Concentration polarization and fouling

~e~fi~~Zjo~,3~ {1980) 59-103 Q Ekevier Scientific Publishing Company,

Einar

Yaxthiasson

Oiv.

of

food

P.0.B.

50,

and Bjiirn

Engineerinq,

S-230

53

Xmst.er&m

in The Netherlands

Sivik

Lund

Alnarp,

University,

Sweden

ABSTRACT Concentration the membrane

polarization

processes

theoretical

Qny

tical

the

of

coupled

these

tions

studies for

models

for

which

on this

concentration

makes

use

the

of flow

the

reason

negative

the

serious

on the

limitation

transmembrane

phenomena have resulted

polarization.

of

for

influence

polarization

system

represent kinds

is often to its

nonlinear

solutions

!lifferent

due

In most

of

the equations

some

assumptions

of

of

them,

in order

in mathema-

solutions

continuity

of

flux.

are sought

and motion.

to simplify

Each

the equa-

phenomenon.

systems

have

been

constructed

in order to reduce the

concentration polarization, The aim OF these flaw systems has majnly been to improve

the mass

Foufino other

transport

often

attention

that

sisted

of recognizing

Later,

efforts

of altering rid

a1 ter

of

the

the

until

Also,

late

membrane

surface

back

to

polarization,

the but

bulk can

solution, also

have

and

1,

~~TRO~~~T~OPl

to fouling as such

negative

of

the

to change

ten

and

to rough?y

effects

feed the

to fifteen

have

solution

years

identify

basically

ago mostly the

foulant.

followed

by a pretreatment

hydrodynamics

of

con-

the

paths

to change

the membrane

module

or or

to

itse7 fthe

of the

lately

oonents

the

basic

revealed

filtration

by the membrane. to the membrane

mechanisms

of

fouling

attracted

little

attention

when for example fouling of an RO sea water desafination

be subdivided

*hey

rejected

fact

seventies

studies

In membrane

the

foulant,

unveiling

could

drawn

composition

membrane

the

membrane

was

to avoid

the

"owever,

the

the

of concentration

reasons.

The

get

from

is a result

into

four

chemistry

and

iq closer

detail

processes Before surface

consecutive physics some

some

steady

of of

of the

state

is bigger

than

steps. fouling the

have

responsible

components

the

in the

convective

that

being

due

flow

takes place at the membrane surface. This

wellknowr

phenomena

on

phenomena.

solution

are

of

cum-

to diffusion

bulk solution_ 8ecause of this an accumulation of the rejected

performed

these

backflow

component

is called

concen-

to

60

MAITHIASSON

tration

polarization

due to

ated

its

with

negative

concentration

on the

problem

transmembrane

polarization

in ~mbr~ne

flux,

Negative

operations

aspects

associ-

are: the driving

for the filtration. If the wall concentration

2.

orecipitation static

or formation

of solute

of a gel

reaches

the saturation

on the membrane

surface

concentratjon,

increases

the

hydro-

resistance. High

3, for

a serious

is often

influence

An increase in chemical potential at the surface reduces

1. force

{CPf a It

AND SIVEK

4.

of solute

concentration

changes

in comoosition

at

the membrane

of the membrane

The deposition of solute on the

te-istic

material

interface

increases

due to chemical

the

can change the separation charac-

surface

of the membrane.

As a consequence commercial

of all

plants

negative

these

is only

Z-10% of the

factors

the

transmembrane

transmembrane

fluxes

for pure

fluxes

in

water.

Therefore it is extremly important to make some efforts in order to reduce

However it

concentration polarization. behaviour as a consequence Fovling

is

permeate

2, 3,

Particulate fouling ChemicaJ reaction fouling

4.

Corrosion

foul i ng

5.

Biological

foul inq

the

is

is

on the

fJux_

possible

then

said

surface

the

to explain

to mxur

the

as well.

of the membrane

this

is applied

to membrane in some cases caused

phenomenon

that

is

macromoJecuJes

to solid

in the

heat

transfer

surf&es

but

is

partly

surfaces. an irreversible

by CP in its

development of strong If the 5~7 is aiso

gel,

true

In the

attractions strongly

adsorption sense

is

fouling

of macromolecules

reversible

gel

lacking

diffussion

is

while

forces

hindered

between by the

between the macromolecules in the yeJattached to the membrane surface the system

very hard to alter, even by washing procedures.

Another

difference

is

that

while the analysis of CP requires essentially

mathematics, fouling requires knowledge about physical chemistry 2

2.1

as weJJ-

~~NCENT~TI~N P~LAR~~ATI~N MATHEMATICAL DEVELOPMENTS in order

flux

fouJing

Freezing fouling, 6. This classification Fouling

always

Epstein (77) classifies

the

Precioitation

gel: formation

not

Fouling

of material

1,

appl icable

is

of CP only,

an accumulation

decreases

also

risks

attack.

to be abJe

one must understand

the

to deal transport

with

the

problem

phenomena

at

of concentration the membrane-solute

polarization interface.

iS

Steady flow reverse osmosis systems are rather well defined from

fluid

mechanical

viewpoint. This means that mathematical ana'lysis using the basic equations of

fluid

dynamic and convective

efforts

have

been

concentration

distribution

the transmembrane flux.

nonlinear

transoort are expected

analytical

made to develop

to be reliable.

rrtodels

to

be abfe

tots

of

to predict

the

normal t0 the membrane surface and its influence on In most

them, solutions

of

system of the equations

the

coupled

of change (1) ‘.

Dn ,=-p(3

Equation of continuity

are sought for

* “v,

(11

Equat-Ton of motion

(2)

Equation of continuity

for

= D 7’

solute

C

i3)

Each of these inodels makes use of some assumptions in order LO simulify the

equations

which represent

the

phenomena.

The wall

velocity

is usually

given

by

the expression

JV

= A

(A?

and the

-

AJ)

selectivity

of

the membrane by the rejection

ilararketer

R, where

r

Reverse

2,l.f

fi)

the unstirred

of

interest

applications where

osmosis

Unstirred

like

the shear

for

systems.

Analytical

stress

The most

studies

simple

of

in the flow

to obtain

a model

osmosis

kind of and for

pharmaceutical

system

reverse

of this

of membrane characteristics

ultrafiltration

the membrane surface together

cell

batch cell. for studies

tive is therefore

conditions

system

batch

systems

IS

are pr-imar-11y

some industrial

and biotDgfca1

solutfons

can damage the product.

that predicts

system

concentration

The main objet-

polarization

at

and the Dermeate flux as a function of time and operation

a given membrane characteristic.

with experimental

These

data to determine

analysis

can be used

the membrane constant

A and the

rejection characteristics R.

In the analysis

of unstirred

batch cell

systel,,s the general

assumptions

are

MATTHIASSON

62

that

the

tration that

length is

the

solved

with

is

the

C KL

Y,1

C (L

-1

IJv!

C (t,

at the

the

cylinder

unnoticable

system the

far

becomes

is

long

enough

so that

any

away from the membrane surface Mith

semi-infinit.

differential

boundary

equation

for

these

the

(Fig,

assumptions

countinuity

concen-

This

means

solute

in

the

0)

infinity_ membrane

(7) (81

+ I) dyC (t’

boundary at

the

‘I=

(I-R)

conditions

beginning

The third

!J,!

state (t=O)

boundary

C (t,

that the concentration is uniform in the

and changes

condition

(9)

0)

gives

in concentration

are

the

of

mass balance

surface.

(

Diffusion -Dd%y

tttwttw

rdiiiiiii \

Convection JVC

\Membrane

Unstirred

form

condition

= co

system

1,

I)_

in

the problem to be

of the

Piston

Fi?

increase

SIVIK

= Co

The two first whole

of

AND

batch

eel I _

not noticed solute

at

MATTHIASSON

AN3

Dresner

(2)

osmotic

pressure

flux,

analysed

and that

case

this

can

be

the closed-form

neglected

with

(8 = FofAp4),

is comrtfetelv

the assumptions

which

means

impermeable

so laolace

that

constant

to solute

oermeat

(R=l).

transforma~ioR

can

the

In this be used

11

) erfc

( K/Z)

+ VT

e -7l/a

+ -?_

(IO)

‘f 2 ?1 = -JoD

where

means that

large

to

solution

cg-‘=l-(--t

(11) the concentration

polarization

increases

1 ~nearly

with

time

nonldeal

membrane

for

TV_

Paridon

et

af

(0 < P -< I)_

c. -

<

I =&

(3)

extended

Bv usino

I-

LP-8

Liu and Williams get

mathematically

above become ‘finear

c \*

This

svstem

the membrane

the equations

obtain

63

SIVIK

a soTutinn

(ZR-1)

(4) over

B in the c~llcwintl

this

Laolace

did the

e

analysis

to be valid

transformation

they

1+

i

for

cot

the solution

,F(P-1 )

also

e.ctend

entire

this

analvsis

~o~centr-~tior

field

bv usino :lhich

Laolace

accounts

technique for

all

to

P and

for-q

(13)

The value This

of

“c’ at which

equation

similar

analvsis

is

the equation

therefore where

they

most useful not

another

above

breakes

when E<
of

dow Yahlab

solutions.

increases et al

(142)

as B decreases. have done

a

MTTHIASSOM et

Vakano when

account

to

al

(5) analysed

constant the

rential

osmotic

(R=l)

solute

case

pressure

breakes

integral

method

polynomial

which

them

treated

the

the in an

to be non-ideal

1

profile

was

of

diffeIn the

the series

B#O

also

of

integral

into

the

technique_

approximated

thickness

o f the

gets

apply

an

as a cubic

the

concentration

method

by treating

technique. analysis

result

but

in this

case

the

membrane

was

r
(161

~>a

cO

IJiiTiam

(6;

1-C <
but when

therefore

Their

(t-7/d3

co + (c/_c)

results

a similar

(O. -

by Runge-Kutta

time-varying

one

Taking

to be impermeable

expansion

They did

iterative

flux.

membrane

a series

time.

results

performed

the

by using

equations

permeate

Dresner

of

is the

approximation

(4)

assuming

numerically

with

diffusion

of constant

concentration

a(?)

improved

and blilliams

taken

was

and

problem

agree

in which

convective

instead

down at low value

1 ayer _ They

as zeroth

L
the

were

in n/a where

boundary

non-linear

(B>O) -

solved

when B=O the results

solution

c =

pressure

they

eqtiation

the

is assuqed

AND SIVIK

used

a Perturbation

Liu and Williams

technique

extended

to study

his

results

the

limiting

to account

case

for

all

when values

yieldino

R,

(17) irhere

=

?’

and

r.R

Using an iterative for

the

case

analysis

good

aocroach

\/hen T"-~

to account

As mentioned aqreement

intermediate

with

(18) they

I fixed

s,

for

by Liu

range

2 -,I?

