Moisture Movement and Moisture Distribution in the Walls of Buildings

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COTJNCIL OF CANADA

Technical Translation TT-361

MOISTURE MOVEMENT AND I'LOISTURE DISTRIBUTION IN

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ViALLS OF BUILDINGS

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Keddelanden fr8n statens forskningskommitt6 far lantmannabyggnader no, 5; 53-76, 1945

translated by Il,A,G, Nathan

Moisture Movement and Moisture D i s t r i b u t i o n i n t h e Walls of B u i l d i n g s

A t t h e r e q u e s t of t h e Swedish Cement A s s o c i a t i o n and t h e Swedish Research Committee on Farm B u i l d i n g s a n i n v e s t i g a t i o n c o n c e r n i n g t h e m o i s t u r e d i s t r i b u t i o n and t h e m o i s t u r e movement i n t h e w a l l s of b u i l d i n g s , w i t h s p e c i a l r e f e r e n c e t o w a l l s of t h e s o - c a l l e d Nopsa t y p e , was c a r r i e d o u t a t t h e Vapour Research D i v i s i o n of t h e T e c h n i c a l C o l l e g e . I t had o r i g i n a l l y been i n - tended t h a t t h e i n v e s t i g a t i o n should be c o n f i n e d t o c a l c u l a t i n g t h e mechanism i n v a r i o u s c h a r a c t e r i s t i c c a s e s and drawing con- c l u s i o n s t h e r e f r o m . However, i t soon became a p p a r e n t t h a t i t

was n e c e s s a r y t o supplement t h e i n v e s t i g a t i o n w i t h t h e e x p e r i - mental d e t e r m i n a t i o n of c e r t a i n p r o p e r t i e s c h a r a c t e r i s t i c of m o i s t u r e movement f o r w a l l and f i l l m a t e r i a l s , A b r i e f a c c o u n t of t h e r e s u l t s t h u s o b t a i n e d i s g i v e n below.

General C h a r a c t e r i s t i c s of t h e Nechanism o f Moisture Movement

A s i s known, t h e m o i s t u r e i n a w a l l of hygroscopic m a t e r i a l c a n move i n two d i f f e r e n t ways, by d i f f u s i o n of w a t e r vapour t h r o u g h t h e a i r - f i l l e d p o r e s and s p a c e s of t h e m a t e r i a l and by c a p i l l a r i t y i n t h e p o r e s f i l l e d c o m p l e t e l y o r p a r t i a l l y w i t h w a t e r , A d i f f e r e n c e i n t h e p a r t i a l p r e s s u r e s of t h e water va- pour on e i t h e r s i d e of t h e w a l l i s a p r e r e q u i s i t e f o r t h e d i f - f u s i o n , A s a r u l e , t h e p a r t i a l p r e s s u r e of t h e water vapour i n t h e c o l d e x t e r n a l a i r i s s u b s t a n t i a l l y lower t h a n i n d o o r s . For t h i s r e a s o n t h e d i f f u s i o n g e n e r a l l y t a k e s p l a c e from t h e i n s i d e - o u t . The c a p i l l a r i t y , on t h e o t h e r hand, i s c l o s e l y r e l a t e d t o

a d i f f e r e n c e i n t h e m o i s t u r e c o n t e n t of t h e m a t e r i a l . The m o i s t u r e c o n t e n t of a hygroscopic m a t e r i a l which i s i n equi-

l i b r i u m w i t h t h e ambient a i r depends on t h e r e l a t i v e humidity of t h e atmosphere and i n c r e a s e s w i t h i t . T h e r e f o r e , i n a s i m - p l e w a l l t h e c a p i l l a r y movement t a k e s p l a c e e i t h e r from t h e o u t s i d e - i n o r from t h e i n s i d e - o u t , depending on whether t h e r e l a t i v e humidity of t h e atmosphere i s h i g h e r o r lower a t t h e o u t s i d e o f t h e w a l l t h a n i t i s a t t h e i n s i d e . I n a double w a l l w i t h f i l l c a v i t i e s and a i r s p a c e s t h e c a p i l l a r i t y , a s w i l l be shown below, i s n o t so d e f i n i t e l y determined by t h e r e l a t i v e h u m i d i t y of t h e ambient a i r .

I f a t any p o i n t i n t h e wall t h e vapour p r e s s u r e a t t a i n s t h e s a t u r a t i o n v a l u e , t h e water vapour condenses, and m o i s t u r e accumulates i n t h e w a l l . This may occur a t t h e o u t s i d e o f c a v i t i e s and a i r s p a c e s and t h e p o s s i b i l i t y i s g r e a t e s t a t low e x t e r n a l t e m p e r a t u r e s , I f t h e t e m p e r a t u r e of t h e i n t e r i o r w a l l i s below t h e dew p o i n t of t h e a i r i n t h e room, w a t e r p r e c i p i - t a t e s on t h e w a l l and i s absorbed by t h e l a t t e r . A correspond- i n g phenomenon may be observed on e x t e r n a l w a l l s d u r i n g r a i n ,

Moi s t u r e i n E q u i l f b r i u m f o r a Hygroscopic M a t e r i a l

-

A s mentioned above, i n o r d e r t o d e a l fundamentally and n u m e r i c a l l y w i t h t h e mechanism o f m o i s t u r e movement t h e mois- t u r e c o n t e n t s of a hygroscopic b u i l d i n g m a t e r i a l i n e q u i l i b r i u m w i t h a i r o f a c e r t a i n t e m p e r a t u r e a t v a r i o u s r e l a t i v e h u m i d i t i e s must be known. The r e l a t i o n s h i p between them, t h e s o - c a l l e d

s o r p t i o n i s o t h e r m , i s r e l a t i v e l y i n d e p e n d e n t o f t h e tem- p e r a t u r e . 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 s u c h i s o t h e r m s were d e t e r m i n e d a t room t e m p e r a t u r e f o r c o n c r e t e , p l a s t e r and d i f f e r e n t f i l l m a t e r i a l s . They a r e shown g r a p h i c a l l y i n F i g s . 1 and 2 . Data f o r a l l t h e m a t e r i a l s i n v e s t i g a t e d

have been assembled i n T a b l e I . The m o i s t u r e i n e q u i l i b r i u m was d e t e r m i n e d i n a c l o s e d p a r a f f i n e d chamber, where t h e a i r was k e p t a t c o n s t a n t r e l a t i v e h u m i d i t y by c o n t a c t w i t h s u l - p h u r i c a c i d of a g i v e n c o n c e n t r a t i o n and by a g i t a t i n g t h e a i r w i t h a blower a t r e g u l a r i n t e r v a l s . The lower t h e r e - l a t i v e h u m i d i t y , t h e more q u i c k l y a c o n s t a n t m o i s t u r e con- t e n t was o b t a i n e d i n t h e m a t e r i a l , t h e r a t e b e i n g s l i g h t l y h i g h e r f o r a f i l l m a t e r i a l t h a n f o r c o n c r e t e and p l a s t e r . I n c o n c r e t e , t h e r e f o r e , c o n s t a n t m o i s t u r e c o n t e n t was t h u s o b t a i n e d a f t e r a p p r o d m a t e l y 80 h o u r s a t a r e l a t i v e h u m i d i t y o f 55%, and a f t e r a p p r o x i m a t e l y 550 h o u r s a t a r e l a t i v e hu- m i d i t y o f 80%. The c o r r e s p o n d i n g t i m e s f o r sawdust were ap- p r o x i m a t e l y 65 and 450 h o u r s r e s p e c t i v e l y , a s i s e v i d e n t from F i g s . 2 and 3. \Tihen t h e r e l a t i v e huniidfty o f t h e atmosphere was 100% no e q u i l i b r i u m was o b t a i n e d f o r c o n c r e t e and p l a s t e r b u t , a s F i g . 2 shows, t h e r a t e a t which t h e h u m i d i t y i n c r e a s e d was c o n s t a n t .

