Model to simulate the structure and performance of cellular polymeric membranes: Structure, flux and filtration characteristics

@ELLINGCELLULAR POLYMERIC MEMBRANES Model to Simulate the S t r u c t u r e and P e r f o r m a n c e of Cellular Polymeric M e m b r a n e s : Structure, Flux and Filtration Characteristics N.M. J a c k s o n Department of Chemical Engineering, UMIST, Manchester M60 1QD, UK Winner of the Filtration Society's 1994 Suttle Award

The calculation of the flux/pressure drop relationship for polymeric membranes using the Hagen--Poiseuille relationship takes only the pore size and membrane depth into consideration, and fails to consider the internal cellular structure. The understanding o! the structure of such membranes has been achieved by scanning electron microscopy (SEM) and image processing techniques, and with such a complex internal structure it is clear that further consideration of the cellular polymeric mesh must be included. A stochastic three-dimensional (3D) geometric model is used to simulate these structures. Predictions of the pore properlies are in good agreement with data obtained by image analysis of SEM photomicrographs. The clean membrane flux variation with pressure drop is predicted by considering creeping viscous flow past an array of oblique cylinders, where the pore edges are assumed to be cylindrical in shape. Excellent agreement between the theoretical predictions and experimental results has been achieved for the membranes studied. The stochastic model is used to predict the transport of latex slurries in dead-end pressure filtration. This has been developed to predict a surface cake and the penetration of particles into the membrane. It is possible to predict the importance of the particle diameter to the pore size rating and the position of fouling in the membrane. Graphical images are compared to photomicrographs, to obtain knowledge of the steric interactions between particle-particle and particle-pore collisions within and on the surface of the membranes studied. In addition, the model is capable of extension to other forms of cellular porous structures.

he tech nology of s e p a r a t i o n p r o c e s s e s using p o r o u s mem-

b r a n e s c o n t i n u a l l y finds more a p p l i c a t i o n s . The choice of T m e m b r a n e d e p e n d s on the feed s o l u t i o n to he s e p a r a t e d , for which knowledge of t h e pore size d i s t r i b u t i o n and the i n t e r n a l s t r u c t u r e of t h e m e m b r a n e is e s s e n t i a l when m a k i n g t h e choice of an a p p r o p r i a t e m e m b r a n e . A l t h o u g h m a n u f a c t u r e r s give very definite and s t r a i g h t f o r w a r d i n f o r m a t i o n a b o u t m e m b r a n e cutoff a nd pore size d i s t r i b u t i o n , l o t e x a m p l e , no a t t e m p t is m a d e to place t hi s ,nfo rmation in a more c o m p a r a t i v e framework. Hence t he (tuestion arises as to w h a t i n f o r m a t i o n can be o b t a i n e d from c h a r a c t e r i s t i c m e a s u r e m e n t s which will help in t h e p r e d i c t i o n of m e m b r a n e perlbrmance. Techniques to c h a r a e t e r i s e m e m b r a n e s vary d e p e n d mg on l,he m e m b r a n e type a n d its r e c o m m e n d e d pore size. Membran e c h a r a c t e r / s a t / o n leads to the d e t e r m i n a t i o n of s t r u c t u r al a n d morphoh)gieal p r o p e r t i e s t h r o u g h such m e t h o d s as electron mi(:roscopy, bubble-point, mercury i n t r u s i o n and permeability, a nd rrom such t e c h n i q u e s a pore s t r u c t u r e is a s s u m e d , a l t h o u g h t h i s is . f t e n c a t e g o r i s e d as e i t h e r a p a r a l l e l - p o r e or p a c k e d - b e d type structure. Therelore, c h a r a c t e r / s a t / o n d a t a for p o r o u s m e m b r a n e s ()ften give rise to m i s u n d e r s t a n d i n g s and m i s i n t e r p r e t a t i o n s , a n d man y c h a r a c t e r / s a t / o n m e t h o d s e s s e n t i a l l y only d e t e r m i n e t h e pore size an d th e por e size d i s t r i b u t i o n . However, it s h o u h l be re a l i s e d I hat even wh en porous m e m b r a n e s have been c h a r a c t e r i s e d in t hi s way, a n d the pore sizes and pore size d i s t r i b u t i o n s d e t e r m i n e d properly, in s e p a r a t i o n processes t h e m e m b r a n e p e r f o r m a n c e is main ly controlled by o t h e r factors, sueh as eake forma t i on a n d i n t e r n a l fouling. For t h e s e r e a s o n s t h i s p a p e r d i s c u s s e s a model which goes into m u c h d e t a i l to d e v e l o p a 3D g e o m e t r i c a l s i m u l a t i o n of the overall i n t e r n a l s t r u c t u r e by s i m u l a t i n g t he l)ore size, pore size d i s t r i b u t i o n , free volume, pore edge d i a m e t e r and length, a n d the ' i n t e r e o n n e e t e d n e s s ' of i n t e r n a l p a t h w a y s t h r o u g h o u t th e structure. With such a model it is t h e n p o s s i b l e to p r e d i c t th e i n t e r a c t i o n s t h a t occur d u r i n g t h e filtration of l a t e x t)article slurries. It is possible to p r e d i c t the clean membram~ l l ux by c o n s i d e r i n g the flow t h r o u g h t h e i n t e r n a l s t r u c t u r e a s s u m i n g t h a t the i n t e r n a l mesh c o n s i s t s of polymeric cTlinders. This is a sig nifican t a d v a n t a g e lot- flux p r e d i c t i o n s o1' p o r o u s media, as t h e

Filtration & Separation

January 1995

p a r a l l e l - p o r e m o d e l c o n s i d e r s only t h e pore d i a m e t e r a n d m e m b r a n e de pt h, a nd fails to c o n s i d e r t he t o r t u o u s flow p a t h s t h r o u g h t h e i n t e r n a l structure. By i m p l e m e n t i n g a g e o m e t r i c a l me t hod, as o p p o s e d to an a na l yt i c a l one, a 3D c e l l u l a r s t r u c t u r e is g e n e r a t e d which is b a s e d on t h e Vorom)i tessellation. This p a p e r defines such a mode l to s i m u l a t e th e c e l l u l a r m e m b r a n e s . An SEM s t udy has been u n d e r t a k e n to e n a b l e this. In a ddi t i on, e x p e r i m e n t a l d a t a l o t clean m e m b r a n e flux is p r e s e n t e d a nd c o m p a r e d to p r e d i c t e d r e s u l t s achieved us i n g a flow model. SEM c o m p a r i s o n w i t h g r a p h i c a l o u t p u t of t h e m o d el af ter s e p a r a t i o n is a l s o s h o w n to e x h i b i t t h e s i m i l a r i t i e s of t h e t h e o r e t i c a l with t he e x p e r i m e n t a l work. As an e x a m p l e of a c e l l u l a r m e m b r a n e , t h e polymeric cellulose a c e t a t e m e m b r a n e is used a t bot h t h e 0.2 pm a nd 0 . 4 5 / t i n pore ratings.

Model structure A Voronoi t e s s e l l a t i o n provi de s a model of a r a n d o m c e l l u l a r n e t w o r k w h i c h is i n c r e a s i n g l y being used in two a n d t h r e e d i m e n s i o n s to describe, analyse and model t he s p a t i a l p a t t e r n s of points.[I.21 In its 3D form it p a r t i t i o n s s pa c e into co n v ex polyhedra, and ma y be t h o u g h t of as a ne t w ork of interfaces formed by t h e i m p i n g e m e n t of e x p a n d i n g spheres, c e n t r e d at th e nuclei, an d growing a t a c o n s t a n t ra t e from t i m e zero. U l t i m a t e l y each n u c l e u s will have a t e r r i t o r y which is t h a t a r e a of s pa c e n e a r e r to it t h a n to any o t h e r nuc l e us point. Such a s t a t i s t i c a l ge om etr ical a p p r o a c h c o n s t i t u t e s a u n i q u e a nd n a t u r a l s t a r t i n g p o i n t for th e an aly s is a n d m o d e l l i n g of c e l l u l a r m e m b r a n e structures. It is based on th e p r o p o s i t i o n t h a t a 3D s p a c e filling t e s s e l l a t i o n will t a k e u p one of t h e mos t p r o b a b l e c o n f i g u r a t i o n s of 3D s t r u c t u r e s . The final 3D s t r u c t u r e c o n s i s t s of a t e s s e l l a t i o n of n e s t e d polyhedra, each m a d e up of i r r e g u l a r polygons. These polygons s i m u l a t e t h e pores, a n d t h e p o l y h e d r o n s t h e (:ells. The edges of t h e s e shapes, on in clu s io n of an edge t hi c kne s s , s i m u l a t e t h e pol yme ri c mesh of t h e m e m b r a n e material, a n d so we can directly c o m p a r e t he s t r u c t u r e to a c t u a l m e m b r a n e s w he re all t h e s t r u c t u r e ' s c h a r a c t e r i s t i c q u a n t i t i e s are calculated. These are p r e s e n t e d in t he n e x t Section. The a l g o r i t h m to g e n e r a t e t he s t r u c t u r e (tan be found in p a p e r s by Watson, la]

0015-1882/95/US$7.00 a

1995 Elsevier Science Lid

69

@ELLINGCELLULAR POLYMERIC MEMBRANES

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Figure 1. Nuclei points in three-dimensional space.