T”=

able

tiu

to get

an assymptotic

and blilliam

(4)

extended

solution

this

3 > 1-B. and

William

experimental

of

were also

and R=l. (4) al7

for

data

time where

these

these

analyses

certain

theories

range don’t

mentioned

of

time.

above

better

agree

show

6ut there than

is

an

105: rrith

:xoeriments, Bellucio cal

solution

Comparisons

for

the (ii)

theoretical velocity of motion

Pozzy

and and of

(7)

tried

approximate

the

solution

intermediate

range

Lamin ar flair

systems.

profile must

that

of

of

flow

with

problem two

both

analyses

experiments

with show

an exact good

shoir good

numeri-

agreement.

agreement

even

time. In comparison systems

must be taken

be solved.

this

These

analysis.

numerical

treatment

to solve

In laminar

to

the

unstirred

are much more complicated into

account.

reverse

This

osmosis

batch

cell

because

system of

the

means

that

the

systems

both

the vetocity

equation

MATTHIASSON

and the the

AND

concentration

feed

65

SIVIK

channel

boundary (Fig.

layers

are

developing

in the

entrance

2. Development

of

2)_

Epb Fig.

region

e

of momentum and concentration

boundary

layers

alonq

the

sur-

boundary

layer

is much

face in membrane filtration.

As the thinner

molecular

than

enough

the

fluid

over

the

solute rization

region

analyzed

laminar rqhich

obtained

By using

But if

the membrane

channel

the

Thus there are concentration gradient

downstream

region

where

the

is

long

two different is increasing gradient

as

extends

at

flow

between

linearizes the

Ceveque closed

parallel

the

channel

plates,

problem.

inlet

simplification form solution

and complete for for

He assumed

The velocity

the the

velocity

the

profile

rejection

of

profile

concentration

pola-

CJCb.

entrance

1 + 1.536

developed

an approximate

modulus

L

and the

concentration

completely_

where

the

to be fully

For the

layer.

jt

to be constant

was assumed.

Plresner

fill

the

channel.

(2)

taken

slow,

bollndary

moves dowrlwards

flux

is

will

entrance

entire

Dresner permeate

velocity

gradients

the

regimes,

was

the

both

diffusion

region

the

solution

were:

5 l/3

(19)

.-. L -=

w

l+<+Sil

-

exp (- 503)) I

< > O-02

(201

‘b where

<=

J; h-L 3 IJ, D *

(21)

l'LcTT!iIASSON AND SIVIK

the downstream region

and for

J* hz 122) %Equation

20 was extended

Sherwood analysis.

et

al

Their

fisher

et

al

(9)

anafysed

solution

(12)

valid

for

orobfem

short

(ICI}. A great f)oshi (22)

studied grad

did

for

It

has been

surface

were

Doshi

et

faminar

tube

flow

Graexz-type

of

betireen rhe

bulk

significant

(27)

out

flo\i

on the

La1 tube

flolr-

type

they

free

and forced

la t ions

found

6y assuming out

that

result

profile. free

analysed

the

dolrnstream

control

the

numbnr in terms

(33)

et al

solution, this al

been

done

and Williams

19),

Dresner

(ZO),

and Srinivasan

(231,

(241,

fiber

Later

improved at

density

and

has alSo been

Tsao

(Z&30)_

Wino-

reverse

Danavati

these

analyses.

the membrane differences

This could cause a secondary free Ramanadhan and Gil 1 (34) treated that free convection can have Hendricks et al (35) and Johnson

convection buoyancy

due to buoyancy effect

7‘n boundary

behaviour,

of Raylei gh number

effects

in laminar

layer

recjion (about

system

series

have

hollow

have

wall

solved

geometry

of solute

layer.

effects.

the mass transfer

the

This

significant

that

(78, (20)

was

of Gil 1 et

plates

Liu

Bansal

al

indicate

velocity

(37) for

convection

for- Sherwood

boundary

(11)

Hendricks

to analyse

and

et

create

buoyancy

confirmed

and Gill

Bansal

concentrations

could

Their

have exoerimentally

exists-

high

39),

system

(nonlinear

solution

tubes.

First

and Gil?

and the of the

analytically. influence

that

systems

because

Derzansky

like

the

Dresner

inside

(26).

and Vinayak

solution

flow

problem

flow

al

Brian

(13),

(16,

This

flux

parallel

(131,

solution.

pertubation

wef’l with

and Tien

investigators

in tubes_

inlet.

between

using numerical

permeate

by using

Sourirajan

laminar

flow

Sourirajan

Hermans

pointed

in laminar

convective

like

(21).

(32)

an exact

channel

of flow

and Rao and Sirkas

systems

as Dresner

variable

agree

Srinivasan

others

(25)

results

analyse

by several

(3:),

(36)

to account

with

obtained

from the

of analysis

(15),

also

al

this

al

well

but with

investigators

and Esoosito

et al

clsmosis

et

(8)

work to laminar

(IO)

and his

other et

al

The results,

number

of

and Elellucci Tien

al

same system

very

this

et

distances

numerically

by number

the

agreed

extended

also analysed by Giil boundary conditions).

{14),

et

_

systems

are

by Gill

horizon-

to be of Leveque

16 diameters)

in their

both

results

corre-

were ootained-

!jh : 0.434

Ra”’

Re = 540

(231

Sh = 0,485

RF

Re > 980

(24)

Chana and Guin was that

when the

(35)

studied

product

the

of the

same system

dimensionless

as Derzansky permeation

and Gill, velocity

(v,}

Their and

result

?lATTHIASSON

sayleigh

AM3

number

mechanism. tive

SIVIK

exceeds

Correlations

transition

effect

on

l/3

Sherwood

length

osmosis

(vw Ra)

at

process)

number

which

where

free

a significant

Sh_and

the

convection

presented

transport pseudo

begins

effec-

to

have

as

WJ)

(26)

-0.16’

and

and

the

numerical

sponding value

salt

varies

with

for

the

one-dimensional

variables-

they

able

were

in the

(iii)

convenient nar

exists

film

is

stance

to

membrarle

radius

Qtber

Reynolds

number

of curvature.

any

film

by convection

are

very

and

effects high

of

so the

are

this

for

in

diffusion.

this The

thickness

oistri-

is very

of

thin

outside

all

la-

gradient rhe

model

resiis

that

to the

oermeare

because

flolr lami-

the

qerpendicular

neglected

film

results

kind

Concentration

the

the axes

R which

a very

flow

accounts made

and

the velocity

for

a

oresented,

fi'lm model

model

transfer

are

used

solution

Nernst

The bulk

are

the mass

and

they

characteristics

Khis

which

that

while

curvature

analytical

problem

concentration.

assumptions

mainly

and

polarization

value

to

3)_

presence

tiJo parameters

transfer (Fig.

The precise polarization

the

flo:g is turbulent:

According

laminar

is neglected

occurs

mass

(41). surface

in the

these critical

corre-

confirmed.

concentration

The so called

and has unifotm

transfer.

surface

the

Brian

the

be constant

and

tlhen the

complex.

at

taken

pumber

systems.

in solving

exist

were those

concentration.

and

membrane

to

flow

polarization

was

by the membrane

give

polari-

approximation

to predict

In the

problem.

wall

40)

convection

the

that

is rather

turbulent

Ipass

axial

curves

maximum

concentration

determined

(9,

only

the

ratio

To be able

By making a diagram draw

fluid

therefore

does

are

of maximum

al

rrhich

concentration

integral

concentration

rejection

o f maximum

to analyse

and useful et

film

occurence

Turbulent

in the

Sherk/ood minar

to

presence

bution

R at

distance.

axial

between

By using

maximum

salt

the

that

(R).

of

of

parameter

exist

ooerating

the connection

parameter

value

model

oarametet-s

studied

an existence

a particular

of rejection

conditions

(39)

rejection

analysis

to

occurs

Wo

Tien

and

Srinivasan zation

to

(the

becomes

v,, Ra > 7~10~

for

t+e

transoort

assymptotic

Ztr

reverse

free

(vbl Pa) o*166

= 1.19

tr

7~10~

for

length

the

Shm = 1.09

z

about

flux

is

Schmidts

is small

compared

68

MATTHIASSON AND S IVIK

Cio.

3.

Ic

Concentration

the

membrane

imoerneable

for

assumed

to be ideally

solute,

to

w-i tten

is

Drofife

a PO-membrane.

r;he mass balance

semipermeable,

for

the

solute

that

is

at steady

completely

state

can be

as

J,,[! = 0 -j+

This

1271

meaos

that

tertialanced

by the

boundary

?ayer

C

:J = 5

J exp

Because

of

diffusive

solute

to the membrane

surface

by

back to the bulk solution.

flow

convection

is

Integration

over

5 qives

(28)

tPe film

thickness

(k}

defined

t’ is unkno~~n one can instead

use

the

mass

transfer

as

(29)

i-J,‘f

tnis

exoressions

into

equation

26 gives

Jv

(-j =

eXD

This

definition

this

case

relatively

Coun-

i

SJb5titUting

c.

flow

(4)

coefficient

%=

the

(301

4

it

of is low

valid

if

zssuped

t: is

that

the

permeate

flux

found

no

flow

exist

mass

transfer

in

reverse

through

the channel

coefficient osmosis

is

qrocesses.

wall

but

ifl

unaffected

by

the

Correlations

of

6Y

MATTHIXSSOS XSD SIVIK

transfer

the

mass

the

1 i tcrature.

is

related

coefficient It

is

for

often

to k according

different

convenient to the

channel

to

ude

geometries

the

are

Chilton-Colburn

available

in

J-factor

irhich

equation

(31) turbulent

For

flow

Chilton-Cofburn

in many

factor

can

different

channel

be given

with

geometries

the

use

of

(no

eddy

emoirical

diffusion)

the

cot-relations

such

as

3 = f/2 where

(32) f is

the

C

\V

2 Jv =

factor.

29 and

30 into

equation

28 gives

SC 2’3

exD f

Cb The Fanninq

(33)

f = 0_08

friction

Pe

or

according

If

the

‘b

.

3s a function

of

to

must case

Revnolds

f

can

oe

qiven

according

to

CJasius

cow-elation

(1)

number

(31’)

other

is

available

not

be included

equation - Jv

n=+JvC

Inteqration

factor

-l/Q

membrane

solute that

friction

of equation

Substitution

-

Fanrlina

correlations

ideally in

semipermeable

the

mass-balance

(32).

(R(1)

equation

the

transmembrane for

tne

boundary

fluv

of

layer-.

In

25 becomes C\, (1-P)

= 0

(35)

qives

Jv 5 (--r 1

C -=w

exD

‘b

P+(l-R)exo(v

J

s'

I

D

(36)

MATTiiIASSON

70

Subs~j~u~in~

equation

C

exn (2 .I”

SC

<=

P, + (l-9)

exo

The cilm

tbeorv

that

eddy

the

analysis and

2/y

inc‘ludes diffusion

(33)

for

SIVIR

34 yields

equation

Ub!