The l o n g t i m e r e q u i r e d t o a t t a i n e q u i l i b r i u m a t h i g h r e l a t i v e h u m i d i t i e s i s n o t e w o r t h y . The samples had a t h i c k - n e s s of 1 5 and 30 mm., r e s p e c t i v e l y , and were d i r e c t l y exposed

t h e time o f a t t a i n i n g e q u i l i b r i u m should be l o n g e r , and t h e mof s t u r e - d i s t r i b u t i o n c u r v e s which were c a l c u l a t e d f o r a w a l l , t h e r e f o r e a p p l y o n l y i f t h e t e m p e r a t u r e and t h e humidity of t h e atmosphere a r e c o n s t a n t o v e r a l o n g p e r i o d .

The hygroscopic m o i s t u r e i s c o n t a i n e d i n t h e f i n e s t

p o r e s of t h e m a t e r i a l . The s m a l l and s t r o n g l y curved m e n i s c i i n t h e p o r e s cause a d e c r e a s e i n t h e vapour p r e s s u r e . The s m a l l e r t h e r a d i u s of c u r v a t u r e of t h e menisci t h e g r e a t e r t h i s d e c r e a s e w i l l b e . T h e r e f o r e , i n m a t e r i a l s w i t h p o r e s of d i f f e r e n t s i z e s t h e c o a r s e r p o r e s d r y out f i r s t . I n a g r a n u l a r m a t e r i a l where t h e m o i s t u r e accumulates around t h e p o i n t s of c o n t a c t between t h e g r a i n s , i n s o - c a l l e d open c a p i l -

l a r i e s , t h e r a d i u s of c u r v a t u r e of t h e m e n i s c i l i k e w i s e be- comes i n c r e a s i n g l y s m a l l e r a s t h e d r y i n g p r o c e s s c o n t i n u e s . I n b o t h c a s e s t h e s o r p t i o n i s o t h e r m has a p p r o x i m a t e l y t h e same c h a r a c t e r i s t i c form. A more n o t i c e a b l e d e c r e a s e i n t h e vapour p r e s s u r e , i . e . , from 1 t o 0.1% i s o n l y o b t a i n e d when t h e d i a m e t e r of t h e p o r e s i s a s s m a l l a s 0 . 1 t o 1,u. For g r a n u l a r m a t e r i a l t h e corr8esponding g r a i n d i a m e t e r i s from

1 t o 1 0 ) ~ . hlost of t h e hygroscopic m a t e r i a l s c o n t a i n a s many f i n e c a p i l l a r i e s a s c o a r s e ones. As t h e r e l a t i v e humi-

d i t y of t h e atmosphere i n c r e a s e s , t h e system of f i n e c a p i l a r - r i e s g r a d u a l l y f i l l s w i t h w a t e r w h i l e t h e system of c o a r s e

c a p i l l a r i e s remains d r y . A t a r e l a t i v e humidity of 100% t h e system o f f i n e c a p i l l a r i e s i n a porous m a t e r i a l becomes com- p l e t e l y f i l l e d w i t h w a t e r , b u t i n a ~ r a n u l a r m a t e r i a l t h e

s y s t e m w i l l p r o b a b l y be f i l l e d o n l y up t o two t h i r d s . The number o f f i n e c a p i l l a r i e s , t h e r e f o r e , d e t e r m i n e s t h e hygros- c o p i c m o i s t u r e c o n t e n t . I n c o n c r e t e , f o r example, t h e g r e a t e r t h e c o n t e n t o f cement t h e g r e a t e r w i l l be t h e h y g r o s c o p i c m o i s t u r e c o n t e n t . T h i s i s e v i d e n t , a l s o , from F i g . 1. I f a n a d d i t i o n a l amount of w a t e r i s s u p p l i e d t o t h e m a t e r i a l , f a r example by c o n d e n s a t i o n o r r a i n , t h e n even t h e s y s t e m of c o a r s e c a p i l l a r i e s w i l l become more o r l e s s f i l l e d .

Because of t h e d e c r e a s e i n vapour p r e s s u r e t h e w a t e r en- c l o s e d i n t h e s y s t e m o f f i n e c a p i l l a r i e s h a s a l o w e r f r e e z i n g p o i n t . Hence t h e g r e a t e r t h e d e c r e a s e i n t h e vapour p r e s s u r e t h e l o w e r w i l l b e t h e f r e e z i n g p o i n t . T h e r e f o r e , t h e l a r g e r p a r t o f t h e w a t e r e n c l o s e d i n t h e f i n e p o r e s r e m a i n s u n f r o z e n r i g h t down t o r e l a t i v e l y low t e m p e r a t u r e s . According t o meas- urements o f t h e Steam H e a t i n g I n s t i t u t e , a p p r o x i m a t e l y 90% o f t h e s a t u r a t i o n m o i s t u r e of t h e f i b e r s i n s p r u c e wood r e m a i n s u n f r o z e n a t - 1 2 ' ~ . T h i s means t h a t a t a p p r o x i m a t e l y 95$ r e - l a t i v e h u m i d i t y t h e t o t a l h y g r o s c o p i c m o i s t u r e c o n t e n t r e m a i n s i n l i q u i d form. On t h e o t h e r hand, t h e w a t e r e n c l o s e d i n c o a r s e c a p i l l a r i e s f r e e z e s . T h i s b e h a v i o u r i s v e r y i m p o r t a n t f o r e s - t i m a t i n g t h e c a p i l l a r i t y i n a h y g r o s c o p i c m a t e r i a l . W i t h i n t h e h y g r o s c o p i c r a n g e , c l e a r l y , t h e r e i s a l m o s t no o b s t a c l e t o t h e c a p i l l a r i t y a t t e m p e r a t u r e s c o n s i d e r a b l y below O'C. The n u m e r i c a l v a l u e s g i v e a n i d e a o f t h e o r d e r of magnitude of t h e volume o f f i n e and c o a r s e c a p i l l a r i e s , For c o n c r e t e w i t h

a weight by volume of 1800 kbln./cu.m. t h e t o t a l pore volume i s 33%, The maximum hygroscopic m o i s t u r e i s approximately

1.2 p e r c e n t by weight c o r r e s p o n d i n g t o 2.1 p e r c e n t by volume, and t h e system o f f i n e c a p i l l a r i e s should t h u s c o n s t i t u t e ap- p r o x i m a t e l y 6b of t h e t o t a l pore volume. For c o n c r e t e w i t h a weight by volume of 2200 kgm./cu.m. t h e c o r r e s p o n d i n g v a l u e s a r e approximately 1 9 and 4 p e r c e n t by volume. T h e r e f o r e , because o f t h e i n c r e a s e d c o n t e n t of cement and because of t h e c l o s e r packing t h e value f o r t h e system of f i n e c a p i l l a r i e s i n c r e a s e s t o approximately 20%. For wood, t h e system of f i n e c a p i l l a r i e s amounts roughly t o o n e - f i f t h of t h e t o t a l p o r o s i t y .

I n Table I t h e t o t a l p o r o s i t y a s w e l l a s t h e f i n e - c a p i l l a r y p o r o s i t y i s shown f o r t h e d i f f e r e n t m a t e r i a l s i n - v e s t i g a t e d , computed from t h e s o r p t i o n i s o t h e r m s and t h e c o a r s e p o r o s i t y . For f i l l m a t e r i a l (sawdust, r o c k wool, c h a r c o a l ) t h e term " c o a r s e p o r o s i t y " r e f e r s h e r e t o t h e p o r e s between t h e g r a i n s which o f f e r t h e l e a s t r e s i s t a n c e t o t h e d i f f u s i n g vapour, and f o r t h e d e n s e r b u i l d f n g m a t e r i a l s e , a l l t h e o t h e r

b u i l d i n g m a t e r i a l s l f s t e d i n t h e t a b l e ) i t r e f e r s t o t h e t o t a l p o r o s i t y reduced by t h e f i n e - c a p i l l a r y volume which a b s o r b s hygroscopic m o i s t u r e when t h e r e l a t i v e humidity of t h e atmos- phere i s 100%. The f o l l o w i n g v a l u e s f o r t h e r e s p e c t i v e weights by volume have been a p p l i e d .

