p o n -d i n g t o RH=0.66) l i e s i n t h e mi-d-dle o f t h e v a r y i n g moisture c o n c e n t r a t i o n v i n t h e c l i m a t e used f o r t h e wet cup, and t h e r e are o n l y t h r e e n a r r o w l y d i s -t r i b u -t e d V values ( c o r r e s p o n d i n g -t o RH=0.80, 0.90 and 0.93) l a r g e r -than vo and one v value s m a l l e r than vo. The t h r e e v values l a r g e r than vo a r e ob-v i o u s l y t o o near t o each o t h e r and t o o few i n number t o make r e l i a b l e

c u r v e - f i t t i n g . Thus t h e r e s t r i c t i o n s o f N i l s s o n ' s method seemingly exclude t h i s method t o be u t i l i z e d w i t h proper r e l i a b i l i t y f o r t h i s case. This has been proven t o be t r u e , as w i l l be discussed i n s e c t i o n 4.2 Wet cups.

The measured data from t h e s o r p t i o n and 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 are i n t h e same s i t u a t i o n as those o f t h e wet cup method. Since t h e em-ployed c l i m a t e s i n t h e t e s t s e r i e s a r e almost e x a c t l y i d e n t i c a l t o those f o r t h e wet cups w i t h vo corresponding t o RH = 0.65 and v corresponding t o RH = 0.31, 0.80, 0.90 and 0.93, r e s p e c t i v e l y , N i l s s o n ' s method i s n o t u t i -l i s e d t o these data. Stamm's method i s emp-loyed f o r a -l -l f o u r e x p e r i m e n t a -l methods. Eor t h e data measured w i t h t h e d r y cup, t h e c a l c u l a t e d d i f f u s i v i -t i e s from S-tamm's me-thod and N i l s s o n ' s me-thod a r e compared.

2.5 Regular regime a n a l y s i s

Schoeber (1976) developed a method t o analyse a s o r p t i o n o r a d r y i n g pro-cess - t h e r e g u l a r regime a n a l y s i s . According t o Schoeber's t h e o r y , a sorp-t i o n process i s d i v i d e d i n sorp-t o sorp-two d i s sorp-t i n c sorp-t p e r i o d s : an i n i sorp-t i a l p e n e sorp-t r a sorp-t i o n p e r i o d and a subsequent r e g u l a r regime p e r i o d . I n t h e i n i t i a l p e n e t r a t i o n p e r i o d , t h e c o n c e n t r a t i o n change a t t h e center o f t h e m a t e r i a l i s n e g l i -g i b l e and t h e c a l c u l a t i o n o f t h e mass t r a n s f e r r a t e i n a s e m i - i n f i n i t e me-dium can be used. I n t h e r e g u l a r regime, t h e c o n c e n t r a t i o n p r o f i l e o f mois-t u r e i s o n l y dependenmois-t on and i s c h a r a c mois-t e r i s mois-t i c o f mois-t h e s o r b a mois-t e m a mois-t e r i a l , i r r e s p e c t i v e o f t h e i n i t i a l c o n d i t i o n . A r e g u l a r regime c o n t a i n s a l l t h e i n f o r m a t i o n concerning t h e c a l c u l a t i o n o f moisture t r a n s p o r t r a t e . For ma-t e r i a l s , e s p e c i a l l y f o r ma-those i n which d i f f u s i v i ma-t i e s are s ma-t r o n g l y dependenma-t on c o n c e n t r a t i o n , a r e g u l a r regime a n a l y s i s o f a s i n g l e s o r p t i o n process w i l l be a b l e t o g i v e t h e concentration-dependent d i f f u s i v i t y . Besides t h e r e g u l a r regime a n a l y s i s a l s o provides a powerful means f o r d r y i n g r a t e c a l -c u l a t i o n s where t h e very e f f e -c t i v e , -c o n v e n t i o n a l method o f -c h a r a -c t e r i s t i -c d r y i n g curves f a i l s t o work f o r such types o f m a t e r i a l s .

To use r e g u l a r t h e regime a n a l y s i s 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 , dimensional treatment o f v a r i a b l e s i s necessary.

Dimensionless (reduced) time

D x t

where D* i s an a r b i t r a r y value o f d i f f u s i v i t y . I t s value may be taken as u n i t y .