(2JvSc

takincl the

Scher

29 and 30 into

AND

some

simp~~ficatjons

is zero

eddy

within

diffusfon

the eddy

(371

Ub)

2’3/f

the

into

diffusivity

known boundary

like

layer_

et al

finaly

got

Gill

for

the

instance

(8) made

the expression

By using

account. they

to be wrong

an

of Gill

equation

(38) = JP, SC F!t

It-R)

exn

[ 2 rl,f9Jb

This

equation

~eynol

nives

number.

ds

difCusivity

term

1

essentially

Thonas was

(75)

the

also

included_

same

results

as equation

an analytical

developed

>jith experimental

comparison

at low

35 except

solution

where

an eddy

resul c showed good

ay-cement, Ultrafiltration

2.1.2

systems

In ultrafiltration

orocesses

the same reason

as in reverse

For

qloverned

by the szw

the same.

are

principles

!3ut in

cules

that

taken

in account,

occurance

the

of concentration

The mechanism

osmosis-

equations

so the basic

ultrafiltration

are concentrated

The oroperties

rhe

which

orocesses means

characteristic

it

that

of concentrated

of macromo~ecu~ar

is

another

solutions

that

polarization

used in

is

of mass transfer

the

to solve hand

first

important

factor

is

the

problem

macromo’iemust

be

macrosolutes. are

most

important

in

this

case are: 1. Yiqh concentration 2.

3, They oresent

can be formed

TO day

the most widely

on the film

theory

viscosity

dependent

low osmotic

a_ ‘27 based

dependent

Low and concentration

ar. high

self-diffusivity

pressure concentration.

acceoted princinles

model (Fig.

is

the gel-polarization

4).

model which

is

NATTHIASSON AND S-NIX

Concentration

boundary Fiq.

4. Concentration

This

orofile

gel-polarization

layer

for

model

is

a gel

notarized

divided

into

1. Where the concentration Polarization the wall-concentration is loner than the 2. &here qel

CJCb

is

concentration In the

osmosis

first

which

large

C !3’

region

enough

the

two regions:

modulus Cw/Cb gel-concentration.

so that

analysis

OF-membrane.

the wail

is similar

is low

~on~en~rat~on

to the

film

SO that

enough is

theory

equal

for

to the

reverse

gave k 1nF

c f39)

b

In the

second

tration

which

solute

leads

must

region

the

is

highest

the

occur

mass

ced

by the

diffusive

the

wal'l concentration

steady

cient

state

is

which

of the

resistance

convective

transfer

which

gel

has

constant

back

reached

for

qiven

bulk

concen-

layer- at the membrane

surface-

This

the

transmembran~

membrane

concentration

concentration

flux

surface

solution.

This the

and

Cq in equation

by substitutjng

gel

of

to the

gel

limiting

build-up

to the bulk

the

the

A17 further

reduces

of macrosolute

transport

can be seen

possible.

concentration

by thiclcening

to an increased

has reached

wall-concentration

until

is counterbalanmeans

that

oermeate

flux

mass

the

transfer

37 instead

of

when at

coeffi-

Cw

C

Jv =klnp In other transport

(401

b words from

the

the

permeate

surface

into

flux the

is entirely bulk

controlled

solution.

by rate

of back-

72

MATTHIASSON AND SIVIK means that

This the

any factor

This

condition_ the

pressure, In order

used

if

the

increases

the

independent

to evaluate flow

is

k dh Sh =D= l-62

of pressure

without

flux

flux

increasing

at steady

state

of

and the

interess

dh 1

(Pe SC T

as it

increases.

transfer coefficient the Leveque solution can be

the mass

laminar

lengths

permeate

transMemb~~n~

why the flux, which initially increases linearly with

explaines

becomes

thin-channel

that

has RO influence on the

back-transport

concentration Leveque

the

profile

is

For all

developing.

gives

sollution

(44).

0.33 (41)

S

\&et-?

is

ah

the equivalent

diameter

113

u & or k = l-62

hydraulic

(---b 1 % L

Substi~utjon

of

142)

this

expressjon

into

equation

39 gives

C In 2 b As can be seen

velocity

and decreasing

For turbulent given

equation

channel

flow

in narrow

flux

increases

the

transfer

constants,

channels

determined

sturdy BlaLcr et al

+?nt

gel-polarized

region,

good but

the quantitative

mass

coefficient

can he

experimentally-

(66)

presented

confirmed

The qualitative

data.

He tried

ultrafiltration

of colloidal

This

is

ohenomenon

have

suspensions

the i-fith

radial

with

been

between

to explaine

a shear-induced

by Michaels

the existence

agreement

predictions

discussed the differences tnat exist

and experimental

the Targe

the

migration

less

(45). of

fn a very

pressure

experimental

data

gel-polarization

theory existing

tubular

of colloidal

are

Porter

satisfactory.

differences

so-called

indepen-

pinch particles

in effectwhich

nossibly have a significant improvement on the hack-transport from the

membrane

surface,

Shen and Probstein

(75)

considered

thar:

theory and experiments could depend on variable transport molecular solution normal to the membrane surface in the layer.

increasing

hr‘ght.

model was first

kite

sity

with

(44)

gel-polarization

comprehensive

could

permeate

= A Rea Scb

a and b are

I:,

This

(Q)

the

by the equation

k d,., Sh = r where

from this

(43)

In the dependences

theoretical

analysis

on concentration-

accounts

were made for

the

difference

porperties concentration diffusivity

between of the macroboundary and

visco-

The results were that the concentration de-

HA’MXIASSON AXD SIVIK

of viscosity

oendence dtpendency

of

the

by means of

out

has little

rather

tion,

than

coefficient

at

by one evaluated

at

region

the

evaluated

bulk

was found

flux

but

Probstein

gel

to be that

concentration.

at the bulk

the

limiting

be ignored-

not

dfffusivity

the

et

al

(76)

found

method that the appropriate diffusivity defining the

an integral

in the gel-polarized

ftux

on the

effect

could

c~~c~n~~a~i~n

This

concentration

concentration

at

the that

means

in equation

gelling

concentra-

the diffusivity 40 should

be replaced

to give

C *

Comoarison

of

Trettin

ment,

experiments

due to

to solve

dC dC uX’Va;j=as; Assuming

linear

=

T

c

result

clained

inaccuracy

with

that

in the

the mass balance

axial got

1

velocity

a close4

l/2

Fq- 1 W

(47)

experimental

data

the disagreements

film

theory,

shows

between

They used

good

agree-

theory

instead

and

an inte-

equation

d

file they finally of the form V

(451

I?b

the anatytical

and Doshi are

method

gral

In

K

F$l

[

Fg = Concentration

and second form solurion

order

pofynormal

exoressed

concentration

in dimensionless

provariables

2/3 *

(a72

iBgl

oolarization

modules

C9/Cb

D 09

=-

ng

x-:b a =- h

n2/(n+1)(n+2)

2

K=

This (76)

equation

when n=Z,

is K=2/3.

TV =

identical

(31)

f(Fq) with

the

equation

developed

by F’robstein

et

al

74

Agreement between equation balance

equation

a4 show less

45 and

the

data was done. They compared in a flux model with the exact solution

exact

than 1% error_

numericaf

MATTHIASSON

AND

analysis

the

of

sIVI:(

mass

!Jo comparison: with experimental

versus Cg/Cb diagram the gel-polarization

at constant

fluid properties.

This

comparison

shows that for

C fC (4 the agreement is quite goad while for C IC >4 {that is 9 b 9 b lower bulk concentration) the exact solution gives higher flux, As a consequence they Point out that if the gel-oolarization theory is used to determine the gelconcentration by extrapolatiofi very high potential errors can arise when the bulk concentraeion iS low (C /C is high), They recommend therefore that if this g b method is to be used, C /C should be lower than 4, Whenever it js possible an g b independent method for determination of C should be used. 9 Kozinski and Lightf~ot (48) analysed the two dimensional stagnation flow about a permeable rotating

disk.

Unlike the gel-polarization

theory

the osmotic

pressure

in ultrafiltration of macromolecular solutions was shown to be important factor in the ultrafiltration model. The effect of osmotic pressure in ultrafiltration processes

was also

Oejmek (51)

Dointed out by Goldsmith (49) and Carter and Newick (SO)-

hydraulic

to determine

resistance

min indicate Qespite

a~ experimental

oresented

which can be used

in

that the the fact

with exoerimentaf

2, Reduction

His results

ultrafiltration,

hydraulic

for

model (gel-polarization

ultrafiltration theory)

of albu-

is correct.

that the qualitative agreement of the gel-polarization model data are good, there are some things observed in experiments

that are not predicted 1. Slow decline

method based on step changes in pressure

relative influence of osmotic pressure and

the

by the theory.

of permeate flux

Most common observations are:

with time

in feed solution-concentration

is not followed

by increase

in

Fermeate flux 3. Permeability red

in

spite

of

loss

due to macrosolute

chemical

polarization

4. Cfianges in solute-rejection

behaviour

of ultrafiltration

to macrosolute solutions. All these deviations show that lot of questions the solid-liquid

or fouling

is not resto-

cleaning

interface

membranes exposed

remains unanswered concerning

phenomena.

MEASUREMENTS OF CONCENTRATION POLARIZATION

2.2

In a great

number of experiments

have been observed, ;n rejection

mostly

the influence

in form of decrease

to get a model

ihe transmembrdne flux.

The

to

test

the

validity

number of

these

of

that direct

models

polarization

in ~ransm~mbran~ flux and changes

As mentioned earlier

characteristics.

have been done in order menon

of concentration lot

describes or

indirect

are limited.

of theoretical this

phenomena studies

of

analysis and this

Liu and Williams

predicts pheno-

(4)

used

electrical

tion

micronrobes

conductivity

in an unstirred

batch

Nwrfricks and ldilliams in a thin prop=

channel

with

reasonable Lolachi

by usinn

were

measured

Ag-AgCf

The aweement

too

the

betwen

experiments

By using

cell

ions

were pood

gradient

technique.

values.

a batch

chloride

ftow

than 1600 the

this

and exoerimental to

laminar

technique.

with

in

for

the concentration

number higher

profile

respond

and

same

to be measured

agreement.

showed good profile

to measure

Peynolds

For

theoretical

theory

theories

ths

with

able

were

thin

that

with

the concentration

concentration

electrodes

oointwise the salt concentra-

measuring

plates

they

between

aqreement

(52)

parallel

the membrane.

faver

for

Comoarison

measured

diameter

down to 20 INI from siona1 boundary

(14)

between

smaller

celt,

for

in

an

the

qot

and

Goldsmith and

a ~ernstian

in

diffu-

They

annulus

fashion

unstirred

batch

cell and the entrance region of the annulus, where in the latter case comparison were done tri th theories

exnerimental

results

calculated

for

geometry

metry

several

different

reverse

osmosis

cal

concentration

(142,

143)

also

used

batch

trations

rav

the

2.3 It

to

ccl

1.