compact m a t e r i a l 1400 kgm./cu.m. C h a r c o a l g r a n u l a r m a t e r i a l 400 " It I t compact m a t e r i a l 1560 I' 11 11 Sawdust g r a n u l a r m a t e r i a l 410 " I t I t

Rock wool compact m a t e r i a l 2650

"

1) It Masonit e t t I t _{1 5 6 0} " 11 I? Sand I t I t ₂₆₅₀ " 11 I t Ceme n t It I t ₃₁₀₀ I' It II Lime It It ₂₇₀₀ I' 1t I t

A s mentioned above, t h e f i n e - c a p i l l a r y volume was ob-

t a i n e d f r o m t h e s o r p t i o n i s o t h e r m s f o r t h e r e s p e c t i v e m a t e r i a l s . Vapour D i f f u s i o n A t low r e l a t i v e h u m i d i t y of t h e a t m o s p h e r e , when t h e m o i s t u r e c o n t e n t o f t h e m a t e r i a l f a l l s c o n s i d e r a b l y s h o r t of t h e maximum h y g r o s c o p i c m o i s t u r e t h e w a t e r f i l l s o n l y t h e f i n e s t and n a r r o w e s t p a r t s o f t h e s y s t e m o f f i n e c a p i l l a r i e s . The r e s i s t a n c e t o t h e c a p i l l a r y w a t e r a b s o r p t i o n t h e n becomes s o g r e a t t h a t t h i s a b s o r p t i o n , p r a c t i c a l l y s p e a k i n g , c a n b e n e g l e c t e d , and t h e e n t i r e movement o f m o i s t u r e t h e n t a k e s p l a c e by vapour d i f f u s i o n . The vapour d i f f u s i o n c o e f f i c i e n t may be d e t e r m i n e d d i r e c t l y f r o m t h i s b e h a v i o u r . The l a t t e r g i v e s t h e amount o f d i f f u s i n g v a p o u r i n kgm. p e r sq.m, o f w a l l s w f a c e p e r h o u r a t a change i n p a r t i a l p r e s s u r e i n t h e w a l l o f one a t m o s p h e r e p e r m e t r e , If t h e r e d u c t i o n i n p a r t i a l p r e s s u r e

a t one s i d e of t h e sample i s b r o u g h t a b o u t by a b s o r p t i o n i n c a l c i u m c h l o r i d e , t h e mean v a l u e f o r t h e r e l a t i v e h u m i d i t y of t h e a t m o s p h e r e becomes s o low t h a t t h e c a s e mentioned above i s g i v e n , and a l l t h e v a l u e s determined by t h i s method t h e r e - f o r e r e f e r t o t h e vapour d i f f u s i o n c o e f f i c i e n t a l o n e . The d i f f u s i o n c o e f f i c i e n t s t h u s determined have been assembled i n Table I . For a i r a t 2 0 ' ~ . t h e d i f f u s i o n c o e f f i c i e n t i s

0,069 kgm./m., atm., hr. This v a l u e may be assumed t o c o r - r e s p o n d t o t h a t f o r a w a l l w i t h a p o r o s i t y of 100%. If t h e m a t e r i a l c o n s i s t s o f porous g r a i n s , t h e vapour d i f f u s e s f i r s t o f a l l i n t h e i n t e r s p a c e s between them, and i t seems t h a t t h e d i f f u s i o n c o e f f i c i e n t f o r a m a t e r i a l of t h i s s t r u c t u r e i s

p r a c t i c a l l y p r o p o r t i o n a l t o t h a t o f a m a t e r i a l of c o a r s e p o r o s i t y ( a s t h a t d e f i n e d and l i s t e d i n T a b l e I ) . However, t h e r e i s an a d d i t i o n a l r e d u c t i o n f a c t o r , which f o r sawdust and r o c k wool i s a p p r o x i m a t e l y 0.9, f o r unscreened sand and c h a r c o a l a p p r o x i m a t e l y 0.55, f o r b r i c k a p p r o x i m a t e l y 0.4, and f o r c o n c r e t e w i t h a weight by volume of 1800

-

2000 kgm,/ cu.m, a p p r o x i m a t e l y 0 - 1 3 . From t h i s t h e d i f f u s i o n c o e f f i c i e n t f o r c o n c r e t e w i t h t h e c o a r s e p o r o s i t y 33

-

2 = 31$, f o r example, can be c a l c u l a t e d a s a p p r o x i m a t e l y 0.069 x 0.31 x 0.13 = 0.0028, compared w i t h a measured v a l u e o f 0.0027 kgm./m., atm., h r .

S i m i l a r l y , f o r sawdust w i t h a c o a r s e p o r o s i t y o f a b o u t 50% t h e f o l l o w i n g i s o b t a i n e d : 0,069 x 0.50 x 0.9 = 0.031, compared w i t h a measured v a l u e of 0.033 kgm,/m. atm., h r . The r e d u c t i o n f a c t o r f o r a l l t h e m a t e r i a l s i n v e s t i g a t e d i s g i v e n i n T a b l e I ,

T h i s f a c t o r seems t o d e c r e a s e a s t h e cement c o n t e n t of t h e c o n c r e t e i n c r e a s e s and i s even lower f o r p l a s t e r ( c f . Table I , 1 2 ) , I n Fig. 5 t h e d i f f u s i o n

coefficient^^

h a s been p l o t t e d a s a f u n c t i o n of t h e c o a r s e p o r o s i t y . L i n e s have been i n s e r t e d a l o n g w i t h t h e names of m a t e r i a l s of d i f f e r e n t s t r u c t u r e and f o r e a c h s u c h l i n e t h e r e d u c t i o n f a c t o r i s g i v e n . The l a t t e r should be employed f o r e s t i m a t i n g t h e d i f f u s i o n c o e f f i c i e n t f r o m t h e p o r o s i t y w i t h t h e r e s p e c t i v e m a t e r i a l s t r u c t u r e . The d i f f u s i o n

coefficient,^^

i s e s t i m a t e d by means of t h e e q u a t i o n - LLd

-

kred x p x 0.069 kgm./m., atm,, h r . , where kred = r e d u c t i o n f a c t o r P = c o a r s e p o r o s i t y , a c c o r d i n g t o t h e above c a l c u l a t i o n , 0.069 kgp./m., atm., h r . = d i f f u s i o n c o e f f i c i e n t f o r a i r . It may now be assumed t h a t t h e mechanism o f t h e vapour d i f f u - s i o n i s f a i r l y w e l l u n d e r s t o o d ,

A t h i g h e r water c o n t e n t s , when t h e p o r e s g r a d u a l l y f i l l w i t h more water and t h e c a p i l l a r i t y t h e r e f o r e becomes more n o t i c e a b l e ,

t h e vapour d i f f u s i o n o b v i o u s l y must d e c r e a s e g r a d u a l l y . However, w i t h i n t h e hygroscopic range, where t h e t o t a l m o i s t u r e i s gener- a l l y low, t h i s d e c r e a s e i s u n i m p o r t a n t .

Non-hygroscopic m a t e r i a l s , which even a t v e r y h i g h r e l a t i v e h u m i d i t y a r e v i r t u a l l y f r e e from w a t e r , c o n s t i t u t e a n o t h e r c a s e .

The movement o f m o i s t u r e w i t h i n t h e a i r - d r y m a t e r i a l c o n s i s t s merely of vapour d i f f u s i o n h e r e . Hence f o r s u c h m a t e r i a l s t h e

d i f f u s i o n c o e f f i c i e n t can be determined i n t h e above manner even i f t h e r e l a t i v e h u m i d i t y of t h e atmosphere i s h i g h . F o r example, f o r r o c k wool w i t h a p o r o s i t y o f 93$, c o r r e s p o n d i n g t o a weight by volume o f 1 9 5 kgm,/cu.m,, t h e f o l l o w i n g v a l u e i s o b t a i n e d : 0.069 x 0 , 9 3 = 0.057 compared w i t h a measured v a l u e o f 0.056 kgm./m., atm., h r . , determined f o r b o t h , low r e l a t i v e humidity ( o v e r c a l c i u m c h l o r i d e ) and h i g h r e l a t i v e humidity ( o v e r w a t e r ) . Only when t h e m a t e r i a l h a s been mois- tened by a d d i t i o n o f w a t e r does m o i s t u r e movement t a k e p l a c e i n t h e open c a p i l l a r i e s of s u c h a m a t e r i a l .