Figure 2. Delaunay triangulation about the nuclei.

]~owyer 141 a n d T a n e m u r a e t a l . [-'] To c o n s t r u c t t h e Vuronoi t e s s e l l a t i o n in t h r e e d i m e n s i u n s the D e l a u n a y t e s s e l l a t i o n , which is an a g g r e g a t e of i r r e g u l a r t e t r a h e d r a , is construct e d. This is t he g e u m e t r i c d ual uf t h e Voronoi t e s s e l l a t i o n , which ('an t h e n he ('onstructed in a s i m p l e step. The nuclei, positi(me(t a c c o r d i n g t,u a I)oisson p o i n t p r o c e s s , d e f i n e t h e p o i n t s of t h e D e l a u n a y t e s s e l l a l i o n which lie at the t e t r a h e d r a vertices. The l o u t ve~%ices ()f each t e t r a h e d r o n lie on t h e s u r l a c e of a sphere, with t he c e nt re uf the s p h e r e being the circumcentre. Hence for all te t ra hc (h' a t h a t sh are a vertex, t h e i r c o n n e c t i n g c i r c u m c e n t r e s lk)rm all t he edges ;rod s u b s e q u e n t faces of a Voronoi polyhedron, whe re t h e e x i s t i n g ~ertex is the nucleus of the Voronui polyhe(h'on. The n u m b e r

densiW of nuclei in t h e real s t ruc t ure , N, defines th e n u m b e r of Poissun points. Thus in t he Voronui t e s s e l l a t i o n a cell is e q u i v a l e n t tu a polyhedron. The Voronoi cell of pore i is rr~, defined by

• a•

•

~,

{:r!d(:r,x, ) < (t(:F, x j )

for all j ~

i}

(1)

where :r I , x2, ..., :rl ..... :~:~. are the co()rdinates of nuclei in the unit

•

q

el

Figure 3. Resultant Voronoi tessellation of three-dimensional space. 70

Figure 4. Largest inscribed circle of a polygon (simulated pore). January 1995

Filtration & Separation

@ELLINGCELLULAR POLYMERIC MEMBRANES Variance (as % of unconstrained model) 100-T- ~----..__~,,,~.._ +Perimeter 90

..........

60

5O

...~-~-~.....

--Surface Area

..................................................

0

10

20

~

30 40 50 Constraint on R (%)

60

70

Figure 5. Decrease of distribution size with constraint increase.

v o l u m e re', a n d d(x, y) is the E u c l i d e a n d i s t a n c e betw e e n x a nd y. In o t h e r words, 7ri is t h e set of p o i n t s which is n e a r e r to t he n u c l e u s x~ t h a n o t h e r xjs. This p r o c e s s is shown in Figures 1--3. The pore (polygon) sizes in the model are c a l c u l a t e d by defining t h e l a r g e s t inscribed circle as shown in Figure 4. However, on c o m p a r i n g t he d i s t r i b u t i o n of pore sizes in t h e s t r u c t u r e to t h o s e of t h e cellulose a c e t a t e m e m b r a n e , one observes t h a t the d i s t r i b u t i o n is muc h wider t h a n t h a t of the m e m b r a n e . This is corrected by i n t r o d u c i n g a c o n s t r a i n t in t h e Poisson p o i n t process. A c o n s t r a i n t d i s t a n c e R is defined su ch t h a t any two nuclei m u s t be a t lea.st a d i s t a n c e /~ a p a r t . Hence, as R i n c r e a s e s , t h e s t r u c t u r e b e c o m e s m o r e c o n s t r a i n e d . This h a s t h e u l t i m a t e effect of r e d u c i n g t h e d i s t r i b u t i o n of polygon edges and also the p o l y h e d r o n volumes, surface a r e a s a n d perimeters. The l a t t e r t h r e e are shown in Figure 5 at varying c o n s t r a i n t distances. The second difference between th e m e m b r a n e a n d the model is t h e edge thickness. This is overcome by a t t a c h i n g a finite d i a m e t e r tu the polygon edges, s uc h t h a t t h e t e s s e l l a t i o n v o l u m e m i n u s the total edge v o l u m e m a t c h e s the free v o l u m e of t h e s i m u l a t e d m e m b r a n e :

A c o n s t r a i n e d Voronoi 3D t e s s e l l a t i o n with edge t h i c k n e s s e s is shown in Figures 6 a n d 7. Figure 6 d i s p l a y s t h e s e p a r a t i n g surface; this is r e p r e s e n t a t i v e of all p l a n a r s e c t i o n s t h r o u g h t he model.

Figure 7. Cross-section of the membrane model.

Figure 7 s how s t he a x i s of filtration ( z - a x i s ) ; t h i s is symmetri,: w i t h t h e x- a nd y-axes. This p r o v i d e s a first e s t i m a t e of t h e s t r u c t u r e of a c e l l u l a r pol yme ri c memt)rane. The c h a r a c t e r i s t i c q u a n t i t i e s are shown i~ Figures 8 - - 1 1 for a t e s s e l l a t i o n of 2158 p o l y h e d r a which wa:~ a c hi e ve d by 3300 nuclei points; t h e s e are t he s t a t i s t i c s of t h , s t r u c t u r e with i m p o r t a n t e n g i n e e r i n g implications. The topological s t a t i s t i c s are also calculated, but are not so i m p o r t a n t here. These are t he c o o r d i n a t i o n n u m b e r of t he t e s s e l l a t i o n (i.e. th e n u m b e r or e dge s j o i n i n g a t a v e r t e x ) ; t he n u m b e r of edges, faces an d vertices, p e r polyhedron; a nd the a ngl e s between edges. The m e a n an d v a r i a n c e are c a l c u l a t e d for all of these.

SEM study of cellulose acetate Previous re s e a rc h s u g g e s t s t h a t the i n t e r n a l c r o s s - s e c t i o n a l view of cellulose a c e t a t e a n d s i m i l a r polymeric m e m b r a n e s is sTmmetric w i t h t h e p l a n a r view, i.e. t h e s e p a r a t i n g surface. V;] As t h i s currenl piece of work c o n c e n t r a t e s e nt i re l y on t he i n t e r n a l s tr u ctu r e, such an a s s u m t ) t i n n c a n n o t be m a d e w i t h o u t physical e x a m i n a t i o n by a SEM study. By p e r f o r m i n g both s u r l a c e a n d cross-section by freeze fi-acture s t u d i e s a c l e a r e r p i c t u r e of t h e m e m b r a n e s t r u c t u r e in bot h p l a n e s ha s been obt a i ne d. The surface SEM s t u d y shows the symmetr3~ of t he s e p a r a t i n g surface (Figure 12). One can observe t he p o r o u s s t r u c t u r e both a t a nd b e n e a t h t he m e m b r a n e surface. The s3m/metlT on t h e s u r l a c e ah)ng bot h axe.,; s i m u l a t e d by th e

frequency (Thousands) 10 .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

6

2 0

Figure 6. Separating surface o! the membrane model. Filtration & Separation

January 1995

3

5 7 9 11 edges per polyhedral face

13

Figure 8. Distribution ot edges per polygon. 71

@ELLINGCELLULAR POLYMERIC MEMBRANES frequency 6OO 500 ........................................................................

~ooI............................~

...........................

~oo 1........................ / .............. \ ........................ ~oo I...................... / .................... \

0.5

....................

1

1.5

polyhedral cell p e r i m e t e r ( m e a n n o r m a l i z e d ) Figure 9. Distribution of polyhedron perimeter.

frequency 500~

=I /

400

I

I

1 O0

L.

/

/ ~

j

.

.

.

.

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Figure 12. Scanning electron micrograph of a cellulose acetate membrane's separating surface.