Dimensionless space c o o r d i n a t e X

r

-Dimensionless (reduced) d i f f u s i v i t y

Then t h e d i f f u s i o n equation expressed w i t h these dimensionless variab-les w i l l be:

ImtialCondition : w«Wj. x-O

BondwyCondition:

w « W 5 ,

r « ± l , T>0

I n order t o describe t h e r e g u l a r regime Schoeber d e f i n e d s e v e r a l q u a n t i -t i e s : Flux parameter:

gxr

8 p " ^

(20) Average dimensionless d i f f u s i v i t y : D « v - -

—

D,dw

^tv-WbJwb (21)

Note t h a t t h e upper boundary o f t h e i n t e g r a l i s average i n s t e a d o f i n i t i a l c o n c e n t r a t i o n .

Average Sherwood number:

2xgp

Shav

(Wav-Wb) (22)

The c r i t e r i o n

dln( 1-É)

(23)

The d e t e r m i n a t i o n o f t h e t r a n s i t i o n p o i n t from p e n e t r a t i o n p e r i o d t o regu-l a r regime can be made by r e g a r d i n g t h a t t h e c r i t e r i o n C r t i n t h i s p o i n t i s i d e n t i c a l f o r both p e r i o d s . While t h e c r i t e r i o n i n t h e r e g u l a r regime i s given by Eq(23), i t s value i n t h e p e n e t r a t i o n p e r i o d i s equal t o :

C n ~

( 2 4 )

which i s deduced from s o r p t i o n r e l a t i o n s i n s e m i - i n f i n i t e medium.

A f t e r e x t e n s i v e analyses o f v a r i o u s forms o f c o n c e n t r a t i o n dependencies o f d i f f u s i v i t i e s , Schoeber was able t o prove t h a t i n t h e r e g u l a r regime, t h e r e l a t i o n o f t h e average Sherwood number Shav and t h e c r i t e r i o n C r t i s near-l y t h e same f o r a near-l near-l cases. Figure 7. This important f i n d i n g made i t

p o s s i b l e t o c a l c u l a t e t h e d i f f u s i v i t y from t h e s o r p t i o n r a t e .

Now from t h e data o f t h e s o r p t i o n r a t e ( f l u x parameter), which i s

ob-t a i n a b l e from p e r i o d i c a l weighing o f samples i n s o r p ob-t i o n , ob-t h e c r i ob-t e r i o n can be c a l - c u l a t e d from i t s d e f i n i t i o n . The f l u x parameter i s equal t o :

8p

dw

av

dt

(25) Shau 4 6 The Criterion 10 Crt

F i g u r e 7. Average Sherwood number versus the c r i t e r i o n f o r m a t e r i a l s whose d i f f u s i v i t y posseses a ( 1 ) e x p o n e n t i a l ^ ( 2 ) power o r ( 3 ) l i n e a r c o n c e n t r a t i o n dependency (Schoeber, 1976).

From the values o f t h e c r i t e r i o n , t h e average Sherwood number can be read from Figure 7. Then from Eq(22), t h e average dimensionless d i f f u s i v i t y i s o b t a i n a b l e :

D

2xgp

rav (W^-Wb)XShav (26)

The reduced d i f f u s i v i t y i s then equal t o :

d f 2 x g p ]

₍₂₇₎

And f i n a l l y the concentration-dependent d i f f u s i v i t y i s c a l c u l a t e d w i t h :

D-DfXD*

₍₂₈₎

The r e l a t i o n between t h e c r i t e r i o n and t h e s l i g h t l y when the d i f f u s i v i t y has a power, on moisture c o n c e n t r a t i o n , as can be seen i i s unknown, Schoeber proposed t h a t t h e r e l a used as a good a p p r o x i m a t i o n . However, s i n e i s known t o be approximately an e x p o n e n t i a l f o r e x p o n e n t i a l c o n c e n t r a t i o n dependency wi was a l s o proposed by Schoeber f o r such a ca

average Sherwood number d i f f e r s e x p o n e n t i a l o r l i n e a r dependency n F i g u r e 7. When the dependency t i o n f o r power dependency be e moisture d i f f u s i v i t y i n wood

f u n c t i o n , t h e Shav-Crt curve 11 be u t i l i z e d i n t h i s s t u d y , as se.