Where t h e c a p i l l a r y s y s t e m i s covered w i t h a water- r e p e l l e n t l i q u i d , e.g. impregnated t a r r e d board, t h i s con-

s t i t u t e s a s p e c i a l t y p e of non-hygroscopic m a t e r i a l . I n s u c h a m a t e r i a l t h e r e i s no c a p i l l a r i t y e i t h e r w i t h i n t h e normal h y g r o s c o p i c range o r when w a t e r i s added. However, t h i s does n o t mean t h a t t h e m a t e r i a l i s impermeable t o m o i s t u r e ; f o r t h e vapour d i f f u s e s t h r o u g h t h e p o r e s . The d i f f u s i o n t h r o u g h un-

impregnated cardboard ( w e i g h t by volume 0.75 kgm./dm.3 and t h i c k n e s s 5.2 mm.) was i n v e s t i g a t e d by ~ e h m a n n - O l i v a G , who

-;st

found a d i f f u s i o n c o e f f i c i e n t of 0.0019 kgm./m., h r . , atm, when t h e r e l a t i v e humidity of t h e atmosphere was 40%. T h i s

--

-

-

Lehmann-Oliva, Z. V D I

.

supplement V e r f a h r e n s t e c k n i k No -1, 1940,

,y--t':-

The d i f f u s i o n c o e f f i c i e n t g i v e s t h e amount of w a t e r i n kgm. which d i f f u s e s i n one s q u a r e metre of a l a y e r o f m a t e r i a l of

one m e t r e t h i c k n e s s when t h e d i f f e r e n c e i n t h e p a r t i a l p r e s s u r e of t h e w a t e r vapour i s one atmosphere.

0.0019

corresponds t o a "seepage f a c t o r " of 0.0015 = 1.25 kgm./sq.m.,

h r . , a t n . f o r cardboard of 1 . 5 rnm. t h i c k n e s s , The impregna- t i o n r e d u c e s even t h e vapour d i f f u s i o n . For t a r r e d cardboard a seepage of 0.1 kgm./sq,m., h r . atm. has been assumed i n t h e c a l c u l a t i o n s of t h e p r e s e n t a u t h o r , b u t t h e v a l u e c l e a r l y de- pends t o a g r e a t e x t e n t on t h e q u a l i t y of t h e impregnation. Coatings w i t h a s p h a l t reduce t h e v a l u e t o 0.022

-

0.051 kgm./ sq.m., h r , , atm. a c c o r d i n g t o a summary by ~ i c k s t r s m ~ . Ac- c o r d i n g t o t h e same s o u r c e only impregnation w i t h p a r a f f i n o r c o v e r i n g w i t h "hydrolen" seems t o p r e v e n t t h e vapour d i f f u s i o n c o m p l e t e l y . However, i n o r d e r t o u t i l i z e t h e vapour r e t a r d i n g p r o p e r t y of such l a y e r s of t a r r e d board t h e seams must be r e - l a t i v e l y t i g h t .

C a p i l l a r i t y

I f a c y l i n d r i c a l c a p i l l a r y t u b e , whose i n s i d e i s mois- t e n e d w i t h w a t e r , i s c o m p l e t e l y f i l l e d w i t h water and i f b o t h i t s open ends a r e i n c o n t a c t w i t h a i r of t h e same r e l a t i v e humidity, t h e r e i s e q u i l i b r i u m between t h e t e n s i l e f o r c e s due t o t h e s u r f a c e t e n s i o n , T h e r e f o r e , t h e r a d i i of c u r v a t u r e of t h e menisci must be e q u a l a t b o t h ends. I f t h e r e l a t i v e hu- m i d i t y corresponds t o t h e d e c r e a s e i n vapour p r e s s u r e of t h e c a p i l l a r y t u b e , t h e c u r v a t u r e of t h e meniscus a t t a i n s i t s maxi- mum v a l u e . Then t h e r a d f i of c u r v a t u r e a r e g e n e r a l l y i d e n t i c a l w f t h t h e r a d i i of t h e c a p i l l a r y t u b e . I f t h e r e l a t i v e h u m i d i t y d e c r e a s e s t h e water w i l l e v a p o r a t e from b o t h s u r f a c e s . There- f o r e , t h e s e s u r f a c e s , w i t h t h e c u r v a t u r e unchanged, b e g i n t o '"8ekstrdrn, K y l t e k n i s k t i d ~ k r i f t ~ NO. 2, 1 9 4 2 .

move towards t h e c e n t r e of t h e c a p i l l a r y tube u n t i l t h e l a t t e r i s completely d r i e d o u t . I f , on t h e o t h e r hand, t h e r e l a t i v e humidity i n c r e a s e s , an unimportant amount of vapour condenses on t h e s u r f a c e s of t h e m e n i s c i , t h u s r e d u c i n g t h e i r c u r v a t u r e u n t i l e q u i l i b r i u m w i t h t h e i n c r e a s e d vapour p r e s s u r e i s a t - t a i n e d . If now t h e r e l a t i v e humidity i s i n c r e a s e d o n l y a t one s i d e , t h e r a d i u s of c u r v a t u r e w i l l i n c r e a s e t h e r e , c a u s i n g un- b a l a n c e between t h e f o r c e s of s u r f a c e t e n s i o n . T h e r e f o r e , t h e w a t e r f l o w s over t o t h e o t h e r s i d e and t h e r a d i u s of c u r v a t u r e t h u s i n c r e a s e s t h e r e , b r i n g i n g about e v a p o r a t i o n i n t h e space w i t h t h e lower r e l a t i v e humidity. T h i s flow, which i s i d e n t i - c a l w i t h t h e c a p i l l a r i t y , i s maintained by t h e d i f f e r e n c e i n t h e f o r c e s of s u r f a c e t e n s i o n . This d i f f e r e n c e i s determined by t h e d i f f e r e n t r a d i i of c u r v a t u r e , which i n t u r n a r e d e t e r - mined by t h e d i f f e r e n c e i n t h e r e l a t i v e humidity. The condi- t i o n s remain t h e same when t h e d i s c u s s i o n a p p l i e s t o t h e open c a p i l l a r i e s i n a m o i s t g r a n u l a r m a t e r i a l . The c o r n e r s between t h e g ~ a i n s a r e more s u f f i c i e n t l y f i l l e d o u t and t h e r a d i i of c u r v a t u r e t h u s become g r e a t e r a t t h e s i d e of t h e h i g h e r r e l a - t i v e humidity. While t h e vapour d i f f u s i o n t h r o u g h a w a l l con- s i s t i n g of a porous m a t e r i a l i s determined by t h e d i f f e r e n c e i n p a r t i a l vapour p r e s s u r e , i . e . , t h e a b s o l u t e h u n i d i t y , t h e c a p i l l a r i t y consequently i s m a i n t a i n e d by a s t a t e which depends on t h e r e l a t i v e humidity on b o t h s i d e s of t h e w a l l . Within t h e hygroscopic r a n g e t h e m o i s t u r e c o n t e n t o f t h e m a t e r i a l i s c l e a r l y determined by t h e r e l a t i v e humidity of t h e atmosphere and t h e c a p i l l a r i t y i s t h e r e f o r e brought i n t o r e l a t i o n s h i p w i t h t h e

d i f f e r e n c e i n humidity o f t h e m a t e r i a l a t b o t h s i d e s of t h e w a l l . G r a d u a l l y , a s t h e humidity i n c r e a s e s t h e c a p i l l a r i e s w i t h i n r a n g e of t h e c a p i l l a r y movement o b t a i n i n c r e a s i n g l y g r e a t e r dimensions and, t h e r e f o r e , i n t h e b e g i n n i n g t h e c a p i l - l a r i t y c o e f f i c i e n t i n c r e a s e s , If t h e humidity exceeds t h e maximum hygroscopic m o i s t u r e t h i s c o e f f i c i e n t g r a d u a l l y de-

c r e a s e s a g a i n , because t h e s n a l l e r c a p i l l a r i e s which a r e com- p l e t e l y f i l l e d w i t h water and which, a t i n c r e a s e d humidity c o n s t i t u t e t h e g r e a t e r p a r t of t h e t o t a l c a p i l l a r y volume, can no l o n g e r p a r t i c i p a t e i n t h e a b s o r p t i o n .