Acrivos

the

due

They

bendinq

to

effects of

out

the

could

ray

The

of

limitation

light

effect

the

deflected

flows

turbulent

that

solute

transoort

to decrease this

to

the membrane surface.

of

solute

this

problem

tanqentially

or high-shear

commercially

ir

concen-

was

and

stress

ta the bulk

accumulation is

it

is

solution

becauser:

therefore

the membrane module

the membrane surface.

the

important

The flow

The most so that is

the

either

The most common modul confjguratjons

faminar,

of

by some means in

at the membrane surface,

to construct

over

arises

used

are:

The membrane is

at vetocity

Plates:

of

back

solution

Tube:

out

transport

solving

feed

presented

rolarizaLion

be able

al

of the results.

POLARTZATIOK

to

et

qradient

accuracy

CONCENTRATION

way of

inter-

beam

concentration

usual

the

data.

oointed

the

of

beam_ Plahlab

even at vet-y dilute

the

a

mathemati-

\/hen measuring

the sal t concentration

that of

the

in a with

the

ma\, be introduced

severely

tracing

:tith

f53).

to measure

oointed

profile

error

deflection

main

tubular

interfero-

lnterfc*-ometer ~11

has been

order

late

and

a significant

agreed

the

batch ccl 1 for

the concentration by using;

results

for

a holograohic

VETHOIX USED FOR lzEDUCIW

increase

feed

that

used

values

in an unstirred

convection

interferometry

analysis

analyze

convective to

is

(53)

the

lower tharl the values

theoretical

measured

His

gradients,

an unstirred A theoretical

(36)

source.

by Johnson

techniaue

the

polarization

Johnson

as a linht

to

\Jelinder

agreement.

system under natural

large

For the dobrnstream reqicq

and tubes.

but compared

solutes,

developed

model

plates

concentration

the

laser

ferometric

used

plates

shobled good

they

flat

fur the annulus kjere considerably

flat

to measure

helium-neon

for

on

the

inside

of

high enough so turbulent

The module

is

so constructed

the flow

that

tube

and

the

feed

solution

recircu-

arises. the

feed

solution

flows

ln a thin

76

MATTHIASSOK AXD SIVZK

channel

between

two parallel

the channel,

sicies of

HO~~CWJ fiber: out

of

This

the membrane

either

OR

the

with fhe

it

feed

flows

together solution

in soiral

made

module :rhere Fnother jocts

in the

examgle

of

these

tion

olate

is

to keep along

central

some simple design

channels

of

turbulent

flow

plates

are

in foulina

due

(56,

67)

showed

that

used

frecuency

a different

by a back

resut ts obtained

ent

increased

q:ere also

the

technique.

They

by a factor

larger

tyoes

orinciote

that

of modules

In this

way

feed

throuqh

the modute.

of concentric

cylinders

meabl e membrane _ ‘hider formed

in the

secondary

flow

annulus,

which

have

the membrane

rotatino. ftow

than

over feed

the value

three,

from

used

et

could

be

Thayer

al in-

et al

at a certain

Compared

with

*he mass transfer

Improvement

layera module

sections,

osmosis

liquid.

the

boundary

the membrane,

of

perwhether

Kennedy

surface

same

hiqher

(64)

salinity.

the membrane

of the

system

al

aim

ooera-

the

certain

a non-rejectinq

in reverse

fin

have shown

give

concentratjon

product

flow

sweot

movement

stirrer

the

feed

attain

deposit

Shaw et

with

coefficient

by putsincl

the

layer

and decreased

transfer

and forth

with

of

boundary

the

sub-

The main

in membrane

thus often

of

tube. of

the coeffici-

in separation

performance

observed.

Different the

mass

central kinds

is not quite

It

to removal

in some places

oroductivity

sionificantly

creased

(62)

alas reolaced

the

Experiments

promotors

55-63).

bv reduction

the concentration

demand and

velocities.

is caused

the

to

different

energy

this

increased

in spiral

surface

(46,

the membrane

modules

of a spirat-wound

the

turbulent

where

traditional

~romotors.

circulation

it is caused

these

beds_

velocity

which

permeate

turbulent

channels

or

the membranes-

the

fluidized

feed

to destroy

between while

as

feed

surface

be

and wounded

and

the

En order

made

can

material

tube

wires

to empty

megbpane

support

to work

flux

decrease

tubes

ment

comnared

by

both

side

soiral

the membrane

lower

of

by inserting

that

same

fine

active

or construction

meat

for

distance cylinder

tanaentially

is to decrease

at

very

to a central

a suitable

is achieved

towards

mass transoort

of The

of porous

attached

modifications the

mixers,

promotors

the

a bundle

no surlports.

the wounded

flows

which

static

or

tube,

solution

are

be on one

tubes.

axially

feed

feed

by forcino

effective

This

of modification

these

the

saaters

leaf

of

needs

can

laminar.

is made out of a elate

side.

years

is

consists

and

of

the membrane

flow

with

like

the

module only

module

to the

tyoe

the

flows

Duri na the last have been

of

CLI outside

This

membrane on each

around

of

tyoe

where

case

material

inside

Soiral-wound:

elates,

In this

annufus exists,

one

can

itself

certain

the

flow

these

inner

that of

recently

rotating

one

beside

regular

the mass transfer

that

and

a so-called

is made out

carries

on

flow stress

rotating

Lopez

(65)

of

is of

the

a oair

the semiper-

vortex

hiqh-shear

vortices

considerably.

based

independent

Taylor

primary

toroidal

are

to the membrane are

modules

is rotating

the

which

parallel

conditions

circumstances

means

consisting

can imorove

develooed or a surface

aLhieve

One of

where

which

been

can

be

flow

inside

a

the

fias claimed,

?MTTHZASSON

in his

newly

EFFORTS So far

that

under

certain

the ma~romo?~c~~a~-

TO hfAKE USE

the

that

increase

back

to the

gel

the

is the

final

seuarate

to

Lir,htfood treated

the

traWiport

of

booed.

siqn

and

the

conditions

layer

and

this

module

can

cow

the concent~-ation

boun-

been

methods

This

deoends

construction

Fnother

with

formation

of qel

been

as a basis

used

possibilities 3. Only

oFten

exoensive

like

oroduct

nroducr.

In

hiqher

tower

enzyme

very

though

off

the

been

difficulties

Lee and

layer.

results.

They

All

as successfu7

associated

often

it is possi-

boundary

pt'omlzino

not

of cancentt-atlon techniques due

prac-

as one

with

oolarization

(Ti-721,

the d?-

is in

!rl this

tc concentration

immobilization

that

both

inert

case

thEt

polarlz~tlon

technique.

Three

i7as

differenr

inhibition

ourification could

this

case

in the of

i~obj~i~~d the

enzyme activity

can arise than the

if

easily

be

the

is the deoend

substrate

by

in excess

to the

same on

profile

concentration

when the

this

so

tie

is very

from

is formed

level,

rechqlns?.

difucec! and

effcccs

so'ltrb'feenz;me

stay the

0~1

lwr~otl~-

Sllb5il~CICe

th?

l:tvels

ooI&r1zatlo~

the enzyme

tie

DE?~*~:iPablE! ED the

c~nc~n~~*a~~on

neqative

of

i3rC?ct7552s.

immooil-rzation

is fully

substrate Some

systems

~on~jn~ous

to conccptration

product.

amount

of enzge

this

but

loss

that

to

the scbstt-ate

substrate

due

and

even

~:t-o ~~zzynt~.

ar: the nter;lbrane silt=

enzyme

senaration

is ~~o~.ki~q at

solution

means

apol icarion

solved

sysrrem cornpaired

can

cf

it is gelifico.

beFore

concencrac-ion

to soluble

when

agawst

activity

is mzde

~rrer~ proteins

whjch

the

beside

a concentration

feed

se1

by oroducts,

substrate

formed

inftrt gt-orein

that

Conpared

enzyme

feed

ael

and

concentration

be obtained

the

the

enzpnes

to the

can

t-erection

so

orotein,

advantaqe

is needed.

than

The

solution

advantaaes

enzyme

high

in this

oroblem

use

enzyme

lorlet- enzyme

seaaration

it is Free,

have

surface

which

From the bulk. sotution.

to skim

obtained

is co-crosslinked

advantaoes has

arise

wherher

70)

surface

feed

the

3 ha\re the at

and

membrane

certain

t-alsed the question

technical

contains

with

has many

system

multaneous

solute

oroduct

immobilization

for- simple

sofution

2 and

is reached

Further-

away from the membrane

a nodule.

the membrane

is ?II the

erzyme

face

Problems

with

concentrated

and

of makinq

enzyme

on

on

treated

exist:

feed

3. The

such

way

is coqelified

Methods

much

the

enzyme

2. Tne

lized

mostly

interesting

has

highly

oossible

(65,

has

sofute

the

This

wre

of

of

conneccian

enzyme

if it

know

rejected

concentrated

theoretically we

POLARIZATION

polarization

dilute

orocess.

wondered

orobfem

the

thus

hiqhly

this

tr'ca7 exoeriments had

of

solution,

aim

(691

OF CO~ICE~TRATIO~

Of concentration

oroblem

bulk

b?e

is

thesis,

both

layer.

2.4

an4

77

oublisbed

eliminate

ofetely dary

_AXZDSWIK

\litn slcan

tnougn

svster;l_ ft is clot

is qelif-ied

as tlhet;

is fctrmed- another-

:rithin

the

qel

layer- whic17

78

MATTHIASSON AND SIVIK

3.

FOWING DIFFERENT

3.1

KINDS

OF FOULANTS

Initially fouling was mostly described as a phenomenon that had a negative effect on the permeate flux (78)

and

G!iley

et

Peri

and

Dunkely

al

(79)

(80),

of

membrane

regarding

Peri

and

processes

pulp

Pompei

and

as

paper

(81)

for

presented

effluent

whey

by

Fenton-flay

treatment

and milk

and

by

filtration

respectiv2ly. Dejmek

(51)

Belfort The

reviewed

analysis

according

to

composi In

reviewed

(83)

of

fouling

the

which

in

fouling

in

foulant

is

of

compounds

group

Merson

3.1

(104).

cases

made

cottage

matrix.

listed.

to

reveal

scanning

cheese

studies

2-lactoglobulin

indicated

(105)

and

importance. This

the

was

rough

and

Stringer

mostly

rather

(82)

and

than

characterises yivinq

its

it

exact

in

approach

the

the

also

The

a general

or

selective step The

specific

interactions nature.