0

i

05 1 15 polyhedral cell surface area (mean normalized) Figure 10. Distribution of polyhedron surface area.

frequency 500 400 300 200 100 0.3

0.65

1

1.35

1,7

2.05

Figure 13. Scanning electron micrograph of a cellulose acetate membrane axis of filtration.

polyhedral cell volume (mean normalized) Figure 11. Distribution of polyhedron volume. Membrane simulation and comparison by image analysis techniques model is also evident. Secondly, Figure 13 shows t h e r e s u l t s of a cross-sectional view. The pore s t r u c t u r e and edge t h i c k n e s s are evident, b ut a layered effect can be seen such t h a t t he m a j o r i t y of pore edges are p e r p e n d i c u l a r to t h e a x i s of filtration. This s t r u c t u r e occurs d u r i n g manufacture, where the m e m b r a n e is rolled a nd t h e r e b y comp ressed, a l t h o u g h originally it is s i m i l a r in s t r u c t u r e to t h e p l a n a r view of Figure 12. F u r t h e r SEM views down t he a x i s of filtration show t h a t t h i s s t r u c t u r e is uniform in t he z-axis. The s a m e s t u d y was also p e r f o r m e d after t h e filtration of d e i o n i s e d water, in which it was shown t h a t t h e s t r u c t u r e was not affected.

72

Ultimately, the m e m b r a n e model will be us e d as a p e r f o r m a n c e tool to p r e d i c t clean m e m i ) r a n e flux a nd flux decline d u r i n g p a r t i c l e s e p a r a t i o n . Before t h i s can be achieved, t he model m u s t be s t r u c t u r a l l y e q u i v a l e n t l.o t he a c t ua l m e m b r a n e for s i m u l a t i o n , in t hi s case cellulose acetate. Ik~o c o m p a r i s o n s can he made; th es e are t h e p l a n a r a nd c ros s -s e c t i ona l mode l s w i t h t he SEM p h o t o m i c r o g r a p h s from t he p r e v i o u s Section. By c o m p a r i n g Figures 6 an d 12 for t h e p l a n a r view it is seen t h a t a good s i n m l a t i o n of t h e pores a nd t he edge t h i c k n e s s has been achieved. The s y m m e t r y in both t he x- a nd y a x e s ha s also been achieved by t he model, as has th e porosity, which was c he c ke d us i ng t he i ma ge p r o c e s s i n g t e c h n i q u e s

January 1995

Filtration & Separation

@ELLINGCELLULAR POLYMERIC MEMBRANES of t h r e s h o l d i n g , edge detection and pixel counting. The only difference is t h e actual s h a p e of t h e pores: l)oth are convex, but t h e SEM sh ows more r o u n d e d pores, w h e r e a s the model's are polygonal in shape, m a d e up of a d i s c r e t e n u m b e r of edges. This r e s u l t s from th e surface t e n s i o n fi)rees which occur at the nodal sites d u r i n g l o r m a t i o n of t h e erystallim~ or solid form of t h e cellulose a c e t a t e metal)rune a n d [)ther polymeric c e l l u l a r structures, ttowever, t h i s difference is believed to he insignifi(ant, since w he n p a r t i c l e s e p a r a t i o n is considere(l, the l a r g e s t inscribed eir('le of t he polygon is used to deline its effective shape. Figures 14 and 15 s how t h e .~tatistical c o m p a r i s o n of pore l)erimeters and areas, respectively. I{oth are i n e a n - n o r m a l i s e d , and t h e m e m b r a n e nmdel w a s a d j u s t e d by scalin g and s e t t i n g the edge d i a m e t e r s to achieve the sam(=" porosity. ']?he p e r i m e t e r s and the a r e a were l h c n m e a s u r e d u s i n g hnage analysis. The second c o m p a r i s o n of the a x i s of filtration (tan be seen by ,'()mparing Figures 7 and 13. I m m e d i a t e l y it is clear t h a t t h e r e is an m('nnsisten(~ wi thin the model, since the m e m b r a n e model fails to s i m u l a t e th e c o m p r e s s e d i n t e r n a l s t r u c t u r e of the eelluh)se a c e t a t e membrane. However, t h i s can be s i m u l a t e d in the model s t r u c t u r e hy p erforming an afl]ne t r a n s f o r m a t i o n on t h e z-axis. C hoos i ng a linear affine t r a n s l b r m a l i o n of the lorm z

~

/~z

w}wrc ,'1 .< 1

(3)

has t h e effect of c o m p r e s s i n g t h e s t r u c t u r e a nd k e e p s t h e u n i l b r m i t y t h r o u g h o u t the z axis. Furthermore, the effect of t h i s ~r a n s f o r m a t i o n includes t h e r e o r i e n t a t i o n of all t h e edges such t h a t t h e i r angle relative to the direction of flow t e n d s to 9 0 . 1/sing image analysis the degree of c o m p r e s s i o n is c a l c u l a t e d t2om t h e ,'elluh)se a c e t a t e cross-section in o r d e r to derive a v a l ue for ~. This method was i m p l e m e n t e d , and the r e s u l t i n g s t r u c t u r e is shown in Figure 16; I~'igure 17 shows the r e s t r u c t u r e d z-axis. Both s houl d be visually c o m p a r e d lo Figures 12 and 13, respectively. A compre-

Per Cent of sampled pores .e-~,~== T

100~

20

..... ~

Ol ~, , .~ . 0

T

T

T

...................... 2-- Cellulose Acetate ......

~-,Memb rane M°de.

0.25 0.5 0,75

1

1,25 1.5 1.75

2

Figure 14. Comparison of membrane versus model pore perimeter distributions.

Per Cent of sampled pores 100 8O

40

-.-- Cellulose Acetate • 0

-+- Membiane Model

0.25 0.5 0.75 1 1.25 1.5 1.75 Mean normalised

2

2.25

Figure 15. Comparison of membrane versus model pore area distributions. Filtration & Separation

January 1995

I¥1UIIlUi

gllll~ IIIUUI~I

UUIJCt

Figure 17. Transformed axis of filtration (cross-section).

2.25

Mean normalised

20

Figure 16. Separating surface of the membrane model.

he ns i ve s i m u l a t i o n of t h e s t r u c t u r e of t he c ellu lo s e a c e t a t e m e m b r a n e is now a v a i l a b l e which can be easily a d a p t e d to s i m u l a t e o t h e r pol yme ri c c e l l ul a r s t r u c t u r e s such as cellulose nitrate, all a t varying pore size rating. Work has been car r ied out on s a m p l e s of 0.2 pm and 0.45 pm.

Pressure flow model to predict the clean solvent flux/pressure drop relationship for cellular polymeric m e m b r a n e s Flow t h r o u g h o u t t h e e n t i r e m e m b r a n e s t r u c t u r e h a s b e e n c a l c u l a t e d by c o n s i d e r i n g flow t h r o u g h t he m e m b r a n e m o d el sealed to t h e a c t u a l m e m b r a n e size. Each cell in t h e m e m b r a n e is c o n s t r u c t e d by a n u m b e r of polymeric edges of varying len g th a n d di a me t e r. These are a s s u m e d to be cylindrical in s h a p e w h e r e a n u m b e r of cylinders j oi n a t a vertex, a nd it is on t h i s a s s u m p t i o n t h a t t he p r e s s u r e flow model is founded. By c o n s i d e r i n g th e v is co u s flow a r o u n d all cylinders a n d t he h)rce e x e r t e d on each cylinder for a given flux, t h e overall p r e s s u r e drop is calculated. A l i t e r a t u r e survey on p r e v i o u s a t t e m p t s to p r e d i c t t he flow t h r o u g h p o r o u s m e d i a revealed t h a t o t h e r mode l s use a s i m i l a r a p p r o a c h , w ith t h e e x c e p t i o n t h a t all cylinders are p e r p e n d i c u l a r t.o the d ir ectio n of flow, K] a nd are a r r a n g e d in r e g u l a r arrays such as body-centred cylindrical paekings, or t h a t t h e flow d e p e n d s on t h e m e m b r a n e d e p t h a nd porosity. [s] These a s s u m p t i o n s are not valid for t h e p r e s e n t model, a nd a more d e t a i l e d a p p r o a c h to t h e p r o b l e m is required. In t h i s case il is ne c e s s a ry to pre(tict £he flow t h r o u g h a 73

@ELLING

CELLULAR POLYMERIC MEMBRANES

.

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Flux (g/s) Figure 19. Flux/pressure drop relationship Ior cellulose acetate membranes.