If t h e m o i s t u r e t r a n s m i s s i o n c o e f f i c i e n t of a sample i s determined over calcium c h l o r i d e a s w e l l a s o v e r w a t e r , t h e n i t i s found t h a t i n t h e l a t t e r c a s e a n amount must be added t o t h e d i f f u s i o n because of t h e c a p i l l a r i t y . The v a l u e s f o r t h e m a t e r i a l s i n v e s t i g a t e d by t h e p r e s e n t a u t h o r have been assembled i n Table I . This i n c r e a s e i s a p p r o x i m a t e l y 50% f o r o r g a n f c m a t e r i a l s and more t h a n 200% f o r c o n c r e t e s . There- f o r e , a t h i g h e r humidity t h e c a p i l l a r i t y d e t e r m i n e s t h e m o i s t - u r e t r a n s m i s s i o n . The e x p e r i m e n t a l v a l u e s f o r c o n c r e t e and p l a s t e r have been p l o t t e d i n F i g . 6 a s a f u n c t i o n of t h e weight by volume. I t i s e v i d e n t t h a t t h e s t r o n g e f f e c t which t h e

p o r o s i t y h a s on t h e d i f f u s i o n c o e f f i c i e n t determined o v e r c a l - cium c h l o r i d e a l s o a p p l i e s t o t h e g r e a t l y i n c r e a s e d v a l u e s of t h e t o t a l m o i s t u r e t r a n s m i s s i o n c o e f f i c i e n t determined o v e r w a t e r . A t h i g h e r h u m i d i t y t h e i n c r e a s e should become somemhat g r e a t e r s t i l l . I n s u c h e x p e r i m e n t s o v e r w a t e r , where t h e r e i s

no d r o p i n t e m p e r a t u r e i n t h e w a l l , b o t h t h e c a p i l l a r y movement and t h e vapour d f f f u s i o n a r e i n t h e same d i r e c t i o n . When t h e 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 house i s h i g h t h e same o c c u r s i n m a l l s o f homogeneous m a t e r i a l and e v e n i n b r i c k s t r i n g s i n w a l l s of t h e Nopsa t y p e . But i n t h e f i l l e d d u c t t h e c a p i l l a r i t y g o e s i n w a r d s and t h e d l f f u s i o n o u t w a r d s . T h i s a l s o o c c u r s i n t h e s e l f - s a m e w a l l where t h e 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 h o u s e i s low, T h e r e f o r e , i t i s e s s e n t i a l t o know e a c h o f t h e c o e f f i - c i e n t s i n d i v i d u a l l y . F o r t h i s p u r p o s e t h e c o e f f i c i e n t o f t h e c a p i l l a r i t y G ,Af was c a l c u l a t e d i n kgm,/m., f , hr. f r o m measurements o v e r w a t e r , assuming t h a t t h e vapour d i f f u s i o n

coefficient,,^^

i n kgm./m., atm., hr. a c c o r d i n g t o t h e above s t a t e m e n t h a s t h e same v a l u e a s t h a t d i r e c t l y d e t e r m i n e d o v e r c a l c i u m c h l o r i d e , The co-

e f f i c i e n t o f c a p i l l a r i t y i s b r o u g h t i n t o r e l a t i o n s h i p h e r e w i t h t h e d i f f e r e n c e i n t h e m o i s t u r e r a t i o ( m o i s t u r e d i v i d e d by t h e amount o f d r y s u b s t a n c e , f ) and t h u s becomes a hundred t i m e s g r e a t e r t h a n t h a t r e f e r r e d t o i n p e r c e n t of m o i s t u r e d i f f e r - e n c e . The v a l u e s t h u s computed h a v e b e e n a s s e m b l e d i n T a b l e I

f o r t h e v a r i o u s m a t e r i a l s i n v e s t i g a t e d . F o r example, f o r con- c r e t e w i t h a w e i g h t b y volume o f 2 , 0 0 0 kgm./cu.m. and f o r saw- d u s t w i t h a w e i g h t b y volume o f 250 kgm./cu.m, t h e c o e f f i c i e n t of c a p i l l a r i t y i s 0.0080 and 0 , 0 0 1 5 kgm./m., f , h r . , r e s p e c t i v e l y . , A c c o r d i n g t o e x p e r i m e n t and c a l c u l a t i o n and by t h e above s t a t e m e n t ,

-

_x-

-

The c o e f f i c i e n t of c a p i l l a r i t y g i v e s t h e amount o f w a t e r i n kgm, which p a s s e s t h r o u g h a l a y e r o f m a t e r i a l o f one m e t r e t h i c k n e s s o v e r an a r e a o f one s q u a r e m e t r e .

Table I , and F i g . 7 , t h e c o e f f i c i e n t of c a p i l l a r i t y becomes 0.002 and 0.033 kgm./m., atm., h r . , r e s p e c t i v e l y , f o r t h e s e two m a t e r i a l s . As p o i n t e d o u t b e f o r e , i t i s p r o b a b l e t h a t t h i s c o e f f i - c i e n t of c a p i l l a r i t y a t f i r s t i n c r e a s e s a s t h e m o i s t u r e eon- t e n t i n c r e a s e s , b u t t h i s v a r i a t i o n was n o t i n v e s t i g a t e d ex- p e r i m e n t a l l y by t h e a u t h o r and p r o b a b l y no r e l i a b l e t h e o r y

can be found. S i n c e t h e m o i s t u r e c o n t e n t , i n t h e p r e s e n t ex- p e r i m e n t s o v e r w a t e r ( c f . Table I ) , i s of t h e s a n e o r d e r of magnitude ( e . g . f o r c o n c r e t e , r e l a t i v e humidity a p p r o x i m a t e l y 727;) a s t h e m o i s t u r e c o n t e n t i n t h e w a l l t y p e s t o which t h e p r e s e n t f n v e s t i ~ a t i o n r e f e r s i t has been assumed, f o r sim-

p l i c i t y , t h a t t h e c o e f f i c i e n t o f c a p i l l a r i t y i s a l s o unchanged. According t o t h e above s t a t e m e n t i t i s p r o b a b l e t h a t when t h e r e l a t i v e h u m i d i t y i s g r e a t e r t h e c o e f f i c i e n t of c a p i l l a r f t y a l s o i n c r e a s e s , r e d u c i n g t h e r i s k o f c o n d e n s a t i o n i n t h e w a l l . With t h e assumption o f a c o n s t a n t v a l u e f o r t h e c o e f f i c i e n t t h e

c a l c u l a t i o n y i e l d s more r e l i a b l e r e s u l t s .

The c a l c u l a t i o n of t h e m o i s t u r e t r a n s m i s s i o n t h r o u g h a l a y e r of m a t e r i a l p r o c e e d s from t h e two e q u a t i o n s which d e f i n e t h e c o e f f i c i e n t s of m o i s t u r e movement, v i z . : Gd

=Pd

P1

-

P2 kgm./sq.m., h r . (vapour d i f f u s i o n )

6

Gf = ,af ' f 2 kgm./sq.m., h r . ( c a p i l l a r i t y )

6

G = Gd

+

Gf kgm./aq.m., hr

.