3. EXPERIMENTAL

Experiments w i t h t h e cup method, s o r p t i o n method and t h r e e - d i m e n s i o n a l met-hod have been performed t o i n v e s t i g a t e and compare these techniques. 3.1 M a t e r i a l s , methods and t e s t c l i m a t e s

Wood-based panels a r e mainly used f o r t h i s i n v e s t i g a t i o n : a h a l f - h a r d

f i b e r b o a r d , a UFglue p a r t i c l e b o a r d and a PFglue spruce plywood. Pine ( P i -nus s i l v e s t r i s ) sapwood i s a l s o used i n order t o compare t h e r e s u l t s o f t h e present i n v e s t i g a t i o n w i t h those o f Svensson (1987) who s y s t e m a t i c a l l y mea-sured moisture d i f f u s i v i t y o f p i n e w i t h t h e cup method. The t e s t m a t e r i a l s and t h e i r d e n s i t i e s a r e l i s t e d i n Table 1.

With t h e cup method, o n l y t h e d i f f u s i v i t i e s p e r p e n d i c u l a r t o panel s u r f a c e are measured f o r t h e t h r e e wood-based panels. With t h e t h r e e - d i m e n s i o n a l method d i f f u s i v i t i e s i n d i f f e r e n t d i r e c t i o n s are measured b u t o n l y f o r f i b e r b o a r d and p a r t i c l e b o a r d samples.

The samples o f t h e s o r p t i o n and three-dimensional s o r p t i o n methods a r e d i v i d e d i n t o two groups, group A and group B, i n order t o reduce t h e t o t a l time f o r experiment. There a r e twelve samples, f o u r i n each s o r p t i o n d i r e c -t i o n o f each m a -t e r i a l i n bo-th groups.

Both t h e d r y cups and wet cups are used f o r t h e cup method, and f o u r samp-l e s o f each m a t e r i a samp-l a r e measured w i t h both types o f cups. For t h e d r y cup, a d r y i n g agent, magnesium p e r c h l o r a t e Mg(C104)2, i s placed i n t h e cup which gives zero r e l a t i v e h u m i d i t y . For wet cups, a water s o l u t i o n o f sodium n i t r i t e NaN02 i s c o n t a i n e d i n s i d e t h e cup which keeps a r e l a t i v e humidity of 0.66 a t 20 °C.

The experiments are made i n s e v e r a l c l i m a t e rooms a t t h e Swedish I n s t i t u t e f o r Wood Technology Research. One room i s kept a t RH = 0.65, another i s v a r i e d between RH = 0.31 and 0.93. A t h i r d room a t RH = 0.80 has a l s o been used. The wood and panel m a t e r i a l s a r e s t o r e d i n a wharehouse b e f o r e they are made i n t o samples. A f t e r t h e samples a r e prepared they a r e p u t i n t h e c l i m a t e room w i t h RH=0.65 a t 20''C u n t i l moisture e q u i l i b r i u m , which i s t h e s t a r t i n g c l i m a t e f o r t h e cup, s o r p t i o n and 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. During t h e experiment, t h e temperature i s c o n t r o l l e d a t 20 'C a l l the time and t h e experiments are made a t t h e r e l a t i v e h u m i d i t i e s and c o r r e -sponding moisture c o n c e n t r a t i o n s as g i v e n i n Table 2.

Table 1. Tested m a t e r i a l s .

M a t e r i a l Density (kg/m^)

( a b s o l u t e d r y ) Thickness Diameter Sample s i z e (mm) CUP METHOD 1. H a l f - h a r d f i b e r b o a r d (wet process) 690 12.1 78 2. UE-glue p a r t i c l e b o a r d 610 12.0 78 3. PE-glue plywood 420 12.0 78 4. Pine sapwood 520 10.0 78 ONE-DIMENSIONAL SORPTION METHOD 1. H a l f - h a r d f i b e r b o a r d 690 (wet process) 2. UE-glue p a r t i c l e b o a r d 610 3. PE-glue plywood 420 4. Pine sapwood 520

Thickness Length Width 12.1 80 60 12.0 80 60 12.0 80 60 10.0 78 (Diameter) THREE-DIMENSIONAL SORPTION METHOD 1. Half-hard f i b e r b o a r d (wet process) 2. UE-glue p a r t i c l e b o a r d (Eive dimensions) 690 12.1 s i z e 1 : 200 2: 100 3: 66.7 610 12 4: 50 5: 40 Note 1. The h a l f h a r d f i b e r b o a r d i s manufactured i n a wet process w i t h

-out a d d i t i o n o f adhesives.