(&sting,

107)

described

also

It which

involve by Jonsson

Substituted

have

of

granules

albumin

of

-globulin that

deduce

the

(3SA)

and

by Lee

that

fouling

con-

turned

both

caused

most

B-lactoglobulin

the

fouling

articles

into

a

formed

published

influenced

et

the

of

a certain

by Lee

the

of

was

to

of the feed, how they and

foulinn.

maior mechanism.

al

that

were

corresnonded

permeate

flux

-

to an

TENDENCY between

mostly

surface,

accumulation, There

a multi

chemical

can

FOULING

interactions

membrane

process. or

concluded

constituents

examples

on the

taken

by others.

of

previous

accumtated

serum

was

studies

formed

bovine

environment

INFLUENCING

Examples

microscope

andx

not

a series

single

chemical taken

FACTORS

3.2.1

also

in

fouling

formed smooth sferical particles. Permeation

however

first

about

x-globulin and

(106)

could

the

with

changes

decline.

Sarnmon and

belonns

more

Z-lactoglobulin

Hickey

They

concerned

It

quite it

electron

whey.

sheets or stands. a-tactalbumin

one

often

are

approach

They

of

porous

such

detai!ed

stituents

3.2

while

treatment.

tion. table

A more

Lee

general,

water

is

also

step

process.

that

might

is is

then

(108)

giving

whether

it

for

question

of

a case are

of

to

any

hints

is

a rough

with

be

what

whether

the

membrane acetate

and

reason.

the

showing

has it

or

process

may be of

liquors the

of

fouling

cellulose a solute

sulphite to

of

identify

poreblockinn

the

foulino

hydrolysis

between

suggested

efforts

for

problem

reaction

membrane

whether

responsible

known

a chemical

phenols

illustrated

a question

a well

and

without

the

be

solute

is a is

a

purely material membranes.

membrane a severe

as flux

TAFlf_E3.1 Descriptions

of fouling

p~e~#mena

and foulants,

Source

Foulant

Author

Heavy metal oxides bacterial slimes CaSC& CaCD3

Organic colloids

Leiserson

(84)

Wiper et Cruver and %Cutchan Grover and

al (85) Flusbaum ;86) and Johnsij,- (87) Celve (88)

and inorganic -

Iron

water, sewage treatment including lrcn coagulation

products

stainless

Microbial

sl ime

waste water from sulfite pul Ging of wood

!liley

a~~mtr~ated sand filtered primary effluent

feuerstein

et

sulfuric primary

Feuerstein

(92)

Beckman et

al

CaSO4

steel

acid, sewage

pal 1uted Casein aromatics

waste

surface

waters

water

Organic acids and polysacharides

pal luted

Protein

milk

Calciumphosphate

complex

et

madarin

C!issol ved organic

secondary

Oil

oily

juice sewage

bilge

surface

effluent

effluent

water

and

sewage

al

(93 f

(93)

(94)

Cruver

and Nusbaum

Beckman et

al

(86)

(93)