( t o t a l m o i s t u r e movement),

where p a t n . = p a r t i a l vapour p r e s s u r e f = m o i s t u r e r a t i o

6

m = t h i c k n e s s of t h e w a l l s u b s c r i p t s 1 and 2 = t h e two s i d e s of t h e l a y e r . The c a l c u l a t i o n i s s i m p l i f i e d by r e a r r a n g i n g t h e e q u a t i o n to L G = ( , b d ~ l + f i f f l )

-

(pdp2 * f i f f 2 ) = F ( p l f l )

-

F ( p 2 f 2 ) , where f o r a given m a t e r i a l a t a g i v e n t e m p e r a t u r e ~ ( p f ) i s a

s i n g l e - v a l u e d f u n c t i o n o f p and f . This r e l a t i o n s h i p i s shown i n Fig. 7 f o r c o n a r e t e and sawdust w i t h t h e d a t a j u s t given. The r e l a t i o n between t h e r e l a t i v e humidity and t h e m o i s t u r e c o n t e n t of t h e m a t e r i a l has been assumed h e r e i n conformity w i t h t h e s o r p t i o n i s o t h e r m s shown i n F i g s . 1 and 2. I t i s a l s o assumed t h a t d e s p i t e t h e movement of m o i s t u r e t h e m a t e r i a l i s i n e q u i l i b r i u m w i t h t h e ambient atmosphere. A c t u a l e x p e r i - ments seem t o c o n f i r m t h i s . The m o i s t u r e t r a n s m i s s i o n i s then

determined simply by means of F i g , 7.

Movement of Moisture t h r o u g h a Wall of Homogeneous Materf a 1

---

It i s i n t e r e s t i n g t o i n v e s t i g a t e t h e mechanism of m o i s t u r e and m o i s t u r e d i s t r i b u t i o n i n a simple w a l l of homogeneous mater- i a l . A s p e c i a l c a s e of t h i s i s demonstrated by t h e diagram shown i n F i g . 8. It has been assumed t h a t t h e i n d o o r tempera- t u r e i s +15O and t h e outdoor t e m p e r a t u r e - 1 5 O ~ . The r e l a t i v e humidity has been assumed a s 757: and 95,6 r e s p e c t i v e l y . The k v a l u e of t h e w a l l i s 0.8, s o t h a t t h e r e i s no c o n d e n s a t i o n on t h e i n n e r s i d e of t h e w a l l . I f , t o b e g i n w i t h , i t i s assumed

t h a t t h e m a t e r i a l o f t h e w a l l i s n o t s u r f a c e - a c t i v e , t h e mois- t u r e t r a n s m i s s i o n i s d e t e r m i n e d by t h e s l o p e o f t h e vapour- p r e s s u r e c u r v e a l o n e . S i n c e t h e vapour p r e s s u r e c a n n o t exceed t h e s a t u r a t i o n p r e s s u r e t h e v a p o u r - p r e s s u r e c u r v e w i t h t h e t a n - g e n t s of t h e v a l u e f o r t h e vapour p r e s s u r e o f t h e i n t e r n a l and e x t e r n a l a i r i s g o i n g t o conform t o t h e s a t u r a t i o n c u r v e . S i n c e t h e s l o p e of t h e v a p o u r - p r e s s u r e c u r v e d e c r e a s e s toward t h e o u t - s i d e t h e m o i s t u r e condenses i n s i d e t h e w a l l w i t h i n t h e r e g i o n where t h e r e l a t i v e h u m i d i t y i s 100%. The m o i s t u r e a c c u m u l a t e s t h e r e , r e s u l t i n g i n a n i n c r e a s e i n m o i s t u r e c o n t e n t , I f t h e m a t e r i a l i s s u r f a c e - a c t i v e t h e m o i s t u r e w i l l move outwards t o b o t h s i d e s o f t h e w a l l ; t h e c a p i l l a r i t y i s g r e a t compared w i t h t h e v a p o u r d i f f i s i o n . T h i s i s t h e c a s e i n c o n c r e t e , f o r example, and c o n d e n s a t i o n can be a v o i d e d a l t o g e t h e r . For a m a t e r i a l which i s n o t s u r f a c e - a c t i v e c o n d e n s a t i o n c a n a l s o be a v o i d e d i f t h e 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 house i s s o low (49;g) t h a t t h e a c t u a l v a p o u r - p r e s s u r e c u r v e i s t a n g e n t t o t h e s a t u r a t i o n c u r v e o n l y a t one p o i n t (shown by a d a s h l i n e i n F i g . 8 ) . C h i e f E f f e c t o f A i r Spaces and C a v i t i e s a s w e l l a s Cardboard L a y e r s on M o i s t u r e T r a n s m i s s i o n I n a n a i r s p a c e t h e r e s i s t a n c e t o d i f f u s i o n i s s m a l l com- p a r e d w i t h t h e r e s i s t a n c e of t h e s u r r o u n d i n g w a l l m a t e r i a l , t h e c a p i l l a r i t y z e r o , and t h e h e a t - i n s u l a t i n g p r o p e r t y inasmuch a s wide s p a c e s a r e concerned a p p r o x i m a t e l y e q u a l t o o r s l i g h t l y

g r e a t e r t h a n t h o s e i n t h e w a l l , T h e r e f o r e , t h e drop i n vapour p r e s s u r e i n t h e a i r s p a c e i s o n l y s m a l l , while t h e drop i n tem- p e r a t u r e i n t h e same a i r space c a u s e s a d e c r e a s e i n t h e s a t u r a - t i o n p r e s s u r e and t h e r e l a t i v e humidity of t h e atmosphere a t t h e o u t s i d e o f t h i s s p a c e t h u s becomes h i g h e r t h a n a t t h e i n s i d e . There i s i n c r e a s e d r i s k of condensation a t t h e o u t s i d e of t h e space and reduced movement of m o i s t u r e by c a p i l l a r i t y i n s i d e

( o r i n c r e a s e d m o i s t u r e movement o u t s i d e ) t h e w a l l s s u r r o u n d i n g t h e space ( c f . F i g . 9, where t h e a i r space i s i n d i c a t e d by double l i n e s )

.

I n a f i l l c a v i t y , t o o , t h e r e s i s t a n c e t o d i f f u s i o n i s s m a l l compared w i t h t h a t of t h e s u r r o u n d i n g w a l l s , whereas t h e h e a t - i n s u l a t i n g p r o p e r t y i s much g r e a t e r . I f t h e f i l l m a t e r i a l i s non-hygroscopic, t h e f i l l i n g c a v i t y has t h e same

e f f e c t a s an a i r space, b u t t h e e f f e c t becomes c o n s i d e r a b l y mope markad h e r e . If t h e f i l l m a t e r i a l i s h y g r o s c o p i c , t h e c a p i l l a r i t y of w a t e r m u s t t a k e p l a c e i n s i d e t h e f i l l because t h e r e l a t i v e humidity i s g r e a t e r a t t h e o u t s i d e of t h e c a v i t y t h a n a t i t s i n s i d e , I f , a t t h e same time, t h e t o t a l amount of m o i s t u r e t r a n s m i t t e d i s assumed t o be unchanged, t h e n t h i s would mean an i n c r e a s e I n t h e amount o f vapour d i f f u s i n g o u t -

s i d e t h e c a v i t y , However, t h i s i n c r e a s e corresponds t o a n i n c r e a s e i n t h e drop of vapour p r e s s u r e i n t h e c a v i t y . A t

t h e same time t h e vapour p r e s s u r e and r e l a t i v e humidity i n - c r e a s e a t t h e i n s i d e and d e c r e a s e a t t h e o u t s i d e , F o r t h i s r e a s o n b o t h t h e vapour d i f f u s i o n and t h e c a p i l l a r i t y i n t h e