2. UE and PE a r e a b b r e v i a t i o n s o f phenolformaldehyde and u r e a f o r m a l -dehyde r e s i n s .

3. The pine samples a r e o b t a i n e d from Barbro Svensson. They are sap-wood o f k i l n - d r i e d pine f e l l e d i n Småland f o r t a n g e n t i a l and r a d i a l d i f f u s i o n (category " I S " and "4S 2" i n her c l a s s i f i c a t i o n ) and i n Västerbotten f o r l o n g i t u d i n a l d i f f u s i o n (40S Eb). R a d i a l d i f f u s i -v i t y i s measured only w i t h t h e s o r p t i o n method.

Table 2. Experimental c l i m a t e s . Temperature: 20"C

R e l a t i v e h u m i d i t y :

ONE- AND TREE-DIMENSIONAL CUP METHODS SORPTION METHODS

V V

Group A Group B Dry cup Wet cup

0.65 = p r e c o n d i t i o n = 0.65 0.31 0.31 \ V V V 0.31 0.80 0.65 0.80 0.65 0.65 0.90 0.90 0.90 0.93 0.93 0.93 (RH i n s i d e (RH i n s i d e 0.65 cup i s 0) cup i s 0.66)

The a c c u r a c i e s o f t h e temperature and r e l a t i v e h u m i d i t i e s a r e w i t h i n ± 0.5°C and ± 0.02, r e s p e c t i v e l y . The a i r v e l o c i t y i s m a i n t a i n e d a t

1.4 m/s. The c l i m a t e f l u c t u a t e s s l o w l y round t h e predetermined values w i t h i n t h e above boundaries i n t h e experiments. The accuracy ranges are d e t e r -mined by t h e design o f t h e c o n t r o l system o f t h e c l i m a t e rooms, and mea-sured s e p a r a t e l y by thermo-hygrometers, which a r e c a r e f u l l y c a l i b r a t e d by a psycrometer f o r each r e l a t i v e h u m i d i t y .

3.2 Sample p r e p a r a t i o n and t e s t procedure

The samples o f t h e cup method are worked o u t i n a d i s k form. Then they a r e placed on t h e eaves on t h e hole i n a p l e x i g l a s s cover and sealed w i t h a very f l e x i b l e m a t e r i a l , which i s a k i n d o f s y n t h e t i c elastomer w i t h o u t s o l -vent, c a l l e d EC-5313, manufactured by 3 M, F i g u r e 1. Each p l e x i g l a s s cover has a c i r c u l a r s l o t on i t . When t h e cover i s p u t upon t h e glass cup t h e t o p edge o f t h e cup i s r i g h t i n s e r t e d i n t o t h e s l o t , as shown i n Figure 1. To secure t h e s e a l i n g between t h e cover and t h e cup, a s i l i c o n e - b a s e d vacuum grease i s spread i n t h e s l o t before t h e i n s e r t i o n o f t h e cup t o p edge. When a d r y i n g agent o r s a l t s o l u t i o n has been f i l l e d i n t o t h e cup, t h e cover i s fastened on t h e cup w i t h two rubber bands. This k i n d o f cup i s borrowed from Barbro Svensson who used them b e f o r e i n t h e Dept. o f B u i l d i n g Mate-r i a l s , t h e Royal I n s t i t u t e o f Technology i n Stockholm.

The samples o f t h e s o r p t i o n method and t h r e e - d i m e n s i o n a l method a r e sawn i n t o t h e s i z e s given i n Table 1. The ones f o r t h e t h r e e - d i m e n s i o n a l method need n o t t o be sealed. The ones f o r t h e s o r p t i o n method are sealed w i t h aluminium f o i l s adhered t o t h e samples w i t h neoprene g l u e , which has been proved t o be a very e f f e c t i v e v a p o r - t i g h t s e a l i n g ( L i u Tong, 1987). The s e a l i n g i s made i n such a way t h a t s o r p t i o n can occur o n l y i n one d i r e c -t i o n , e i -t h e r p e r p e n d i c u l a r l y -t o -t h e panel s u r f a c e o r i n one o f -t h e o -t h e r two p a r a l l e l d i r e c t i o n s f o r panel samples. The pine samples a r e t h e same i n shape and s i z e as those used i n t h e cup method, and t h e s e a l i n g i s adhered to t h e edges o f t h e disk-formed samples.