Figure 18. Angles of flow past an oblique cylinder.

r a n d o m array of cylinders, where each cylinder is ohlique to t h e d irectio n of flow a c c o r d i n g to t h e angles 0 a n d O, w h e r e ~ is t h e an gle m a d e with the x - a x i s on the x - y p l a n e and 0 is t h e a ngl e with t h e a x i s of filtration ( z - a x i s ) . The angle 0 has no effect on t h e flow, as t h i s r e l a t e s to t h e cylinder p o s i t i o n relative to t h e x- a n d ya x e s ( t h e surface a x e s ) ; however, the angle 0 is vital to t h e flow of t he liquid a r o u n d t h e cylinder. If 0 -- (Y t h e n flow is p e r p e n d i c u l a r to the cylinder, while 0 = 90 ° implies flow p a r a l l e l to t h e cylinder. By l i n e a r i s i n g t h e p r o b l e m s of p e r p e n d i c u l a r and p a r a l l e l vi s c ous fluw a r o u n d a cylinder, the flow p a s t an oblique cylinder ]nay be c a l c u l a t e d by c o m p u t i n g the c o m p o n e n t s in both d i r e c t i o n s tu o b t a i n the r e s u l t a n t flow. This is shown in Figure 18, w h e r e t h e two c o m p o n e n t s of flow are derived, a n d the r e s u l t a n t flow o b t a i n e d d e p e n d i n g on t h e angle 0. By c a l c u l a t i n g the s h e a r r a t e on t h e parallel and p e r p e n d i c u l a r cases a n d deriving the s h e a r s t r e s s (a f r e q u e n c y d i s t r i b u t i o n is a s s i g n e d to d e s c r i b e t h e c y l i n d e r ( , r i e n l a t i o n s ) , t h e forces of all cylinders in t h e x, y and z d i r e c t i o n s are calculated. These result: in zero in t he x and y directions. ']['he force in z is nonzero, as it r e l a t e s to t h e p r e s s u r e (hop. This is divided by t h e t o t a l m e m b r a n e a r e a to give t he t ot a l iwessure dro p nf t h e m e m b r a n e at an initial veh)city l.~.

Experimental work to determine clean membrane flux at varying transmembrane pressures for cellulose acetate membranes I.'xperimental work w a s carried out to d e t e r m i n e the f l u x / p r e s s u r e dro p r e l a t i o n s h i p for W h a t m a n cellulose a c e t a t e m e m b r a n e s of 0.2 ffm and 0.45 ffm pore size r a t i n g with m e m b r a n e d i m e n s i o n s of 25 mm in d i a m e t e r and 125 y m in depth. The e x p e r i m e n t s were t a r r i e d out in a l 0 ml Amicun m i x e d (:ell u s i n g d e i o n i s e d water, and th e r e s u l t s are shown in Figure 19. The e x p e r i m e n t w a s r e p e a t e d w i t h o u t a m e m b r a n e , in u r d e r to o b t a i n the p r e s s u r e d r o p ( a u s e d by t h e m i x e d cell. The a c t u a l p r e s s u r e drup a c ros s t h e m e m b r a n e is therefore c a l c u l a t e d by s u b t r a c t i n g t h e p r e s s u r e d r o p c a l c u l a t e d w i t h o u t the m e m b r a n e .

Comparison of theoretical predictions with experimental results The 3D model r e p r e s e n t s a p o r t i o n of t h e m e m b r a n e , and is m u l t i p l i e d to s i m u l a t e the total 25 m m d i a m e t e r and 125 Izm d e p t h o lume of the membrane. The flee v o l u m e of t h e l n e m h r a n e is used h) d e t e r m i n e the total v o l u m e of m e m h r a n e mate ri a l , a nd ff()m SEM work the mean polymeric edge d i a m e t e r is cah'ulated. Using Ihese r e s u l t s t h e overall length of polymeric edges w i t h i n t h e m e m b r a n e is calculated, and with the cylinder length a nd me a n ( l i a m e t e r the p r e s s u r e flow rondel d i s c u s s e d in t h i s p a p e r is i m p l e m e n t e d . However, the cylinder angles m u s t be known belore I he flow and p r e s s u r e d r o p are calculated. Initially it. was a s s u m e d t h a t th e an gles were evenly d i s t r i b u t e d relative to the surl'ace a n d the d e p t h of filtration, w h e r e a s from the SEM work it is c l e a r t h a t 74

a l t h o u g h t h e a ngl e s of t h e e dge s are evenly d i s t r i b u t e d on t h e surface, t h e a ngl e s of t he edges t h r o u g h t h e m e m b r a n e d e p t h are more h o r i z o n t a l t h a n vertical, a l t h o u g h lor i s ot r o p ic m e m b r a n e s t he a n g l e s in both p l a n e s would be evenly d i s t r i b u t e d . With t he know l e dge t h a t t he W h a t m a n cellulose a c e t a t e filters are a ni s ut ropi c , t h e Voronoi mode l is a d j u s t e d in t h e z-axis. Image p r o c e s s i n g t e c h n i q u e s e na bl e c a l c u l a t i o n of t he value of ~ for Expr. 3. With all t h e p a r a m e t e r s in pl a c e t he p r e s s u r e / f l u w model is i m p l e m e n t e d such t h a t t h e flow a r o u n d t he edges is derived, a n d a t h e o r e t i c a l f l u x / p r e s s u r e drop r e l a t i o n s h i p is calculated. This w a s p e r f o r m e d in t h e s a m e r a n g e of p r e s s u r e s as for t h e e x p e r i m e n t a l work. A di re c t c o m p a r i s o n of e x p e r i m e n t a l r e s u l t s with t h e o r e t i c a l p r e d i c t i o n s w a s therefore a v a i l a b l e to t e s t the viability a nd a c c ura c y of t h e p r e s s u r e / f l o w model; t h e r e s u l t s are shown in Figure 20. It is c l e a r t h a t for bot h sizes of m e m h r a n e th e p r e d i c t i o n s are ve~' close to the e x p e r i m e n t a l results; hence it can be c o n c l u d e d t h a t t he p r e s s u r e / f l o w mode l a p p l i e d here p r o v id es a very precise tool lbr p r e d i c t i n g t he p r e s s u r e / f l u x r e l a t i o n s h i p of c e l l u l a r m e m b r a n e s . In a ddi t i nn, t he d e v e l o p m e n t of the p r e s s u r e / illow model allows for s i m u l a t i o n of flow t h r o u g h o t h e r anisot.r(~pic s t r u c t u r e s w he re t he relative c o m p r e s s i o n ~ in t h e z - a x i s of th e m e m b r a n e is known. This is found by SEM a nd i mag e a n a l y s i s work, a nd is a c e o u n t e d for in t h e model by t h e i n t r o d u c t i o n of a w e i g h t i n g function w i t h i n t he p r e d i c t i o n calculations. Using t h i s m e t h o d a l ong w i t h t h e pressure/'flow model i1 is r e a s o n a b l e to c onc l ude t h a t a good p r e d i c t i o n of f l u x / p r e s s u r e drop in o t h e r a n i s o t r o p i c m e m b r a n e s t r u c t u r e s can be achiew,d. The model, in its u n t r a n s f u r m e d s t a t e (Figures 6 and 7), a p p l i e s directly to isotropic s t ruc t ure s . By identifying is o tr n p ic m e m b r a n e s t he clean f l u x / p r e s s u r e drop thr,:mgh any size of

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Figure 20. Experimental versus theoretical results from the flow model, January 1995

Filtration & Separation

@ELLINGCELLULAR POLYMERIC MEMBRANES

Figure 22. Fouled surface of membrane model.

Figure 21. Fouled surface of cellulose acetate.

zsotropic m e m b r a n e can be c a l c u l a t e d by the p r e s s u r e / f l o w model. In th is case t h e weighl.ing function would be 1.