w a l l s s u r r o u n d i n g t h e c a v i t i e s d e c r e a s e t h u s r e d u c i n g t h e t o t a l amount of m o i s t u r e t r a n s m i t t e d t h r o u g h t h e w a l l , Thf s means a n a d d i t i o n a l i n c r e a s e i n t h e drop i n vapour p r e s s u r e i n t h e c a v i t y s i n c e t h e t o t a l drop i n vapour p r e s s u r e i n t h e w a l l i s c o n s t a n t . The r e s u l t w i l l t h u s be a v e r y c o n s i d e r a b l e i n c r e a s e i n t h e drop i n vapour p r e s s u r e i n t h e c a v i t y and t h u s a c o r r e s p o n d i n g i n - c r e a s e i n t h e amount of vapour d i f f u s i n g o u t s i d e t h e c a v i t y , As n u m e r i c a l c a l c u l a t i o n s f o r sawdust w i t h s u r r o u n d i n g con- c r e t ~ w a l l s show, t h i s l a t t e r i n c r e a s e i s many t i m e s g r e a t e r t h a n t h e t o t a l amount of m o i s t u r e t r a n s m i t t e d t h r o u g h t h e w a l l . S i m i l a r l y t h e c a p i l l a r f t y o f water t a k i n g p l a c e i n t h e c a v i t y must be of t h e same o r d e r . Hence, because of t h e i n c r e a s e d drop i n vapour p r e s s u r e i n t h e c a v i t y t h e h y g r o s c o p i c i t y of t h e f i l l m a t e r i a l means reduced r i s k o f c o n d e n s a t i o n and a

d e c r e a s e i n t h e t o t a l outward movement of m o i s t u r e i n t h e w a l l , A l a y e r of t a r r e d cardboard, which has no c a p i l l a r i t y and which has ~ e l a t i v e l y l a r g e r e s i s t a n c e t o d i f f u s i o n , i n c r e a s e s t h e vapour p r e s s u r e and t h e r e l a t i v e humidity i n s i d e t h e l a y e r and d e c r e a s e s them a t t h e o u t s f d e of t h e l a y e r . The r i s k o f c o n d e n s a t i o n i n t h e p a r t s of t h e w a l l o u t s i d e t h e cardboard l a y e r i s t h u s reduced. The outward movement of mofsture, b o t h i n t h e form of d i f f u s i o n and i n t h e form1 of c a p i l l a r i t y i s r e - duced,

Hence i n a w a l l w i t h h e a t - i n s u l a t i n g c a v i t i e s

-

f i l l e d o r u n f i l l e d

-

t h e r e i s always i n c r e a s e d r i s k of c o n d e n s a t i o n .

T h i s r i s k i s & r e a t e s t when t h e r e i s o n l y one c a v i t y b e c a u s e t h e g r e a t e s t jump i n t h e s a t u r a t i o n p r e s s u r e would t h e n be o b t a i n e d . The ~ r e a t e r t h e number o f c a v i t i e s c o n t a i n e d i n a w a l l and t h e more t h e s e c a v i t i e s r e s e m b l e e a c h o t h e r w i t h r e s - p e c t t o h e a t - i n s u l a t i n g p r o p e r t y , t h i c k n e s s , and c a p a c i t y f o r c a p i l l a r i t y , t h e more c l o s e l y t h e s a t u r a t i o n c u r v e w i l l r e s e m b l e t h a t a p p l y i n g t o a homogeneous w a l l . I n t h i s c a s e t h e r i s k o f c o n d e n s a t i o n a ~ a i n d e c r e a s e s o f c o u r s e . If t h e c a v i t y i s f i l l e d w i t h a s u r f a c e - i n a c t i v e m a t e r i a l t h e movement o f m o i s t u r e i n - c r e a s e s i n t h e d j i r e c t i o n o f t h e t e m p e r a t u r e d r o p , b u t i f t h e m a t e r i a l i s s u r f a c e - a c t i v e t h i s i n c r e a s e d e c r e a s e s t h e more s u r f a c e - a c t i v e t h e m a t e r i a l i s . If t h e a b o v e s t a t e m e n t i s a p p l i e d t o w a l l c o n s t r u c t i o n s o f t h e t y p e s Nopsa I and I1 t h e f o l l o w i n g r e s u l t s w f l l b e ob- t a i n e d : B o t h t h e c a r d b o a r d l a y e r i n Nopsa I and t h e a i r s p a c e i n Nopsa I1 ( i , e . , i f t h e o u t e r d u c t i s u n f i l l e d ) r e d u c e t h e r i s k of c o n d e n s a t i o n i n t h e f i l l l a y e r i n a s m u c h a s t h e c a r d b o a r d l a y e r r e d u c e s t h e movement of m o i s t u r e t o t h e p o i n t w h i c h i s c r i t i c a l f o r t h e c o n d e n s a t i o n w h i l e t h e a i r s p a c e i n c r e a s e s t h e m o i s t u r e movement f r o m t h i s p o i n t . A t t h e same t i m e , t h e e f f e c t of t h e a i r s p a c e s h o u l d b e s m a l l e r h e r e t h a n t h a t o f t h e c a r d - b o a r d l a y e r . From t h e c o n d e n s a t i o n p o i n t o f view i t i s f a v o u r - a b l e t o s u b d i v i d e t h e Nopsa 11, w h i c h h a s two c a v i t i e s , p a r t i - c u l a r l y when b o t h d u c t s a r e f i l l e d . However, t h e o u t e r c a v i t y s h o u l d n o t b e f i l l e d , s i n c e o t h e r w i s e t h e a i r s p a c e w i t h i n

c o n d e n s a t i o n a t t h e o u t s i d e of t h e f i l l e d c a v i t y t h u s i n c r e a s e s , provided, o f c o u r s e , t h e t e m p e r a t u r e and m o i s t u r e c o n d i t i o n s a r e

such t h a t condensation can o c c u r . I n o r d e r t o reduce t h e r i s k of condensation t h e f i l l m a t e r i a l should have a g r e a t c a p a c i t y f o r c a p i l l a r i t y s o t h a t a r e d u c t i o n i n t h e vapour p r e s s u r e a t t h e o u t s i d e of t h e c a v i t y i s o b t a i n e d by r e a b s o r p t i o n of water. For t h e m a t e r i a l i n v e s t i g a t e d by t h e p r e s e n t a u t h o r , t h e f o l l o w - i n g v a l u e s were o b t a i n e d f o r m o i s t u r e t r a n s m i s s i o n t h r o u g h saw- d u s t and c h a r c o a l : 0.033 and 0,017 kgm./sq,m., hr

.

,

r e s p e c t i v e l y , a t a drop i n vapour p r e s s u r e a t one atm. p e r metre f o r t e s t s over calcium c h l o r f de and 0,046 and 0.024 kgm./sq.m., h r . , r e s p e c t i v e l y , f o r t e s t s o v e r w a t e r , The c a p a c i t y f o r c a p i l l a r i t y i s a p p r o x i - m a t e l y g i v e n by t h e p e r c e n t a g e i n c r e a s e i n m o i s t u r e t r a n s m i s s i o n

i n t e s t s over water i n r e l a t i o n t o t e s t s o v e r calcium c h l o r i d e . This v a l u e i s 39% f o r sawdust and 41% f o r c h a r c o a l , t h a t i s t o say, t h e s e two m a t e r i a l s a r e e q u i v a l e n t from t h i s p o i n t of view.

I n Nopsa I t h e p e r m e a b i l i t y t o m o i s t u r e i s reduced by t h e cardboard l a y e r and i n Nopsa I1 i t i s i n c r e a s e d by t h e a i r s p a c e . The e f f e c t o f t h e c a v i t y f i l l e d w i t h sawdust i s a p p r o x i m a t e l y i d e n t i c a l i n b o t h c a s e s . A l t o g e t h e r t h e p e r m e a b i l i t y i s t h e r e - f o r e g r e a t e r f o r Nopsa 11. This i s a l s o confirmed by computed examples. Nopsa I1 w i t h b o t h c a v i t i e s f i l l e d o n l y l e t s a r e - l a t i v e l y s m a l l amount of m o i s t u r e t h r o u g h . The amount of mois- t u r e p a s s i n g t h r o u g h t h e w a l l s i s s m a l l compared w i t h t h e amount of water e v a p o r a t i n g i n a b a r n , For t h i s r e a s o n t h e e v a p o r a t e d water must be removed from t h e l a t t e r by v e n t i l a t i o n . The t o t a l

p e r m e a b i l i t y t o m o i s t u r e i s i m p o r t a n t f o r t h e f o l l o w i n g r e a s o n . I n c a s e of c o n d e n s a t i o n t h e amount of condensing m o i s t u r e w i l l be s m a l l i f t h e p e r m e a b i l i t y i s s m a l l , b u t a damp w a l l w i l l d r y o u t more r a p i d l y i f t h e p e r m e a b i l i t y i s g r e a t .