and Brooke

(95)

~~~inturn (96) et

al al

(97) (98)

Bashow et al

(99)

\!atanabe

et

I’infield

(101)

Jackson et Bhattacharyya

water

(79)

al

Bevege

Til ter

al

Lim et

Hayes et

Pectin and insoluble cellulose-like material

and humic

water

whey trickling

salt

brackish wastes

material

material

water

Carter et al (89) Agrawal et al f9p)

Glover

plating

Ga, P, organic

surface

simulated

material

Organics

Calcium acid

pH-adjusted

whey

Polyhydroxy

Organic

test

loop

Corrosion

Saxon

al

al

(iC0)

(iO2) et al (103)

and Strinoer

(82) -

XATTHIASSONAND SEVIK

80

Purely

have

most of

the

physico-chemical

reasons

This

gives

possibilities ion-dipole

type

(Deanin,

vinyl

methyl

small

accompanying

amounts of reason

is

in the

plasma

In trying

feed

in “nuc?eaction“

lead

(112)

a number of bonds.

found

increase

the

salt

retention

of

&cd

amounts of with

noticed

tk

pofy-

onl-y a

that

ethylene

of

are of

small

glycol.

as the protein

The

covers

orocessinq.

interaction

that

takes

that

specific

tration

surfactants

solute-membrane

place

- soecific

sites

are

or

involved

steps,

~A-membranes in uftrafil

specific

types

bonds

retention

the conclusion

cationic

different

small

poly

in

- membrane

Hydrogen

that

by one or more additional

anionic,

that

of

in the solute

- membrane interactions

to

effect.

filtration

They stem from differences

(110)

the

- a mechanical

in membrane

Busby and Ingham (111)

what kind of

have

nonionic,

They concluded

could

met in food

followed

Palmer et al

et al

enhanced

often

- tests

107).

to formation

to be solute

to reveal

nonspecific

encountered

and dipole-dioofe

decline,

proteins

a case

are

(Kesting,

Michaels

flux

believed

the membrane,

taining,

lQ9),

ether

by way of comoaction

that

in the atoms or molecules

1 i ke ion-ion,

system,

bonds

occur

problems

of electrons

distribution

last

interactions

physica'l

However,

of

and other

a solution

nonionic

interactions

occur

con-

solutes.

at low solute

roncentrations. tiopfenberg other

et

nonionic

al

lmoortant

for

Pristounil

performed

They concluded

of

molecule

solute

the existence et al

(174)

fuf ly

with (102)

found

that

the smaller

faster

The pH influences takes

shattacharyya bilge

oistilled

of

ion of

and

characteristics,

the membranes are

immobilized

probably

protein

immobilized

The proteins

bjinters of

particle

describe

(103)

synthetic

films

by short-ranoe

do not become

flux

lowering.

the

ionhydroxide permeate point

to be attached

coawto the

and growth.

fouling system

led

increasing

isoelectric

narticles

sites

control

colloidal

or with

Vear the

large

lubricating

The deterg~Rt~~~ater

by small

size

size:

formincg too nucleation

causing

fouling

particle

diminishin al

- or-or&h mechanism

\ras pet-formed the

et water,

water,

interactions

the

thereby

place

:,e,llbt-ane thereby

result

are

a nucleation

The nucleation

surface

they

like

surfactants

fouling.

Cl-i2 - CHCI-groupings,

oarticles,

by oily

of

various

charge

the formation

that

nembr-ane foul i ng. flux.

tha t factors

and magnitude

numerous

blith

uncoiled.

Jackson

latiorz

tests

and surface

described

on P~fC-membranes and conclude interactions

similar

solutes_

activity

surface

(113)

of

oil

non-cellulose

and nonionic

caused

In the system

reversible also

acetate deterrlent

membranes in

detergent-membrane

containing

oil

a

results,

and Isquith a sequence

(125) of

reoorted

events.

thar microfouling

1. Chemical

condition

in some cases of

the surface

is

a

b)f raaid

81.

Fl4Tl-HIAS SON AND S IVIK

of

absorption cular

molecular

weight

substances

by other

microorganisms.

4.

Accumulation

nit particles. The adhesion-inducing mer which

is

active

adsorption

albumin

to

the

from

feed

process

et al

with

second

(116)

occurs _ The third surface The

stage

is

reviewed

cases

situation,

like

and

pli of

3.2-2

Membrane properties

Membranes of

in turn the

bulk

different

first

is

lasts

drop

took

ooly-

caused

olace

by

adding and above

as a three

less

reached

adsorption

example

reflecting

the

hydrofobicity

flux

between

and monolayer

stage

thar; five

seconds.

a< the interface.

The

on the membrane surface mechanism which

membranes are

less

prone

proteinacious

Membranes with

may

differ

an asymetric

frequency (119)_

produces

a

factors

solute

degrees

that

prooerties

influenced

form

and

by the

the

processing salt

concen-

solution.

(105)

resoond

in different

investigated

- of three

membranes.

have noticed

to fodlinq

than non-cellulose What

might

aspects.

UF-membrane

potential

to the same

moisture

Horrever,

solutions. in many

nays

the monolayer

content

-

no correlation

was found,

and many others

and zetapotential zeta

important

properties,

moisture

Lee (105)

Eykamo (1?7), processing

Lee

of

to varying

composition

For

and

are

differs

Freeman

with

acetate-

for

this

made

elctr-okinetic

that

pore

size,

oore

According

production

when

difference?

(118)

properties.

solute,

cellulose

membranes at least

be the cause

concluded

important

that

exoeri-

shape,

to Kaneko

tennerature

and

concentration.

The information surface

exposed

the

interface

him be 125 pores/E’ Further potential,

important all

about

oores

to the soltite

Freeman reveals ting

flux

process

by a reaction

at a number

are

situation.

al

The

solute

memb&ne

tration

solute

is a slycourotein

mg/ml adsorption

profile

governed

point

They

et

constants.

concentration

parameters_

pore

Coloni-

and inoraa-

gel.

fouling

ments

3.

detritus

when continuously

formation

an ultrafiltration

one to ten minutes,

stage,

material

low mole-

started_ time

state

of

by bacteria.

debris,

the permeate

by gel

Below 0.01

describe

distinct

A ouasi-steady

caused

solution.

mg/ml gel formation Howell

concentration

low concentration. discriminate

could that

of

polymeric

in exceedingly

Ingham and Busby (111) protein 0.1

, and

substances. 2. Attachment and colonization

weight

zation

large

that

there

also

are

and coalescing of the

an

idea

about

how

larae

rhe

trtie

50 A wide

tubules

to 300 A tubules.

and 50 There

A

wide

should

slots

oenetra-

accordinn

50 A pores.

properties

of which

gives

is.

are

can be drived

surface from

tension, the actual

surface

charge,

composition

of

surface

the

to

MATTHIASSON AND SIVIK

82

membrane

_

the three

(105) describes

Lee

Polysulfone

is

The oxygen

characterised molecules

rise

to strong

Fig.

5. The

repeating

Polyamide

the

unit

have

sulphone two

reoeatina

unshared

or solute

units

electrons

(Fig.

to donate

molecules.

repeating

units

of hydrocar5ons

linked

by amide

6).

H

-A-C-(CH*)4- C-h(CH& tl 15

I

- (CH*)4 -c-N-(Ct-&

Ls

8

Fig_

6, A seouence

The

amide

bonds

cause

tension,

of a polyamide

that

polarity

are

possibility

Cellulose acetate (CA) membranes (Fig.

for

high

to form

consists

surface

energy

hydronen

of acetylated

7).

R

Fig.

7,

The repeating

unit

-

material_

responsible

with

H

H

H

-tic

5). givincr

of polysulphone.

contain

(Fig.

-SO2

to solvent

bonds

membranes

2 - c - p1!-

groups,

of

hydrogen

membrane tyDes he used in the fol lowina way.

by diohenylen

of a CelluloSe acetate

membrane.

and

surfate

bonds. ISglucose

units

H_4T-l3iIASSON

AMI

S LVIK

The polarity descri

bed

Interaction

is

llhen is

- caused

by charge

expected

dipole

to

interactions

acalled

by an uneven

density,

occur

become

a solubility

distribution

moment with

polar

appreciable

factor,

and

the

electron to

clouds

-

is

form

hydrogen

bonds.

are

modified

by what

species.

the

i.e.

of

capacity

cohesive

chemical

forces

affinity

of

the

species

for

the membrane.

3-z-3

Influence

Salts with

may either

the

al

et

and

or

(98)

sample (105)

fouling

great

the

classes

and

in

and

et al

solution.

increased

whey

results with

of

proteins,

of

the

rather

membranes

rrith and

role Ca,

competititon

with

studied

t’le

of

but

However,

of calcium.

concentration

at

higher

DhosDhorus

concentra-

leucin

solutes

others.

for

different

he showed

is affected

?lactoglobulin.

phosphorus

in

the of

Hot/ever,

tha t its binding

and

and

indicating

containing each

lactose

flux.

role

inconclusive

systems

of

permeate the

with

solution.

components

are

interact

Seouesterinq

to a certain

UD

natural

important

addition

the about

calcium

of

of the

be the

decreases Too much Bevege bentonite

actions

the

of Its

solubi

removal

1 i ty.

produced

between

clay

explanation

lization

with

in

Indications

bindina

to

on humic

acid.

and

the

the

membrane

orotein at

size

surface ions

cations.

the occurs of

the

a whey of

t-ather

than

- increasing

solubility

molecules, high

Ionic

the the

was

believed

strenclth

calcium-caseinate

and complex.

deposits.

trivalent

a destab:

in”

to

a thinning

s-trennth

“Salting

simulated

acid

EDT?, atidition

caused

ionic

out”

EDTA reduced thicker

- humic is

polyvalent

“salting

and

strength of

ionicsheatharound

with

divalent

ionic

by calcium.

ooposite

(97),working clay,

an

calcium

importance

actions

formation reason.

effect

similar

the

specific

possible

cations

F!aCl of

indicating

sheet,

possibility to

(120)

CaC12 and

protein

to

the

2)

seen. Lee

due

of

an

by the

of multi-binding were

role The

that

foulants,

in foulin?.

conclusion

strength

different

plays

ways

pH 6.2

the

pressure.

calcium

stability

ionic

dealing

comparing

phosphorus

different

the

the

of UF-membranes.

complexity

that

in

of

any

is likely

involved

studied

to

of

osmotic

role

justify

that

increases

He also

whey

not

solubility

the

the

of

states

simply

1) the

increase

studied

did

may be directly tions

3)

pH adjustment

a control Lee

sat ts influence

membrane

Hayes EDTA

of

and

humic

ization Another

water

in

trace

acid

of

including

humlc

amounts,

noticed

- multivalent

polyelectrclytes

possibility

ions. through

is

adsorption

acid,

interOne neutraof

tne

MTTHIASSON AND STVIK

84

Effect

3.2.4

Mullet-

of pH and

et al

(121)

under

djfferent

above

pH = 4.5

for

et

(98)

Hayes

al

one

of

wheys

of

the

to a certain

influences

the

ionic

of

fouling

of

influence

particle

size.

observed

in UF and RO. At this

membrane,

AL

the

and

et

al

(102)

example

whey systems,

the

point

point

Jackson

charge

thus

isoeiectric

of

whey

increased

related (Lee,

of

the

protein

(zeta

large

observed

of

the

calcium

casein.

a membrane is

characteristic

strength

two kinds

was low but

The combined effect was con-

protein aggregation and to the mode of aggregation corresponds

UF of rate

pH-deoendence.

coagulation

pH in the

of

the

only.

investigations a strong

be a selective

The effect

rate

Below pH 4 -3-4.5

of the

noticed

on fouling

the permeation

in their

also

to

studied

pH conditions.

concentration sidered

temperature

the

degree of

This in turn

proteins.

influences

solubility.pH

potential

particles

the

to

105). pH of a solution

= 0) a low

flux

form and settle

opposite

when working

is

on the

with

iron

hyaroxide. In for

some constituents polymers

in the

\!infield of

(101)

secondary

by Hayes

not work

well

thar

agents,

pH 6 gave

of whey proteins (98)

in UF.

casein

Care has also

other

in

adsorb

natural

systems,

on membranes

and

bind

higher

fluxes

9H 5 and DH 7 in PO

than

effluents.

The denaturation reported

as flocculating

also

to the membrane.

noticed

sewage

1 i ty betrleen

act

may

feed

but probably

and Muller

The

by means of (121)

mechanisms

components

to cause

is thought

to avoid

the

temoerature

a flux

increase

to be ag?reuate

and 5-lactoglobul

to be taken

high

has been in RO,

but

did

oossibi-

forming,

in.

formation

of

apatites

which

is pH

depending.

3.2.5

Effects

?arallel effects (C5j

shear

stress

pressure

and

to looking at what causes the fouling it is natural to

of

it

observed

and

hoL/ it

how the

can

also

Thomas

counteracted,

flux

permeate

the retention

Sometimes,

be

drastically

changed.

Kuiper

et

al

dronoed saw

(171,

as a result

a decrease

which

lastly common, Belfort (122) also observed a decrease in operatim RO membrane.

after

An increase

the addition

The flux

decline

due

mot-e severe

decline

with

by Gutman (123). surface 122).

is In

was

a protein

some cases

to

the

to fouling

The feed

of major

noticed

high

a threshold

a system

also

flux

velocity

et

on the

shear al,

at

the

e’E al

of fOUlinq. seems

to be

a protected

poly

ethylene

glycol

(111) _

than with

or rather

(Jackson

filterin?

solution

deoends

initial

velocity

importance

in

feed

look

Kuiner

102,

initial

flux

low flux-

This

stress

over

Pinturn,

has to be suoerceded

the

96,

showing

is

a

predicted

membrane

Hiddink

in order

et al,

to avoid

55

X4TTHIASSON XXI SIVIK

drastic

fouling

(Kuiper,

show how the fouling Especially

85).

the effect of raised stress is positive.

In general

in RO of skim milk

at higher- pressures

Hiddink

depends

on the aoplied

MPa

influence

than

2.5

high

shear

the

et al

(124)

also

nressure.

of fouling

becomes

important. suggests

Some evidence extent

the negative

Madsen

f125)

based

reasonable thickness ness

fouling of

forward

the

3.3,1

Model

Kimura

and

membranes

but

stress

and

higher

fluxes

of wave and vortex

different theory

of milk.

Sulk

by Kimura

and

IYakao f127)

the

diminish

to a large

than

theoretically

pore and

models

He shows

and

concludes

oscillatinr

the

the

format ion pore

on deposit

dependence

in a thlr; that

orlenlncls

a

aive

resistance of deoosit

and tilick-

concentration,

OF FOULING tuakao

based

on a modification

no1: hinder

does

it can

Gerndel (126) presented a study

results,

NATEMATtiICALMODELLING

3.3.

to the

theory

diffusion

in ultrafiltration

on shear

itself

65)

it.

considers

on a long-jump

stress

(Lopez,

as an explanation

channel system. He also model

of

effects

has

Fe puts

calculated.

that

process

physico-chemical

of

their the

model

gel

of fouling

polarization

of CA

model

tubular

by tllchasls

PC and ‘jr (45).

Jv = k In ($1

f52)

b

It is extended

to accunulation C

J

V

- 'b The

deposit

- k Cb

In

resistance

g/C

b

of

under

unsteady

stare.

dl = -: dr

to flow

resistarce

of a deposit

the

the membrane reslstarce

consists

of

layer

- 7,

at

P,,4 and tie

JY = R--Sk-T 1 m -ig

R

Introduction dependence less

form

21 dfl FE 1

and

yields

of a dimensionless a dimensionless

equation

flux

55 where m,

-c fl - r = - '11 ml

resistance

(t)

f, t is

Jv = -J-

(F)

= {t,'

ana writing

thg’dimensionless

1

and

its

time

eq 53 on dinlension-

time.

-1

(55)

MATTHIASSON AND SIVIK

86

eT -

P

0

(561

*C

aTo Jv~

b

FT. expresses

the

In r = k

J

Equation

For can

flux

decline

and

r is expressed

by ee.

57.

55 can

ul trafil

be solved

tration (ml

or

numerically

low

= 0) and

if

eq.

m

r

1”

reverse

pressure

55 can

be

and

5 T are

osmosis,

qiven, the membrane

compaction

integrated:

T

There

is no

indication

Model

3.3.2

Carter

depends

Hoyland

of

rates the

how well

and (128)

in turbulent

on the

thickness

on

by Carter

and

~~-membranes

of

it fits

with

experimental

results.

Hoyland describes

flow.

deposition

The

the

build

up of

development

rd

and

rust

fouling

of a transient

removal

rr of

rust,

layers

fouling E is

the

that

dE dt = rd

- Kl

h = half

the

removal

depends

directly

on the

shear

~~~ at

the

surface

I~, - E

l

and

channel

9E = Reynolds

effective

f59)

= proportionality

Integratjng

on

layer

layer.

rd - 'r

Assuming

El

of the

(57)

be neglected

bE=

constant

vo

r

dt

time

c <

constant.

exchanging

height

number

?w according

to the

Blasius

eouation

yields

rlives

rate

The

stress

a7

AND SIVIK

MATTHIASSON

at

of build

up and

the membrane

final

thickness

are

surface

but

that

neither

of the

Instead

the

strongly

insensitive

to flux

deoendent rate

and

on the

ferric

shear

hydroxide

concentration.

3.3.3

Model

Gutman found for

RO.

bursts

of it from

The

dm __=r dt

-r

Carter for

down

This

from

into

rate

two

previous

introduces

fouling

models

a “turbulence

burst

a fouling

the

laminar

layer

is ascribed

sublayer

to occur

is found

have model"

and

at time

remove

intervals

to a small r?

g/TW.

is

the

nett

rate

of

foulin

(62)

e did

not

count

increased

He arrives

membrane with

Jf

particles

sweep

the wall.

point

R, proportional

smaller

of

which

to 1GO

starting

d

acceptance.

reentrainment

The

proportionat

oniy

remarks

widespread

turbulence part

by Gutman

(123)

for

to the weight at

an

time

or larger

of

integrated

for than

extra

any

resistance Gutman

pressure.

osmotic

the

the

fouling

equation two

twice

cases

due

foulinn

a hydraulic

layer

but

resistance

layer.

describing where

to the

introduces

the

the mass transfer

flux

the

fouled

decline

membrane

flux

of

the

is either

coefficient.

< 2kg Jv A, ?? kg

- U (AIU

+ :.a2r (63)

Jv exp

Jf

J” -=. Jf

k9 +

> 2 kg

A,

2 (A,U

- U + ;%aJ]

Comparison change

with

foulant

in the

and

parameters

the

experimental

data

shows

tha t accordin?

to the model

the

flux

time depends UPOTI the initial flux J,, the co~centr~t~o~ of the

with

feed

(a)

the

3 and

%ed

velocity

(U)

the ma5-S transfer

coefficient

kg

At.