The experiments were made between A p r i l and November, 1987. The samples o f the cup method were placed i n a c l i m a t e room kept a t a constant c l i m a t e and then weighed p e r i o d i c a l l y , once o r t w i c e a day. The weights and weight changes were recorded. When the weight change r a t e s o f a l l samples had been constant f o r some time, t h e cups were moved t o another c l i m a t e t o s t a r t a new t e s t .

The samples o f t h e s o r p t i o n and three-dimensional s o r p t i o n methods are mea-sured i n a s i m i l a r way t o t h e cup method. The samples a r e p r e c o n d i t i o n e d a t RH = 0.65 u n t i l moisture e q u i l i b r i u m , which i s judged by t h a t t h e i r weights ceased t o vary w i t h t i m e . Then they a r e p u t i n t o another c l i m a t e , t h e i r weights are measured r e g u l a r l y u n t i l e q u i l i b r i u m i s approached again. The samples a r e then p u t back i n t h e c l i m a t e w i t h RH = 0.65 and t h e i r weight measured p e r i o d i c a l l y u n t i l e q u i l i b r i u m . This process goes on and on t o t h e end o f t h e experiment. The purpose o f using a c l i m a t e w i t h RH = 0.65 a f t e r every other c l i m a t e i s , f i r s t t o compare t h e d i f f e r e n c e o f d i f f u s i v i t i e s measured from a d s o r p t i o n and d e s o r p t i o n ; secondly t o o b t a i n t h e average d i f f u s i v i t y between two c l i m a t e s w i t h higher p r e c i s i o n by E q ( 5 ) . The balan-ce used i n a l l t h e measurements has a accuracy o f 0.01 g.

Views o f a t e s t room w i t h square samples f o r s o r p t i o n methods and c i r c u l a r samples f o r cup methods.

4. EXPERIMENTAL RESULTS: DIFFUSIVITY BASED ON MOISTURE CONCENTRATION IN THE AIR

From the data accumulated i n t h e experiment, d i f f u s i v i t i e s based on moist u r e c o n c e n moist r a moist i o n bomoisth i n moist h e a i r and i n moisthe moist e s moist e d m a moist e r i a l s a r e c a l c u l a -ted. Whereas t h e former a r e presented i n t h i s s e c t i o n t o serve t h e b u i l d i n g i n d u s t r y , the l a t t e r a r e i n c l u d e d i n Appendix 3. The r e s u l t s a r e expressed i n t h e forms o f graphs as w e l l as t a b l e s . But f i r s t o f a l l , b e f o r e t h e c a l -c u l a t i o n , s o r p t i o n isotherms o f t h e m a t e r i a l s a r e determined t o a i d t h e c a l c u l a t i o n s o f d i f f u s i v i t i e s on t h e two bases, which i s g i v e n i n Appen-dix 1 .

4.1 Dry cups

The s t e a d y - s t a t e f l u x from d r y cup measurements and corresponding average d i f f u s i v i t i e s c a l c u l a t e d w i t h Eq(2) a r e l i s t e d i n Table 3.

Table 3. Steady-state m o i s t u r e f l u x e s and average d i f f u s i v i t i e s from d r y cup t e s t (RH i n s i d e the cup i s 0 ) .

Fluxes (E-7, kg/m2*s ) R e l a t i v e h u m i d i t y o u t s i d e cups 0.31 0.65 0.90 0.93 1. Fiberboard 2.54 6.19 9.43 9.97 2. P a r t i c l e b o a r d 2.02 5.09 8.27 8.85 3. Plywood 0.217 0.667 1.22 1.36 4. Pine, t a n g e n t i a l 0.72 2.65 5.27 5.98 5. Pine, l o n g i t u d i n a l 16.3 49.3 103. 111 Average d i f f u s i v i t y (E-6, R e l a t i v e h u m i d i t y o u t s i d e cups 0.31 0.65 0.90 0.93 1. Fiberboard 0.575 0.668 0.734 0.752 2. P a r t i c l e b o a r d 0.450 0.540 0.639 0.662 3. Plywood 0.0487 0.0714 0.0949 0.102 4. Pine, t a n g e n t i a l 0.135 0.236 0.349 0.372 5. P i n e , l o n g i t u d i n a l 3.06 4.70 6.65 6.92