Experimental investigation of a (latex) particle challenge .<,lurries o1' l a t e x p a r t i c l e s in d e i o n i s e d w a t e r at, d i f f e r e n t ~ o n c e n t r a t i o n s were prepared. Within the e x p e r i m e n t a l work t h e (,ffect of p a r t i c l e d i a m e t e r was s t u d i e d by using s l u r r i e s of different particle d i a m e t e r ( m e a n and v a r i a n c e ) . The use of l a t e x s l u r r i e s is a recognised t e s t p r o c e d u r e by m e m b r a n e m a n u f a c t u r e r s , and is used to p r o d u c e flux decline d a t a at l i x e d pressures. The a l m o s t perfectly s p h e r i c a l s h a p e of t h e s e p a r t i c l e s is veLw." s i m p l e to e e n e r a t e with in the model, and so c o m p u t e r s i m u l a t i o n s of l a t e x i)article c h a l l e n g e s on the m e m b r a n e were p e r l o r m e d . In l h e s e s i m u l a t i o n s t h e s t e r i c effects are c o n s i d e r e d b e t w e e n p a r t i ( : l e - p a r t i c l e a n d p a r t i c l e - - p o r e interactions, such that. a pml.icle 5~u]s a pore if the p a r t i c l e d i a m e t e r is g r e a t e r t h a n t he pore diameter. The pore d i a m e t e r is c a l c u l a t e d by the t e c h n i q u e shown in Figure 4. If a p a r t i c l e p e n e t r a t e s into the m e m b r a n e mode l an i n d e p e n d e n t r a n d o m walk occurs t h r o u g h t h e pores, d e p e n d i n g on Ihe size of t h e p a r t i c l e a n d the size of t h e pores it: encounters. Furthermore, as t h e s i m u l a t i o n progresses, t h o s e p a r t i c l e s which •a n n o t p r o g r e s s beyond t h e surface p o r e s lorm a cake. The cake is t~,rmed by p a r t i c l e - - p a r t i c l e i n t e r a c t i o n s , and m i n i m i s e s t he q u m b e r of p a r t i c l e s filtered by the m e m b r a n e in the l a t t e r s t a g e s ,l" a p a r t i c l e c h a l l e n g e test. Ultimately, the cake be c ome s a ~(,cundary filtration device. P)I SEM work was p e r t b r m e d to confirm )r disp ro ve t h i s h y p o t h e s i s a b o u t p a r t i c l e fimling wit hi n a nd on the m e m b r a n e surlhce. Figure 21 shuws t h e m e m b r a n e snrface a t a mgber m a g n i t u d e al~er p a r t i c l e fouling h a s occurred. P¥om t he !-'igures it is e v i d e n t t h a t p a r t i c l e s arc s e p a r a t e d both on a nd h(,neath ( w i t h i n ) t h e m e m b r a n e surl~tce. F u r t h e r m o r e , s ome lmrticles a p p e a r to be fouling directly over the surface p o r e s as lw(~dicted by t h i s model. Figure 22 shows a s i m u l a t i o n of t h e surlhce of the m e m b r a n e after filtration of a l a t e x t e s t slurry. The d e p o s i t i o n of p a r t i c l e s onto the surface and position of the p o r e s of the s t r u c t u r e are shown. The fouling m e c h a n i s m s p r e d i c t e d by t he model are in accord ~fith t h e e x p e r i m e n t a l o b s e r v a t i o n s seen with tim SEM (see Figures 21 and 22). These Figures deal with the d e p o s i t i o n observed on the s u r l a c e and in the s t r u c t u r e a,s seen in a

Filtration & Separation

January 1995

p l a n e p e r p e n d i c u l a r to t he flow. A section of t he m e m b r a n e t a k e n in a d i r e c t i o n p a r a l l e l to the llow is s h o ~ l in Figure 23. The d e p o s i t i o n on t h e surface, b u i l d u p of cake a nd p e n e t r a t i o n of p a r t i c l e s into t he m e m b r a n e is shown. A s i m u l a t i o n using th e model for s i m i l a r c o n d i t i o n s is shown in Figure 24. The q u a l i t a t i v e c o m p a r i s o n of t h e s e results, e x p e r i m e n t a l ve rs u s theoo~, is guod. Qualitatively, t h e model is provi di ng an a c c u r a t e level of p r e d i c t i o n for t h e i n t e r a c t i o n s which t a k e place d u r i n g filtration of l a t e x slurries. Quantitatively, t h e p r e d i c t i o n of c a ke t h i c k n e s s an d v o l u m e of p a r t i c l e s finding t he m e m b r a n e i n t e r n a l l y a n d t h e i r relative pos i t i on to t h e suri~tce have also been calculated, a n d c o m p a r e well with t he q u a n t i t a t i v e d a t a o b t a i n e d from th e SEM. With such a m<)del in place it has been m a d e p o s s i b l e to c a l c u l a t e cake t h i c k n e s s , i n t e r n a l fouling, r e d u c t i o n in m e m b r a n e free volume, t h e p o s i t i o n of fouling p a r t i c l e s a n d p a r t i c l e e n t r a i n m e n t l h r n u g h the m e m b r a n e fi)r different p a r t i c l e size d i s t r i b u t i o n s . F urt he rmore , t h e efli~ct of bactm, a s h i n g to r e j u v e n a t e m e m b r a n e

Figure 23. Fouled cross-section of cellulose acetate. 75

@ELLINGCELLULAR POLYMERIC MEMBRANES p o s s i b l e f i l t r a t i o n s i m u l a t i o n s of l a t e x p a r t i c l e s l u r r i e s , by c o n s i d e r i n g t h e p a r t i c l e - - p a r t i c l e a n d p a r t i c l e - p o r e in ter actio n s . S i mpl e s c a l i ng of t h e model can c h a n g e m a n y c h a r a c t e r i s t i c s , a n d any p a r t i c l e size m e a n a n d d i s t r i b u t i u n can be introduced, m a k i n g t h e r a n g e of t h e m o d e l a n d s i m u l a t i o n s very w i d e indeed. Visual c o m p a r i s o n s of m e m b r a n e fouling s how good a g r e e m e n t with e x p e r i m e n t a l SEM work, which also confirms t he p r e d i c t i o n s a b o u t t h e physical i n t e r a c t i o n s which occur d u r i n g filtration. It is from t h i s p o i n t t h a t t h e p r e d i c t i u n of flux decline d u r i n g s e p a r a t i o n can be calculated. This w ork is c u r r e n t l y be i ng done by c o n s i d e r i n g flow p a s t a single s p h e r e a nd an a rra y of s p h e r e s to s i m u l a t e i n t e r n a l fouling p a r t i c l e s a n d t h e sud'ace fouling cake, respectively.

Acknowledgments The a u t h o r w oul d like to e x p r e s s his t h a n k s to Professor G.A. Davies a nd Dr D.J. Bell, a nd to fundi ng l'rom t h e UK Science & E n g i n e e r i n g Research Council a nd BioSep ([IK A to m ic Ener~kv Authority).

Nomenclature

Figure 24. Fouled cross-section ot membrane model.

flux can be p r e d i c t e d using the p r i n c i p l e t h a t a pa rt i c l e t a k e s an i n d e p e n d e n t r a n d o m walk back to the m e m b r a n e surface on flow reversal.

Discussion The m o d e l l i n g of a m e m b r a n e is a c o m p l i c a t e d problem, a n d m a n y models oversimplify t h e s t r u c t u r e by a s s u m i n g t)arallel pore c h a n n e l s or a p a c k e d bed a r r a n g e m e n t . On t h e o t h e r hand, t he model d i s c u s s e d in this p a p e r provides a nontri vi a l c n m p l e t e geometric d e s c r i p t i o n o b t a i n e d using an a l g o r i t h m ba s e d on t h e gruwing of nuclei to i m p i n g e m e n t r e l a t i n g directly to t he a c t u a l m a n u f a c t u r e of m a n y foams, c e r a m i c s and -- in t hi s case celluh)se-based materials. The SEM t e c h n i q u e s a p p l i e d here for m e m b r a n e c h a r a c t e r i s a t i o n provide a d i r e c t soluti on for unders t a n d i n g of a structure, and have alh)wed direct m e a s u r e m e n t of the pore sizes and polymeric edge d i a m e t e r s . These s t a t i s t i c s , co upled with t h e p o r o s i t y of the m e m b r a n e and i n t r o d u c e d intu t he m e m b r a n e model, provide an e x c e l l e n t s t r u c t u r a l s i m u l a t i o n . F u r t h e r m o r e , t h e SEM f r e e z e - f r a c t u r e s t u d y h a s s h o w n t h e a n i s o t r o p y of t h e c e l l u l o s e a c e t a t e m e m b r a n e , w h i c h w a s prev iously a s s u m e d to be i s o t r o p i c a n d s y m m e t r i c w i t h t h e m e m b r a n e surface. The d e v e l o p m e n t of a s t r u c t u r a l model ha s e n a b l e d a s t u d y to be carried out on the flow t h r o u g h t h e membran e. A p r e s s u r e / f l o w model has been c o m p l e t e d which gives e x c e l l e n t t h e o r e t i c a l r e s u l t s for the f l u x / p r e s s u r e dru p r e l a t i o n s h i p when c o m p a r e d to e x p e r i m e n t a l results. The s t a t i s t i c a l knowledge on the st~aeture h a s also m a d e