The experimental initial flutes do not agree well with the th~o~~ti~a? values, but

final

3.3.4

flux

values

are

better

predicted

Model by Betfort and Marx

Belfort

and

Marx

(122) have for

performance converted the standard trztion eauation which describes as a function branes

of

with

accumulated

respect

the

sake

=

1 during

n = f3 during

and

. = constant = rr(I> for I‘~ = wCa) For

=

the

dividing

initial

the

steady

state

for

suspended

constant

ilitita!

V and

of membranes

to a modified of oermeation normalizes

ccl

fil-

coefCicient

different

the

Equation

later

~~~oac~ion.

(65)

(1c:v")

oeriod

oeriod

feed concentration

suspended

transient

steady

stage

of

state

meq-

of the rn~rnbr~~~

characteristic

variable

comparison

feed

period

with

concentration integrating

(n=l),

Z with the

C e~u~t~~n

above

by if.

11 the

For

transient

the

easy

volume

permeation

tc fouling

of

filtration equation the accumulated flux

1

R

of sewage water,

in processinfl

the

period

initital

period

(n=3)

after

67 and 68 should join smoothly

which is analonous to the standard

~~t~qrati~~

as V -e =,The

filtration

eouation..

the

enuation

eouation

becomes

becomes

and

59

NATTl-fIASSONAND SIVIK

The feed

correspondinn

~~ = (“p

-

also

/

water

surface

can salts

the

calculate

be

Jv = (“*/R,)

a plot

the

flux

(7b’,Rm)

in

be calculated

exp

the

knowledge transfer

to

( Jv/k,)

of

sol Ids

suspended

to can

of

eouation

UD of

ohysical

at

pronercies Then

exp

70 and flux

be seen

when

solutes

-_ = C. the

of it

is

membrane

the

1ac:cs.e

possible

59

71.

(Yb2/R,)

eq.

experimental

this

btiild

coefficients.

ecr.

-

oermeate

fouling

of

the

mass

accordin?

71 and

from

occurs

accordinn

a plot

magnitude eq.

decreasinn

71 and

versus as

exoerimental

osmotic

the

(7’ )

tJv/k21

results From

oressure.

difference

bec;geen

the

s,~ch

curve

results.

MET;dOOS FOR FOULING ANALYSIS

3.4

Fouling

anaiysis

characterizing The

hydrates. use

of

the

macro

analyses

(104)

used

in combination

et

al

aromatic

Watanabe

deposited

can

be

classifying

metal

or

deDosits in

identifyin?

materiat

as

components

forof

substances,

nresent

determining

the

in for

deoosits,

for

membranes.

identified

the

non-metal

are

s and

large

examole

example

the

in

degosit

nroteirls, enourlh

references as or-nan:c

fats

auartities

Fe, Ca,

orqanic

or

carSo-

to

allo::

acids,

noly-

P, etc.

Jonsson

analysis.

of

for

techniques suspended

the membranes

Normally

et al

proteins

and

substances,

sacharides,

tifying

on

It is a matter

inorganic

Lee

requires

solutes

deposits

85-103.

the

the

calculated

to

also

with

nivinq

be visualized

according

or

can

permeate

The fluxes

exponentially

polarization

described

-

for

qiven.

62) ,

flux

thus

the

also

Rm

concentration

and

can

are

~7)

The oure If

equations

concentration

(100)

(108)

SDS-gel with

used

compounds used

on a membrane.

gel

electrophoresis

scanning

mass in

the

filtration

The pectin

electron

spectrometry

in identification microscopy

and

nas

and

of whey

oermeatlon

chromatography

when

when

nect:n

studies.

iden-

membrane. and layer

calorimetry was washed

off

the

analysinn membrane

nrior

to

MATTHIASSON

90

Glcrver

analysed the structure of a deoosit with

(95)

mi croscopy . Lee

(105)

ultrafiltration

experiments,

spectrometer.

Kaneko

used

(119)

radio

actively

The

counting

measured

label took

led

In an article are

MAIR,

metry, critical

tension

MAIR and ellipsometry

tion-

of material index give

surface

attenuated

to be analjrted

respectively. further

fouling

The

regarding

about

solid

and

potential

which

allows

and

thickness

contact

surfaces

potential that

are

spectrascooy,

and contact

methods

composition

tension the

techniaues

infrared

might

Pretreatment

In table

3.2

OP PREVENT

of the

pretreatment

feed

determina-

microsconic and

determinations prove

useful

et et

(981 (129)

FOULING

are

listed.

3.2

Pretreatment

methods

Process

Product

Operation

Author

Heat treatment

&hey whey

UF PO

Hayes Smith

ptf adjustment

whey whey

RO UF

Lee

ion exchange

whey whey

RO UF

Hayes et al (98)

Hhey

RO

po~ypeo~id~, enzyme

IJF

whey

UF

Lee

whey

UF

Lee et al (120)

whey

UF

Lee

and

pH adjustment

Ca-sequestering

agents

(EDTA)

Glycerol solution

addition

to feed

*

Change

of ionic strength

Modification ~sulfhydry~-, Pre-ul

traf

of side chain carboxyl-1

i 1 tration

Smith et et al

Smith

amounts

refractive

solution

methods

listed.

ellioso;

studies-

3.5.1

TABLE

optical

surface

information

METHODS TO DIMINISH

3.5

determination

are

in

by Freeman (118).

of experimental

reflection

leucine

scintillation

under a reverse osmosis pro-

zetapotential

(139) a number

by Baier multiple

and

in a liouid

cess. Similar eTectrokin~tic experiments were p~rfo~~d

They

SIVIK

t~~ansmission electron

phosuhorus

place

AND

al al

al (129) (120)

et al

(129)

Smith et a? (129) Lee et al (120)

et al

et al

(120)

(131)

in

31

XiTTHIASSON XSD SIVIK

Many in the

of rhe

reasons

previous

increased

the

flux

the

BSA

~-~acto~lobulin

vent

retention

foulin!

showed

modification

allowed.

Lee

et al

EDTA-addition Apart

of unit the

3-5.2

Change

hydration

erouos

be

of

but

there

exist

chains

methods

which

are

methods,

has in-

examnle to nre-

involved

ooint

parts

of

in water

of view

treatment

the purification,

adsorption

methods,

of

were pY-chanve

that

a large also

coagulation,

nays

of altering

membrane

aim

number to channe

filtration

nrooerties

of

membrane

etc.

are

listed.

orooertles

Product

Process

Author

membranes

sulohonate polymer sulphonation, amination electrically nolarizedelectret membranes Immobilization on the membrane

Use of small current

The

cover

milk, raw sewage albumin, haemoclobin

UF UF

I'ano et al (135) howell et al (116)

colloidal

PO

Belfort

that

fouling

the

use

has been

of charoed

(137). Immobilization

higher

than

naked

UF of reconstituted

when processing

milk

membranes

twt forward

ChNinabaSaDDa fluxes

oarticles

et

al

(122)

electric

suggestion orevent

Greoor C-renor (132) Yomura et al (133 \!allace et a7 (134)

of enzymes surface

Use of orotective fixed dynamic

crease

for

as an example

additives

a commercial

- and

pronerties

different

of manipulation

Charged

partly

of

explained

(13@)

in order

be renarded

if the

been

feed

the membrane

of side

should

from

of

the

~-lacto~lobulin

performed

that

have

(1C '<) to

3.3

Chances

Type

could

oretreatments

Modifications

conclude

of membrane

3.3

feed

of qlycerol

be feasibfe-

‘listed

biological

in table

TABtE

(120)

of

increased

improvements

that

operations,

feed;

by

or carboxyl

could

the

from

use

addition

of oroteins.

some

chemical

or

the

The

- nossibly

creased and

behind

chapters,

of enzymes

membranes.

"ano

during

50 first

the

sewage water.

as a means

as a nreat

et al

future

to at

least

Potential Qroven

bv to nive

on membranes

has

(135)

a 9c! % increase

reoort

orocessinn

hours

and

a 12 '1.in-

in

92

MATTHIASSON

They also of

present

a Mel layer

lation

and the

exr?eriment

and

tective

cover

brane)

a model

or

of

type

includes

z-membrane that

the enzyme.

Belfort

et

a RO-membrane,

precoat

and

by Spiegler

a potential

The membrane serves of

theirenzym

A fair

al

either

protection,

agreement

(122)

suqqests

fixed


Increased

the growth

between

caicu-

the use of

fluxes

SIVIK

a pro-

Nuclepore and

mem-

decreased

result.

P US patent mA/cm'

kinetics is shown.

top of

or a dynamic

rejection

for

AND

(136)

claims

difference

as anode

of

that

2-20

use a small

V has

and the cathode

electric

a oositive

is a metal

current

action

on the

electrode

10-100 flux-

in the center

the tube.

3.5-3

Change

In table tions

in process

3.4

conditions

changes

at-e listed.

in process

Essentially,

it

and

conditions is

of

optimization

flow

conditions

and ootimization

a question

of

changing

of the

flow

shear

condlstress

at the membrane surface. T4XE

3.4

Changes

in process

Type of

aanipulation

CIl-,ered linear

conditions

Author

velocity

Hiddink et al (124) Thomas et al (17) Kuiper et al (85)

tise of static disglacement

mixers rods

i'se of

rn a f‘luidized

Cse

beads

of movinq

!Sse of

aiming

oolarization. module

viscous

products

demand.

The

action

at

increasea

rotates, (65)

and the

of the

of

promotors

at the membrane surface fouling

or eroding

the

where either

in processing

but has up till (glass,

module,

has

concen-

bed system.

apolication

beads

as ire11 as of

rotary

fluidized

Bass process,

fluidizing

(65)

at-e the

has a potential

in a single

as turbulence

effect

(124)

(138)

forces

shear

developments

et al

et al

Lopez

the deteterious Recent


IS either

Hiddink Lowe

to diminish

The rotary

bed

membranes or elements

Xanipulztions tration

Dejmek (51)

balls

rotating rotating

been used

and

now a large

2-3 mm diameter) surface

highly

gel

layer

energy

reoorted (124).

>l.ATTHIASSON AND

Cleaning