Both Stamm's and N i l s s o n ' s methods are a p p l i c a b l e t o t h e average d i f f u s i v i -t y da-ta i n Table 3 s i n c e -the r e l a -t i v e h u m i d i -t y and mois-ture con-ten-t a -t one s u r f a c e o f t h e samples ( i n s i d e t h e cups) a r e always z e r o .

The e q u i l i b r i u m moisture c o n t e n t s o f t h e t e s t e d m a t e r i a l s a t every r e l a t i v e h u m i d i t y i n Table 3 a r e c a l c u l a t e d w i t h t h e i r s o r p t i o n isotherm equations i n Appendix 2. Corresponding t o the MC d i f f e r e n c e between the two s u r f a c e s o f a sample, a moisture c o n t e n t i s c a l c u l a t e d w i t h Eq(17) a t which the mean value o f t h e average d i f f u s i v i t i e s becomes approximately t h e t r u e d i f f u s i -v i t y . From t h i s moisture content an e q u i l i b r i u m r e l a t i -v e h u m i d i t y i s

de-r i v e d w i t h t h e s o de-r p t i o n i s o t h e de-r m a g a i n . The de-r e l a t i v e h u m i d i t i e s and code-rde-re- corre-sponding t r u e d i f f u s i v i t i e s o b t a i n e d i n t h i s way a r e l i s t e d i n Table 4. Table 4. D i f f u s i v i t y from d r y cup c a l c u l a t e d w i t h Stamm's

method ( u n i t : E-6, m2/s) RH F i b e r - RH P a r t i c l e - RH PIywood RH Pine board board PIywood tang. l o n g . 0.138 0.575 0.156 0.450 0.168 0.0487 0.179 0.135 3.06 0.356 0.668 0.386 0.540 0.432 0.0714 0.436 0.236 4.70 0.636 0.734 0.672 0.639 0.729 0.949 0.719 0.349 6.65 0.677 0.752 0.712 0.662 0.772 0.102 0.759 0.372 6.92

From t h e data i n Table 4, t h e expressions o f d i f f u s i v i t i e s a r e o b t a i n e d by c u r v e - f i t t i n g w i t h Eq(18).

By means o f N i l s s o n ' s method and the i t e r a t i v e r e g r e s s i o n Eq(16) an expres-s i o n o f the d i f f u expres-s i v i t y w i t h e x p o n e n t i a l c o n c e n t r a t i o n dependency i expres-s a l expres-s o d e r i v e d from t h e average d i f f u s i v i t y data i n Table 3. The d i f f u s i v i t y ex-pressions o b t a i n e d both by Stamm's and N i l s s o n ' s methods are l i s t e d i n Table 5.

Table 5. D i f f u s i v i t y expressions from d r y cup method (20°C) (Relevent f o r RH from 0.31 t o 0.93).

Expression:

8 = 806'^

Q: c o r r e l a t i o n c o e f f i c i e n t

D i f f u s i v i t y c o r r e l a t e d w i t h D i f f u s i v i t y c o r r e l a t e d w i t h E q ( l 8 ) from data c a l c u l a t e d Eq(16) from data c a l c u l a t e d by Stamm's method by N i l s s o n ' s method

do k Q do k Q (E-8, m2/s) (E-8, m2/s) 1. F i b e r b o a r d 54.77 27.50 0.984 57.62 23.48 0.988 2. P a r t i c l e - 40.91 39.17 0.998 43.83 34.34 0.994 board 3. Plywood 4.089 68.56 0.996 2.335 103.0 0.983 4. Pine, 10.38 99.02 0.993 11.28 95.94 0.993 t a n g e n t i a l 5. Pine, 236.5 86.57 0.997 l o n g i t u d i n a l

Erom t h e expressions i n Table 5, d i f f u s i v i t y curves are p l o t t e d i n Eigure 8a, b. The curves i n Eigure 8a a r e d i r e c t l y f i t t e d from t h e measured p o i n t s from Stamm's method w h i l e t h e curves i n Eigure 8b are o b t a i n e d w i t h N i l s -son's method.