76

References l Fiehm, E.: 'Mathematical ecology' (Wiley, New York, l,q77). 2 Klein, R.: 'Voronoi diagrams in the Moscow metriC. Technical Report no.7, lnstitul for lnformalik, Univemit/il Freiburg, Germany, 1988. 3 Watson, D.F.: 'Computing the n-dimensional I)elaunay tessellalion with al)plication to Voronoi pol~opes', The Computer ,lour~al, I981, 24 (2). 4 Bowyer,A.: 'Compuling Dirichlel tessellations', Tt~e C~Jmp~ter Journal, 1981, 24(2), p. 163. 5 Tanemara, M., Ogawa, T. and Ogita, N.: 'A new algorithm fi)r three dimensional Vornnoi tessellation', J. Computational Physics, 1983, 51, pp. 191 - 2O7. 6 Mulder, M.: 'Basic t)rinciples of membrane lechnolog.~" (Kluwer Academic, London, 1991 ). 7 Bird, R.B., Stewart, W.E. an(t Lightfnol, E.N.: 'Transporl phenomena' (Wiley, London, 1960). 9, Dullien, F.A.L.: 'Porous media: Fluid transpnrt anti pore slruclure' (Academic Press, Lomhm, 1979). 9 Jackson, N.M., Bell, D.J. and Davies, G.A.: 'The pre(tiction of flux decline and blinding in cellular ceramic microliltration membranes'. 8th Symposium [m Separation Science & Techm)h)~', Gatlinburg, Tennessee, USA, Oclober 1993; to be published in ,~paration S<~ience& Technology.

January 1995

Filtration & Separation

TRACTS OFREFEREEDPAPERS Achieving enhanced filter backwashing with combined air scour and subaluidising water al pilot and operational scale Erzielung einer besseren FilterrQcksp/Hung durch eine Kombination van Luftspfilung und subfluidisierendem Wasser im h a l b i n d u s t r i e l l e n M a f l s t a b u n d im n o r m a l e n B e t r i e b s m a B s t a b I ' o , M . J . Chipp.~, M . J . B a u e r u n d R . G . Br~:qley t ,let~Tag~ e*wMfelC wet)el Oasm Condoner Slauoammen get4)e.ctmtte #asset rot oWt we~eten t ~ , ., ~'1} ; K:nld~ffl~J,~wassel Oh.q~O~n Ftt,sal/ yon Koagutat~onsmqlo~, oa~r VorcLlol: ;o0 aultecr,~/'Je:l',a~eo ;.! Me:h'J(~r, :¢I; A~saevldn3 or.~ W,~k~a.~ke,', *ioi, Fr~et-H,J:.'ks~PJOO ~ * de~ Re,D~ha#ueg .~mDo~ot #;9.n,*d4.~ unltd~]len 0,~! I a t x ) t a t ! o ! ~ n u l / a : b c k b ~ ! o~aq¢$~.ho i;,'~($aeratq;Intr~ct~ S!OI~P.~OWtt' ',l.'Je,I X'M:')l~l'u1~kt~*.~op;~ !lr~ ~e UtffPIIUCBI:tI~ ~01, T ~ | / e l ; ~ I~uckvoth..~e: "~ll~t;oF*.tCP'~'q BOt.f '.t.:k~I) #,~"q m~t I t,ll~4:U~b~:g .~.qO!O!VO.~ Wa,~...PL~#Ung. ohne kcm~rveil¢% i dtt dnO W~s~rM~lum *~n~ ~.'tl illF ~ltl/u¢.n'chet.o ~ern O~ F,ffe~ff,cd,Po ~dilO¢* /:* haIfe,i D,e~¢ i n f f ~ verwsachte "~':,t~h~,'.f$:l:¢Kbt /;i;$fe. schwa.,~ano ~. F,tha!:ll,8,:al unO - ~t~e.'~V,c.h - ~as A!almter, vet, R,sser, ,n, vel P*/;k,~[JUl~,ltl; t~'l f':'K*: K',;ffICtttdl~;P H:t' I I*/I d:13 Wa.~t;tw be* S~J~//Le;¢.~,s~lJ'K~,ta.ee$010~0 h;I .~.t~O ''ch.%/I';bf'q[$C [':;l;at'Jui#:;al II:hq ~t,t*l;{]e D,.ckver;uMe '..~ :e,~'/; tL~l ('~ Wlll.q~.~, i~a!ell Vt')tl ,'tz;:',t:;~l;*c'~(!r' At)';KP~ ,~)W*O H:t' VO;/,P' Ft'l~ot/ .x'e~N~l~JOt.Air,get, /';'l t~tt'.Ct; ~JI;. ~/0" ~J~ ~ 0

Relrolavage

F,~lae~n dutcq langlame Sandf'Jf~ beharlOett wilde D~ untetsuchten L L41~ou~JngMalen ~ zmschot 20 dno ~0 n~h Fte~u~ ,Ira1 wurder, m~ Wasset ~qRalen van 7 - 12 m~h verbur~en ~ese Ralen ware~ tr~.nmt.~t ,J~er$c,'t~ff~,chen AqeP yea FRetmed~n et/otg/e~.,h, ZU Oenen t~woh! s~at~ffardwalB~et .t0 7 ,rod gtoDe~ (l 2 rc,ml F~aetsaPO ale auch DuablteO,entYaem fAnlhtaz~lSanO) gehoaen Dm Rucklpuka'~$ wascn~J~,l~on und -~onlRdtal~t~ w,Jrden enltand de~ N o r m a l b e l r ~ n ~ g e au,lgeweqet UnO ai: ausscr, i~geber.d t'J~ d~e erie;gin
amelior6

d e s f i l t r e s b s a b l e b I ' a i d e d ' a i r et d ' e a u en r e g i m e de s u b - f l u i d i s a t i o n b I ' e c h e l l e p i l o l e et i n d u s t r i e l l e /mr" M J C h [ p p s , M.J. B a u e r et e.G. B a y / c q tru~.vo:~$ de (ondt$.s avanl ~a ~X~at,o~ ul~eneu~e t x o k ~ u e ~ r tlffIRS a sat~e .~t$. 1(~ VffRs&es 0"8# . t !!a!. ltou; n~3rMt~ht ~:~ pP*lotalal:z;e.~ e ~P~ i,+tm..cfirs tgt,eb .'~la¢,!a,t~ "alJale~ loll f~i eJaJ~w~nt ~ S .tt~',~:'~s re,moor de 20 a 50 m/h ef eta~,nl corot;mars i, de read a 7 - 1 2 mtn Ce$ wless~ eta~an; ~;t;P.*lPtlatMe$p o ~ ~J#Jr~L~J~Sl y ~ d e ,tlo~;a ddfereN$, ,rlC~Pt ~ hltta$ a MtJ~, $ 1 a ~ t d (0.7 ffk~) ~ ~tlme ae,¢,,c~e d¢l f S v ~ ~ hff/t~ q ~ / ~ / C~S a,qalrses de la~,~falo*fe ~N# e'~ ,,,~!,eres oL~a.mq!lPs ('1 I I - 2 mini el ~es I~ifzest~coucl~s tammac;Ir~sabie), l a c o W , tarpon du S t e r n e de ravage a M~ Muo~e a ",,[,¢la~:, !. n,c~scop~* oiecItoB~ue a t~31aya(le~ .rex3mende I'evohat#Jt; rk~, l~,tle~ :1oCh,it~ ~'JI le I~ ! e ~/ilfi,~ ecl~ilo ~, On a ~rou~e qu*e#e etaIf oo IX,We ~rnpoqanc.e Pout une rHent~oP Ou medal ~ e m @ 13rage a,t,ead POut ~ eau= COtllenar~ de~ ~gar~mPs v~va~$, kes tesulfals corJ~neN ~JX ~ U ~ ~l el[l ¢e,lllat~l il d CO.tiLt': a dO.~Orgies (]c C~al~ ~u!~a~ P-~I$9~w2es. a u ~ QG~M9~ I hllrdi eatlutY~ ¢~en!a; vO~; !heGt.
Realizar aumento