As mentioned above, t h e c o n d i t i o n s f o r a r i s k of conden- s a t i o n a p p l y o n l y a s l o n g a s t h e w a l l i s n o t i n t e r r u p t e d by windows, c r a c k s , e t c , I n s u c h a c a s e t h e c o n d i t i o n s may be e n t i r e l y d i f f e r e n t . A s e x p l a i n e d i n d e t a i l t h e r i s k of c o n d e n s a t i o n i n a w a l l i n c r e a s e s i f t h e l a t t e r i s provided w i t h a h e a t - i n s u l a t i n g c a v i t y , t h i s r i s k d e c r e a s i n g t h e more s u r f a c e - a c t i v e t h e mater- i a l i s , A s examples computed on t h e b a s i s o f approximate v a l u e s f o r t h e c o e f f i c i e n t s o f c a p i l l a r i t y and d i f f u s i o n show, t h e

c a p a c f t y f o r c a p i l l a r i t y seems t o be s o g r e a t f o r sawdust t h a t t h e r e i s no r i s k of c o n d e n s a t i o n u n l e s s t h e h u m i d i t y of t h e atmosphere i s v e r y h i g h b o t h o u t s i d e and i n s i d e ,

Close t o a window t h e warmer p a r t s of t h e w a l l c o o l down a s l o n g a s t h e vapour p r e s s u r e i n t h e a i r a t t h e i n s i d e of t h e w a l l i s i d e n t i c a l w i t h t h a t a t p a r t s of t h e w a l l s which a r e f u r t h e r away from t h e window. T h e r e f o r e , c l o s e t o t h e window t h e r i s k o f c o n d e n s a t i o n i s g r e a t e r , and condensed water f i n a l l y s p r e a d s t o a d j o i n i n g p a r t s of t h e w a l l due t o c a p i l l a r i t y and t h e e f f e c t o f g r a v i t y .

If t h e r e a r e l e a k s ( c r a c k s , e t c . ) i n t h e i n n e r s u r f a c e of t h e w a l l , t h e n owing t o chimney e f f e c t warm a i r from w i t h i n f l o w s o u t , c a r r y i n g water vapour t o t h e c a v i t y f i l l e d w i t h sawdust, t h e water vapour condensing i n t h e c o l d e r c a v i t y . Even a v e r y s m a l l l e a k i n a w a l l w i l l r e s u l t i n a n amount of c o n d e n s a t i o n which i s many t i m e s g r e a t e r t h a n t h a t which c a n normally o c c u r i n a w a l l ,

0.035

0.030

. C E M E N T P L A S T E R

-

0.025

1 I- B A S T A R D STUCCO - Z W I- C O N C R E T E 7

0

0.2

0.4

0.6

0.8

1

.O

R E L A T I V E H U M I D I T Y

RELATIVE HUMIDITY

0

400

800

1200 0

0.4

0.8

T I M E

IN

H R .

R E L . H U M I D I T Y

/ 0 0 o R.H. 0.5

Fig. 4. The weight of the sawdust sample a s a function of the time and of the

relative humidity of the ambient atmosphere.

R.H.= 1.0 040-o-o-

- -

-

I I I I I I F

-

-.- -

-

-.

o*@ I 0 I ~ R . H I = o - - - . - - - 0 . 5 4 7

- - - -

I - - I . . - , - ,

- - -

I I I I /

-

-

-

.-

- -

I R.H.= 0.8 0 1 core-0-0-0 0 -

- - -

-1.-

-

- -

- - -

- -

-

- 0 1

- -

-

.-

-

-

- - -

Fig.

5.

Diff'usion coefficient

pd

as a function of porosity.

RES

a

LL

2 0 0 0

2 5 0

WEIGHT

B Y VOLUME

"0

4

8

12

16

P. I

o3

ATM.

Fig. 7. Diagram for calculating the moisture transmission by means of the relation

The moisture movement through a wall of thickness

b

m., having a temperature of

6'10~.

and a vapour pressure of pl atm. at one side and a temperature of

Q20c.

and a vapour pressure of p2 atm. at the other, becomes

0.8

TEMP.

Fig. 8. Moisture distribution in a homogeneous wall with vapour diffusion alone (no capillarity).

HOMOGENEOUS WALL WlTH WALL WlTH FlLL

WALL AIR SPACE CAVITY, BUT NO

CAPILLARITY

TEMPERATURE

- - - _{SATURATION PRESSURE} - - VAPOUR PRESSURE

- - - -

R E L A T I V E HUMIDITY

WALL WITH FlLL WALL WlTH

CAVITY

a

CARDBOARD

CAPILLARITY LAYER

Fig. 9. Fundamental e f f e c t o f a i r space and f i l l c a v i t i e s a s well a s cardboard layers on the d i s t r i b u t i o n of vapour

Table 1

I

1. Charcoal, 0.7 m. 7. Concrete, cement t o sand 1:9 p a r t s by w t . 12. Lime p l a s t e r , lime p l a s t e r t o sand 1:3 parts by vbl.

2. Sawdust 8. 11 n 11 n 1:9 n 11 n _{13. Brick}

3. Rock wool 9. II w II 11 1: 4 w II N 14, 15. Class spheres of 0.5 and 1.9 diam. respectively

4. Masonite, hard 10. Cement p l a s t e r , cement t o sand 1:3

_garts

by 16. Siporex

5. b s o n i t e , poroua 11. Bastard stucco, 30% cement p l a s t e r y ut. and

6. Sand, 0.7 mm. 70% l i n e plaster.

1 ) After ~ r i s c h e r - ~ % r l i n & VDI

Verfahrenstechnik No. 5, 1938

'.

4 no. 1 2 3 4 5 6 7 8 9 10 11 12 13 11 Weight by vol. kgs./cu.m. 222 211 19 5 997 3% 1800 1800 2000 2200 2000 1700 1750 1600 1860

-

15 16 I 450 I Thickness of sample in m* 0.015 0.030 0.015 0.030 0.015 0.030 0,055 0.0041 0.0115 0.030 coarse c a p i l l a r y 'coarse 44 h9 93 16 71 32 31 23.5 1 5 21

T;;

-

Pprosity t o t a l P 8h 86 93 36 77 32 33 26 19 27 38 j5 40 i n % fine-cap- i l l a r y 2.3 6.3 0 20 6.0 0 2.1 2.5 4.0 6.4 -- - .2 39.5 39.5 83 I 28.5

1

28.5

Coefficient of moisture transmission

i n kgm./m.atm.hr. and mean value of

-

_p Pd 1.41 1.39 1.36 1 1.31 1.78 1 3.7 0.66 0.81 1 (0.65) 3.2 3.35 3.25 3.1 2.75 3.4 : l o ) 8

over calcium chloride

0.018~) 0 , 0 2 2 ~ ) I 0.037 I 39.5 39.5 (83) Reduction factor pd

-

0*069 'coarse 0.56 0.98 0.88 0.038 0.16 0.57 0.13 0.0074~) over p 0.024 O.OL6 - 0.045 0.0% 0.00055 0.0135 0.0125 0.010 0.0086 0.0074 0.0065 0.0026 0.0020 0.0037 0 . 6 5 0 . 0 0 6 5 , 0.010 P d 19 19 19 19 19 19 I

0"

::

:

i

I Capillarity coefficient Pf i n k ~ . / m.f.hr. 0.0017 0.0015 - 0.000 --. 0,0000017 0.00U 0.011 0.13 0.080 0.W3 0.095 (0.04) water Rel. Hum. % 68 63 65 68 67 66 72 72 72 72 72 72 72 72 72 72 Rel, Hum, 0.015 0.030 0.015 0.030 0.015 0.020 . 0.015 - 0,015 0.0080 0.0015 0.0018 0.0027 0.0022 0.0020 0.00083 0.00135 0.0019 (0.0010) i % 0.017

1

32

1

0. 8 0.033 0.0% 0.00042 0.0076 0.0027 36 36 24 31 19