To compare t h e d i f f u s i v i t i e s c a l c u l a t e d w i t h Stamm's and N i l s s o n ' s methods the curves i n Eigure 8a, b a r e p l o t t e d t o g e t h e r i n Eigure 8c. We can see t h a t d i f f u s i v i t i e s from these two methods d i f f e r s t o a c e r t a i n e x t e n t i n slopes. But t h e i r order o f magnitude f o r a l l t h e samples are n e a r l y t h e same.

80 ^ 70 E ^ 60 I UJ > 50 20 10 O plywood (perp) 10 20 30 40 50 60 70 BO 90 100 Relative Humidity (X) V Nilsson s method 30 40 5Ö 60 70 Relative Humidity (%) 80 90 100 120 110 100 90 BO 70 60 50 40 30 20 10 O - : Stamm's method : Nilsson s method ly,woodlperP| 10 20 30 40 50 60 70 80 90 100 Relative Humidity (%) V

F i g u r e 8. D i f f u s i v i t i e s from d r y cups c a l c u l a t e d w i t h Stamm's and w i t h N i l s s o n ' s methods versus r e l a t i v e h u m i d i t y .

4.2 Wet cups

The s t e a d y - s t a t e f l u x e s and t h e average d i f f u s i v i t i e s from t h e wet cup mea-surements c a l c u l a t e d w i t h Eq(2) are l i s t e d i n Table 6.

Table 6. Steady-state f l u x e s and average d i f f u s i v i t i e s from the wet cup t e s t (RH i n s i d e t h e cups i s 0.66). Eluxes (E-7, kg/m2*s) R e l a t i v e humidity o u t s i d e cups 0.31 0.80 0.90 0.93 1. Eiberboard 3.60 1.56 2.74 3.16 2. P a r t i c l e b o a r d 3.10 1.39 2.47 2.89 3. Plywood 0.328 0.171 0.353 0.445 4. Pine, t a n g e n t i a l 1.71 0.993 1.83 2.20 5. Pine, l o n g i t u d i n a l 33.3 17.3 34.4 40.7 Average d i f f u s i v i t y (E-6, m2/s) R e l a t i v e humidity o u t s i d e cups 0.31 0.80 0.90 0.93 1. Eiberboard 0.722 0.784 0.801 0.823 2. P a r t i c l e b o a r d 0.612 0.687 0.711 0.740 3. Plywood 0.065 0.0851 0.102 0.115 4. Pine, t a n g e n t i a l 0.283 0.411 0.442 0.474 5. Pine, l o n g i t u d i n a l 5.52 7.20 8.30 8.77

In t h e same way as f o r t h e d r y cups, t r u e d i f f u s i v i t i e s measured w i t h t h e wet cups are c a l c u l a t e d w i t h Stamm's method and t h e r e s u l t s are l i s t e d i n

Table 7.

Table 7. D i f f u s i v i t y c a l c u l a t e d from Stamm's method ( u n i t : E-6, m^/s).

RH Eiber- RH P a r t i c l e - RH Plywood RH Pine

board board tang.

0.556 0.722 0, .561 0.612 0.565 0.0652 0.562 0.283 0.758 0.784 0, .760 0.687 0.759 0.0851 0.759 0.411 0.836 0.801 0. .838 0.711 0.838 0.102 0.840 0.442 0.859 0.823 0, .864 0.740 0.870 0.115 0.866 0.474

With t h e r e g r e s s i o n method o f Eq(18), an expression o f t h e d i f f u s i v i t y w i t h e x p o n e n t i a l c o n c e n t r a t i o n dependency i s d e r i v e d f o r each t e s t e d m a t e r i a l from t h e data i n Table 7 and i s given i n Table 8.

Table 8. D i f f u s i v i t y expressions c o r r e l a t e d w i t h Eq(18) from data c a l c u l a t e d by Stamm's method f o r wet cups (20"C).