/~/0 d1~tkO~S;d,e~',~'JO tea.ht:ff I e.'ti~ $;o;'llre

~;~I ~ COt'O'I;Ot'LO'J t~l~va~l~J Oe ~vseule ;':t110~CIde ia matu~atmn Ou t~tm SUt fa OuaMe du t~ral (8 l ~ g S . I0 h:l~ 2 l~CS 5 rots I

de lavamiento

al rev(~s en f i l t r o s c o n u n a c o m b i n a c i o n d e f r e g a r c o n a i r e y a g u a s u b f l u i d i z a n t e , a e s c a l a s p i l a t e y o p e r a c i o n a l p o t M . J . (.THpp.% M..I. I - t a u e r y t¢.G. B a q l e y • II;;;',.d. e:.nfO.vffd;~,O,~.K,~Q:R' OL':%*o.~ffo:#qua .~f~.i,ol~.oa$~t(,;3vltglo~ac ill tflh,~ (h~ ~Jl,o.~.'~'0¢~1tq~'.tU,t da!as OP platIfas pe;cm r d~ l a ~ a s a g~an escala tgama 200- 790 MLDI fratando agua guard~de de los ;,i h&,H*:h' .I*/P t ~ u a vn .;¢):n~);lt~eOCt'I)~lO .'?.*dOILY'!ei let~o~,l~llc, d la ~lg~ ~ l:~tos ta[J~o$ b~J~o On~a/SeS ~ I eeOlos, aofe$ ~ rna$ tgltac~)n tJ~ologtca gn Idlros ffeS~8".tOS de atotla. $8 ~ eMU~qldO .I,f~l;IC I'SlO~ ';ttto,~ .,e emo~.a,i p lta aqua de pos Oe sas f;e~ra$ Dale& ~R use de co~Ju~anles o ta,'~nes ~ h e , a t cop e,re desOo 20 haste 50 trdt)rda ~ t~e. en comOmacKm COn ague a 7 - 1 2 n~ho~a. : , CIt)e'ti,,I.O'l !!'celia.~. lie .ip,(~.~t I j e~g?;/~,a Oe; layallNf~Dlo ~l I ~ OTI fe~lO~ #ate ma~|or¢l tr,edr:J$ "~g,q~ ,*'K*~.~'I' a~3h~&~~Ooralo?lo ~ matc,t,~s (vgar~a> e ,n~'gamcas tc~n~ta$, m,c~o~eoom ek:ct:on~a Ql.~a.~a l1 2 mini r meo~o debar fanl~aofa;a~ena) Se nan evalu~o s ~ y conhgutaOon del iava.'nk~r~o al ., ,,:'! ~ t~,sO~ de l,.,;~,ncl=~ ev; delos pa~a pOI~Oa de a#!#a d~. ca~/,l con ea~l ttmp,a ope~ac:onal ~eve$ a qtar, .~ala. q~e se hat~ c~t¢o a la ~ffrade tffenc~n d~ranlo Mvam~lrl*o ~ n a d o LOS ..,,z::e.,,n at tP*PS Con , r e Imganfo con .It~ lavatr~'nlo s~g¢¢.nfe de a.qua .~.1ura etap~ comb, naOa de ~ESd~aOOSCOP ~ ¢ a QGe CDt~l~nO alqar~n~s WVOSc~lh~man fas leco~el~ac~ones ~ olios autO!aS, .~a ao ;¢qiJa a !*r~ C a r d vat,ate. O~ r,;l/;L,/o V a I uff:trx;, a ~a apal:c,~n Ce gt~l;t.~ en ~a cape rk~ IWrO , . am,*'r:;z ,l: t( ~e.~OCt' de;: cuml)~I~iCK)t. Oe alto y a~,la ,I ~a/:ln ~zb!tdd'~/ar,:e. ase~;u/a C,1'J'J~d,c~w~anfe • tP,,::r., , 'ncll;l~.~ ~).~ l)~eil.dn- ¢~! a~bta , ~ ?a~la de ague COt, e:ll~.~ #lr*p.,.~ Se hen c~r~Pq:Jtdo

]~ ~

~laer~s !tan O e r , ~ $ a ~ a s , ¢ t ~ s w..,Uom,naofamerffe ;eact,vas en a~aa ~ [:l QfaOo de maOole/ des I,~ro. ai,Du'do a caoas L~")/g~in~case ~m.tpanK:as. ~e effluyo CaP el mode ~W lavamaento ai areas Se msouM el m ~ t o de. mead:el ~ ' ; I,e:o a la ca~e~ de !~¢aOo (8 ~a:ls. 10 t..m,s. E la~:.. 5 tufa)

/~"]

Improved technique Ior river water flocculation Verbesserte Methode zur FluBwasserflockung t o n M . S . tf~lmee
Re~e~a~~M~ ~~MIai~#~r~he~ ~

Amelioration

M~`

ResP~.~lplg von SchwebeMollen ~ow~ekutze~e Yetwetizeff Oel~lkl ,~ ~Jl.16 a ~ . ~ r~.)

d e la t e c h n i q u e d e f l o c u l a t i o n d ' e a u d e rivi(~re

t m r M . N . t l r l m e e d , T J . M ' t * h a m r t w d et A . A . S a p r ~ : .~a~kunlK~qde~t~PstÈl`~*s~(~danskP.seai~dP~£v~ae~n~-~tP~UC~u~det~Cr~J~che$ expet:w,emakts O b l O ~ Or~ t ~ l ~ e q ~ ~ tloculaleut a lUL~OShekcotOa,,~x condu~ a une me#/TJfe ~ ;a,s (~s ann~.~. ;xu;t her,m~ d am~..~o~et ;e des~v ~.. i c¢.:mnm~e des m P l ~ cen~l,~s te e l ~ m ~ o n Oes sohdes en susDens~n avec un g;a~en~ de vqesse l)lus ~ el ~ l ~ de ~ ~ ~~ ! d ~ avig~C~.~-~b h*L~C(~u~ eht ~M~$ ~ W r ~ ~f~F~tL.~.*r*| ~ a ~ ~ a~!~ ~$ ~ ; ~ l ~ $ C ~ l ! compa~es au lm lesl class,que et. Ya~temenl O'eau. f6 p~Jjs. 161e~s 22 r6ffs.*

T e c n i c a m e j o r a d a p a r a la f l o c u l a c i o n d e a g u a d e r i o p
el OWRal afttelotldo O~ ~or.dosc u & o t ~ s , co~ ~ a ~ a m~s bai& de v e ~ d a o ~ feel~oo de delencebn ~ s ~ f o . ~ m ~ s Ct~;' L', ttalarPJottlo de a~f~l con la Dfu-'Vo~a !afte coft~c~)Pel. (~ ~lg$. IB fm~s. 22 ¢els )

~

Model to simulate the structure and performance of c e l l u l a r p o l y m e r i c m e m b r a n e s : Structure, flux and filtration characteristics M o d e l l z u r S i m u l a t i o n d e r S t r u k t u r u n d L e i s t u n g v a n z e l l e n t 6 r m i g e n p o l y m e r e n M e m b r a n e n : S t r u k t u r - , FluB- u n d F i l l r a t i o n s m e r k m a l e ran N,M. Jackso*l t~, , ~ R(~cct.,uRv riP..;Vofrk3~l.~_so.s;tw$Ctl~n F~.? Id,d Druckablar, Ix,, lz)lVn~.re. Memrdaot~ rtut HM~ "#obet davon a u s g e g a t ~ wtrd dab de, Potem~no~ z r f ~ r ~ ~mt s ~ . 7 m s c ~ o ~ l~tet~.r,c h ~

u.ir~. ~.l:G~¢,dl~ V~h #Ifn~sses i~*tdet; t~l~ o,o PoJeeg:Qlfe u,~d A~b:,~t.l:~le m ROIhYCIll q e / O ~ l ~.l l ~l (~' :PIPII)OZO~IIS//IIk.%J{ r ad.~t Ac,/~ 0J~lbl ~ Sff;skh# Oetall,Qet ~vn~a:~: t~l m;lllLven,t~. ~blch ~t,qe>,~lar,enff.ktO~d~op~" ISFM; uod BddeP~a:t~lh;pgsmefhooo:~ H.us!an(P,ch ;cwoldee; . l i d m '~:'t:.~tIll e'net O*.,talf ~():.QDM~OI?to/err.eli Sl~eklut YP~t e~ .~l! (J¢.~Han:l d.L~ e ~ " r.at~e~e~trach!urKj .

~.~'¢'J*.~; I .bf%M O ~ ~.~ll~ ~Y~UI/[ 0~}$0 S;t~JklUlP.qlb SdRUhOIeP..I)q~ VOtl)P*.~Jt~Y~de: Po,ene~get.~:haflon J: gl;hP ura~l~pl~l~ltrnul;(] II~1 De}!O:l (119ddtCh RdOat~lt~.va~H;I' ~;M {:'ROl1.1kleDd~03 f:lmltlOd ~l~deR

Un mod(~le p o u r s i m u l e r la s t r u c t u r e el les p e r f o r m a n c e s

des membranes

' `~!~`de~;:~qa;~n~l~u~r~u~edepe~ss,~qp~u~u¢~smem~a~v~D~ym~tr~uesapai!~t~:~Ha~

. ..~ .~.e ,)P D,en~t en consxtetaPon ouc ~ a~meem O ~ oo;es et l'epal.vaeu~ Oe la r r e m ~ a ~ (~ ~ , ~ ~ct.i,e ,,~'L~ne c~!k,~a~e l "elude o~ ta shuclum de le~s m ~ , b , ar¢~. a ere ellcclw#e p~t rne,:toscop.e . Itui;~|l;c a ~lt:lya :/~ IS~M/et 8 I*agla#~fJI (I e.'~a~egt av ~ tJl~ Mtuc~{lte iq~.t~, d..is~ c c ~ 1 ~ 9 , d L,~ • quftf;nd~valtellvlsR~¢.tOOlteCt~tches~dlJsa~Jol:N'.dees UntT~)OP)B~/eoerlell,q.JeallOis~rt~et;s:on$ ~qa,,,l,q~e e~J ul~$e pt;t,r ~ t n d ~ ce.s Mluct~es ~ ~.Sptetl~l~ps O~Sp:cw,eto~ ~!s ~X~leSsam 9n boq c*o ;*v(~'k's m ~ a t s rie "aoa;rseur o'~ages e~ave~ ~s pt~e'Jmec¢ograp~.,r~ S; M I a vat:al~on du liu~ Oe ~:mc~ar~e ~ p ~ e a ~ c la pe~e d~ ct~a~geust p~PrMeen c ~ n t ~ an~ un ec~urerr~'~ v ~ u x ~ ~ ~ - fl~ ~)q.,l~lle$ ~*P(~ZtL~~.lnl ~'*~041~Ifial~& fJPP~o01e.~:)r/ISat~O~Ob'll~at!oil !lee.~ ~Ot~" c r ~ l l q u e U ~

Vo,Polsage un'3 dep e~pe~memelien Et,jeb~s~n ~t bo~ ~ unfetsucNen Me~ltxanen a u ~ z e c h . , ~ e Ubem~s!,mmung et~el~ #omen Des stochaM,sctte MOOOfi d~enl /tit Voftlefsa~ des TraPspO~I$ vo~ i atexaulsoh~an',mungeP Dg.:Ft~Mtang.O~uckl~ffal~n unff WUtde !weeks Vort~ ¢l~ge e~nes Obetflachenkuche~s ~no Ors Vot~mgens yap Patf~=m ,n ~*e Memtxan enh~¢kML /:a ~ mo0#ch, d~e Bedeueung des Paq,l(ei~drchm~.&se,s l u t d ~ PorrngtoP~r, om~utung und die PostluDe Oat Vo[scllm~tung ~r. dee MemO~an vort;otl,jlaQep Gfal~cth~ B I ~ F W~rO~P n~l Fo~Gm~lDOl~Oetn vetgb,$~n Um Ftel~kClt m ~ M e t ~ L ~ Wect~sP;w,.'ku,~g~Y. /w,sonet; Paa~kai-Parl~kel- und Patlixel.Pomt~-Kothr~oneo ~u gemnr*e~, sowot~ m,,etr, a¢ aS auch un de~ Obertlache o ~ ,.mte~s~.~.~ Men,bear,an Da,ube~ t~aus kann Oas I,to~e~ auch au! andefe FoJmen Zel~lcrmigef ~ ) t . q ~ S~¢u~t,~en 'dbOtUa~en watson (8 $,1.24 ebb. 9 tel)

cellulaires

polymeriques:

S t r u c t u r e , f l u x et c a r a c t e r i s t i q u e s

de filtration

mce!;e~fecancotga~ceentmkesp~ed~ct,onsfneonqueseHes~ats~auxa~u~ membtanes d t ~ Le ~ sWchasleOue osI .jfd~s~Dou~ j~,,J~e une f~raf~n sous ~ m s ~ ~ ~ de suspems,o~s tta latex C.,x:~a ~ c ~ po,~ pledge up pillea~ en s~dace et la o~v)M~al~on de ~J~lt?¢l;~ d~ns la memb~arm If eel poss,?,tede o t ~ e r~oonapoe du Cmmmre des DarXcu~e~pout ~ ch~x Gbu,amojle~tsl)otes~soq;Bflb~r)c~s,ltl'eoctas~ll!t~la~8~ lestma~ms~afJV~uessom com.pateo$ aux pnolo,'n~crogtaph~.s ~Oul eonna/!~e las InlcractPons st~r~/t~as des calks!one ~rl~cufe; pa~l¢l~e el pamcuket pore a f ,n!br~eur el a la surlace des ,P~J~)tanes #tude.e~ De ~tus ~e mode~ eat .v~sceooblc o'~fte Otendu a O'aut~es lo~m~s Oe sble:h~e cequla~ras~ e u ~ (81~g$, 2 4 1 ~ . g ml¢~

M o d e l o p a r a s i m u l a r la e s t r u c t u r a y r e n d i m i e n t o

de membranas celulares polimericas: caracteristicas de estructura, flujo y filtracion p o t A;M. ,lru:ks.~z ~cm~ son c~nOw:os Se /~a haMdo ~ acl.~to~J chirr tos pwn~st¢os leoncos r los m~atedos ~;,dte,'l.Po~..v#~. I¢~le el~ cberJa .~HamenR., el M,'n~no (~ Dotex y es,o('~'Jca do ~r~r~,btal~a. y fd#a ox~.~,~entales :on/as n~r~'anas escog~l.¢ S~ eml~/ea el moo'elo oata I~ora~¢,ar el Itar~ooae de :~):;".,rdeJ;, Id os~luct,.#a ,~tema arid;at Se na k;gVddO una comDren~n ~q~ la PStl~t'J'a de laPS ~ , ~ e , q s r o r ~ ltlez en t#ftsc~n o~tecta. So 'e/la ~sarrot~gO f~lta D t O ~ K ' S r ~ Iotla s u l ~ l l r ~1 , I(.!nb:ands con fPc..~..~s de mr.'tO,SCO~a e~et/o.¢a 9scane~ tMFE) ~ Woce~) de ~ a ~ n e s y COP fat pom.,ttac,on Oe ~arl*cutms e~ la rrmm~ana FBposd~e~'edeca' ;a tt~oor/anCal d e ' o~dlmettode par/~'u/~ n la :,, :r~'l~ea mtema romp!eta es cla~o q'Je se Oce/a:nc#J~rmas c o ~ a c ~ n de ;a mar~4 ",:P;ulalD o t a l ! c a caasax:acr'~ des tamale de p~'os y el ~ de obaaa:~n en la mem~ana Se cotr~oatan mmgeoes g M h c u * I elT~o;eado U~ ~ It~¢ff)Qt~S'Oelalq ~ l ~ G ~l~la stmu;~l ~Jab e~tl,cRda~ PrOqOS~lC.~O~ laS cnn ! o t ~ c r o ~ a l ~ s oa~a conoce~ las ~tetaceooes e~er;c~s e~tte patPculu, Y choq~,s entre ~lrbcu~as y ; ,, p:,~ouaes de ,'as ,x)rcs es~a,~de ~',.re,do col, dales o~e.l~os ~ ana,~s ~ c t ; de Iolo,,~:mg~at:a ooms Oenlro r so~e la supea,cm de las rr~mo~ana~ Arlemas. el nxm~o l)ueOe emylearse con o~¢as t.fk ~ Se p*ede=e la ~anac*c¢~~ llu~Ode una membrane lemp,a con ca~a de. p ~ e ~ , p ~ ::o~s~e'a~; de flelll*C!£PaS Celd~ge~ ~l~Ota~S (8 p~OS 24 liftS. 9 t ~ I I , t w.¢fcNt~pto:e'fPFttn')~t)# (J~'~lt~g~"d/~ lip COt~dfleP~ CJ~I~(J?ooO~.~UOS..$¢tU¢;/*~r~.J[;¢;UOJO~IMtdC,.~(]e IO3 54

January

1995

Filtration

& Separation