Expression:

8

Q: c o r r e l a t i o n c o e f f i c i e n t ^•o (E-8, m2/s) (E-3) k Q 1. Fiberboard 57.76 23.48 0. 989 2. P a r t i c l e b o a r d 43.83 34.34 0. 994 3. Plywood 2.335 103.0 0. 982 4. Pine ( t a n g ) 11.28 95.95 0 993

D i f f u s i v i t y curves drawn according t o t h e expressions i n Table 8 and t h e d i f f u s i v i t y data i n Table 7 are p l o t t e d i n F i g u r e 9. The curves from d r y cups c a l c u l a t e d w i t h Stamm's method i n Figure 8a a r e a l s o r e p l o t t e d i n Figure 9 t o make comparisons between t h e wet cup and d r y cup. I t i s c l e a r t h a t t h e d i f f u s i v i t i e s measured w i t h t h e two cup methods a r e very much s i -m i l a r . There a r e so-me d i f f e r e n c e s , probably caused by t h e e r r o r i n t h e - mea-surement, b u t they a r e s m a l l . f -F i g u r e 9. 1 0 0 90 80 o) 7 0 CD 50 10 3 0 ?.o 10 Stamm's method : wet cup •• • : dry cup ^ ^ ^ ^ WwoodlperP' 10 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 Relative Humidity (X) V

D i f f u s i v i t i e s measured w i t h wet cups (dark l i n e ) and dry cups ( d o t t e d l i n e ) , both c a l c u l a t e d w i t h Stamm's method. The p o i n t s are measured data o f t h e wet cup.

Since t h e r e l a t i v e humidity i n s i d e t h e cup i s 0.66, o n l y t h e average d i f f u -s i v i t y mea-sured a t t h e RH o f 0.80, 0.90 and 0.93 can be u-sed t o c a l c u l a t e t r u e d i f f u s i v i t y w i t h N i l s s o n ' s method. N i l s s o n ' s method w i t h t h e i t e r a t i v e r e g r e s s i o n was a l s o employed t o t h e data measured a t these t h r e e RH i n

Table 6. The r e s u l t a n t d i f f u s i v i t y curves showed r e l a t i v e l y l a r g e d i f f e -rence t o the ones from t h e d r y cup a l s o c a l c u l a t e d w i t h N i l s s o n ' s method, compared t o t h e d i f f u s i v i t i e s from t h e d r y and wet cups c a l c u l a t e d from Stamm's method ( F i g u r e 9 ) . This, however, should most probably be a t t r i -buted t o t h e r e l a t i v e l y l a r g e e r r o r i n v o l v e d when N i l s s o n ' s method i s app-l i e d t o t h e few data o f t h e wet cup. As we know, c u r v e - f i t t i n g from t h e measured d i f f u s i v i t y - r e l a t i v e h u m i d i t y values can c o n t a i n a l a r g e e r r o r since t h e t h r e e r e l a t i v e h u m i d i t y values i n t h i s case a r e q u i t e near t o each o t h e r .

Therefore t h e r e l i a b i l i t y o f t h e d i f f u s i v i t i e s o f t h e wet cup c a l c u l a t e d w i t h N i l s s o n ' s method a r e very much q u e s t i o n a b l e . I t i s n o t presented here. On t h e o t h e r hand, t h e r e l i a b i l i t y o f t h e d i f f u s i v i t i e s from t h e wet cup c a l c u l a t e d w i t h Stamm's method i s much higher because t h e curves a r e

f i t t e d i n a much l a r g e r range ( f r o m about RH = 0.56 t o RH = 0.86) and no c u r v e - f i t t i n g i s needed i n Stamm's method.

For t h e r e s u l t s o f t h e wet cup i n t h e present study we may conclude t h a t the r e s u l t s o f Stamm's method should be r e l i e d on. F i g u r e 9 i s t h e c o r r e c t r e l a t i o n s h i p o f t h e d i f f u s i v i t i e s measured w i t h dry cups and wet cups

- they are very much s i m i l a r . N i l s s o n ' s method i s n o t s u i t a b l e t o use when the average d i f f u s i v i t i e s a r e measured a t s e v e r a l RH values t h a t a r e very near t o one another.

The c l i m a t e s employed i n t h e present study f o r t h e s o r p t i o n and t h r e e d i -mensional s o r p t i o n methods a r e i n n e a r l y t h e same s i t u a t i o n as t h e wet cup, so N i l s s o n ' s method w i l l n o t be used e i t h e r . Only Stamm's method w i l l be a p p l i e d f o r them.