3.5.4

of

Cleaning

biological revjell

membranes

standard listed

water In for

techniques the

works

membrane

and

some

degree

there

are

mation

in

about

Balet-

mentions

takes

and

The

condo

and

in

process

dt-aIJ and

for

foul?nq. in

adhesion This

nw

at-e

fibrinogen,

“PROCES!j

like

blood

these

of

cellblat-

be

but

to

clean

tissue,

oral

of

material.

environments

at

in

uterine

solid tionetfor-

the

surface.

In the

case

that

the

evidence

and

and

chc

points

sDec ies

some

infor-

The condi anchor

sneclflc.

are

‘leasr

foulants,

further

a conditloninq

reasonably

at

oossible

crovldes

there

in mat-1 time

the to

TIO collect

interface

to

in

cases.

EC\tJIFMENf”

filtration

ity

of

inLet-face, and

enzymes

a

waste

in orher

disability

ft-ow ccl lular

considered

in

in municioal

LJor-kinc! lrlth

systems

has

oroblem.

a gossibil

_ In each

micro-

(83)

used

the

membrane

equipment

ilater the

also

pt-oteolytic

a 1 arqe

muco-oolysacchariaes

tioners

is

is

to

a non-physiological

ditioner

of

used

are

aoolications

flux

of

before

with

use

a certein

Belfort

R&membranes

OF OTh’ER i;II;I?S OF

proteinacious.

bonding

the other

adhesion

sea

zlace

Dredomantly

stronq

kinds

to maintain foulants.

mentioned

encountered

reasons

saliva

of

methods

the

only

parallels

(139)

surface

blood

not

the

cleaning

restore

all

some

cavities,

is

is

of

get

in many

PARALLELS TO FOULING As fouling

obder

rid

to

industry

but

to

in

as

the

dairy

well

performed

for

Many of

examole

3.6.

is

is

as well

renovation_

detergent the

93

SI.vIh:

t’le

of

ccn-

oral

cavl

the

studies

it

ty

a glycoprotein. This

infotmation

foul inrJ of Foul inq

can

a transpot-t

exarrwle

From

the

different longer

place

there

boundary

free

surface

gradient There (Baier,

from

as

layer

and

i:“lere

as

a number

139):

multiple

to

concent*-zte

of

(1W)

in

gradient_, temgerature analysis

vierr

the or

Itnowledne

1 Ike

unfo’ldlno,

describe

of

fluid.

F\nqstrb;ms_

ootential gradient methods

attenuated

: nternal

tension

determination,

is

one

ilznd

orientation

pt-ot?ln

.z!K! JS

aboui

needed

Chdrws

adsorntio~

on

p31:/-

*/ie\;.

has

layer

neglecred 1Jall

of

one

bulk

on the

more

Doint

boundary

normally

of

pbenonenon

Thus

othet--

the

those

surface

an sdsot-otion

Lyklema

ooint

are

are

critical

about

a thermodynamic

micrometers

energy well

hints

macromolecules

within

from

mm or m but

the

with

engineering

takes

as

on the

Nor&

surfaces

happens

nietry.

regarded

ohenomenon

For

styrene

be

some

_

ahenomenon

adsorption etc.

2ives

membranes

to

realize

and

that

The scale Important

thar

everytiinn

t5e

conaitio~s

of

t-eference

dr-ivlna

in ena:neet-in? gradlent.

ot-actlce stt-eam:np

tizt at-E_ 3~1~ is

forces for

nr,

~:ithlfl e~ai~;r?e

Qotentiaf

141) -

(Sandu, available reflection

contact

for

surface

anal?ls

suectrosconv

elligso-

Dotenilaf

determination

and others, Till chemical’ly creation solutions

now membrane inert

manufacturino

membranes.

of tailor-made with

the

aid

has mostly

However,

aimed

additional

at

efforts

nroducino may result

surfaces that are resistant to foulina

of methods

and apDroaches

like

high

those

even mentioned

flux,

in the of complex above.

95

MATTHIASSON AND SIVIK

Symbols = membrane

A

=

Al a

p&lO!I

constant,

equation

Jl

= 3Ub/tl

filtration

= soeciqic

a1

= concentration

a2 !3

resistance

of foulant

= lTo/co

C

= concentration

9

= diffusivity

E

= eFfective

cu

=

of solute coefficient

= equivalent

dh

hydrolic

diameter

thickness of the fouling layer

'w"b = Fanning friction coefficient

f

= Jv/Jvo

7 + CI

= gravitational

acceleration

h

= half channel hight

J

= Chi 1 ton-Co1 burn

J, ,'

factor

= oermeation

velocity

= oermeation

velocity

iyvl

= absolute

I.1

= 1 imiting

permeation

= constant,

equation

!

'V'L

K Kl,

4

K2,

value

K3=oroportionality

of

of

fouled

the

oermeation

51

constants

= hydrolic

k

= mass

transfer

coefficient

= mass

transfer

coefficients

k2

k3,

k4'

kg'

kg'

resistance

k,,

k9

= liquid

L

= channel

1

= thickness

F

= mass

ml

of fouling

for

layer

lactose

= constants

kg

side

mass

transfer

coefficient

length of deuosit

of foulant

= coefficient

velocity

veloci',y

KLl kl,

membrane

per

layer

unit area

of membrane

n, n1

= constants

0

= aoplied Dressure

AP

= oressure

drop

AP,

= oressure

c!rop across

'i

= rejection

Pm

= membrane resistance

Ra

= liayleigh

across

coefficient

number

comoaction

membrane the

cake

oer

unit

and

mass

salt

respectively

= Reynolds

number

= = intrinsic =: rate rate

of

re-entrai

=

rate

of

removal

=

exposeo

surface

=

Schmidt

number

=

Sherwood

=

time

7

axial

nment

area

for

transport

number

velocity vel oci ty

=

transverse

5

accumulated

=

dimensionless

volumetric

throughput velocities

permeation

mass average

vet oci ty

of

feed

time

a

=

turbidity

q

axial

=

transverse

or

radial

coordinate

=

transverse

OF

radial

distance

distance

coordinate from

membrane

surface

letters

KitfRm

Lc

=

3

= average

1

resistance

of deuosition

z

=

-creek

membrane

specific

cake

resistance

i.?

= fraction

of

z1

= membrane

constant,

:

= boundary

layer

::. ?-

= parameter

defined

according

to

equation

21

= Parameter

difined

according

to

equation

14

2

= accumulated

=dynamic ,kinematic

surface

cleared equation

by turbulence

burst

63

thickness

time

viscosity vfscosity

= osmotic

pressure

= osmotic

oressure

difference

=osmotic

Pressure

of

lactose

across

membrane

97

‘Tib2

osmotic

Dressure

P

= = fluid

c

= Staverrrtan

T

= shear

of

salt

density

1

reflection

stress,

coefficient

time,

(eq

53)

Subscrids b

= bulk

9

= gel

0

= condition

cl

= oermeate

condi t-ion

w

= membrane

surface

condition condition at

channel

condition

Cherators “nab1 a” operator substantial

inlet

lierivaxive

or

zero

time

MkTTHIASSON AND SIVIK

98

LITERATURE

1

R-3.

Bird,

W.E.

2

L. Dresner,

l!iley & Sons,

water

3 4

by

Stewart

Inc.

New

Boundary

reverse

R.J. Raridon, H-K. Liu and

and

E.N.

York

tightfoot,

Phenomena,

built-up

in the

Oak Ridge

Cat.

deminerafizaticn

Lab.

Reut

362t

Williams,

Int.

J. Meat

Mass

of

sa?t

f7964f.

L. Dresner and K.A. Kraus, Desalination F.A.

John

(1960).

layer

osmosis,

Transoort

(7966) 210-224.

Transfer

13 (1969)

1441-1456. Y_ Ffakano, F-A_ F.

9

10

C. Tien

GIIiams,

and

Siam

Bellucio

A.

and

ll.N_ Gill,

L.J.

John

Wiley

& Sons,

T.K.

Sherwood,

Lab.

Rept

295-f

W.N.

Gill,

C.

&.I?'. Gifl, Appl.

J.

Pozzy,

Int.

Derzansky Inc.

P.L.T_

and New

A.I.Ch,E,J.

Math.

17

York

Brian

59-73.

Mass

Transfer

J. Heat t4.R.

and

Doshi, (1971)

R.E.

13 (1967)

(1964)

Surface

1092-1098.

18 (1974)

and

945-951.

Colloid

Science

IV,

261,

Fisher,

6T.I.T.

Desalination

Pes.

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and

D.W.

Zeh,

ind.

Eng.

Chem.

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C (1965)

433-439. 11

P.L.T.

12

R.E.

fisher,

Lab.

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Ind_ T.K.

295-5

13

5.

14

T.J.

Hendricks

15

!I. R.

Doshi

Eng.

Fdndam.

Chem.

Sherwood

and

P.L.T.

Osmosis,

Logos

4 (1965) Brian,

439-445.

M-1-T.

Oesa7ination

Res.

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Scufirajan,

Peverse and

, A.K.

F.A.

Uilliams,

Dewan

and

Press

I!.N.

Gill.

London

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Desalination

(1970),

g (1971)

A.1.Ch.E.

Symo.

155-180. Ser.

68

(1971)

323-339. Srinivaisan

5.

Ind.

C. Tien,

D.G.

Thomas,

M.K.

Liu,

Desalination

f4.K.

Liu.

AppJ,

I__ Dresner,

0.S.W.

Bellucci

and

5.

Srinivasan

B. Bansal,

C.K_

Desalination

Chem.

Res_ Res.

26

Dev,

N.. Esposito,

and

Fundam.

9 (1971)

C. Tien,

Tsao,

Dev.JProgr.

25

Y,

26

G;,H_

&inograd, Rao and

f.1. Tot-en

27

J.J.

Hermans.

28

6. Bansal,

K.K.

8 and

Sirkar,

f157c’)

3A9-360_

Progr.

Rept

Membrane

A theoretical Ph.D.

thesis,

897

A.R. (1973).

(1970)

234-258,

Solan,

1,

No.

27

W.P.

College

Doshi

74 (1974)

(1978)

3 (1972)

experimental

Clarkson

Dewan,

127-13?,

OesaIination

Desalination

and

181-191.

9 (1971)

854

Digest

3?6-flD5.

(1973).

28ff979)

Desalination

A.

339-156,

12 li'o_d (1973)

Desalinatron

Rept

Desalination

5 (1968)

181-191.

R_ De,Iuca, t. Derzansky,

Res.

osmosis,

Erg.

Sci.

F.

O.S.!J. 24

and

and

?.A.

Shaw,

173-187.

9%fl6.

45.

study

of hollow

of Technology,

fiber

Postam

reverse (1973).

~~TT~~ASSO~

AXD

99

SIVTK

29

B,

Bansal

and

I!.N. Gill,

A.:. Ch.E.

30

tl_N_ Gill

and

B, Bansaf,

A.I.Ch.E.J_

31

M.S.

Danavati,

32

M.R.

Doshi.

N.K.

Vinayak,

33

M.R.

W.N.

Doshi

Gill

M.R.

and

and

U.N.

V.N.

Doshi

I!ater Symoosium

and

19, Gill,

Kabadi,

W.N.

(l97d).

FJo. 4 (3973). Chern. Eng.

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Gill,

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Enq.

30

(1975)

(1977)

Commun,

577.

765.

3 (1979)

339-365. 34

K.

35

T.J.

Ramanadhan

11

and

Hendricks,

(1972)

W.N.

3-F.

R.A_

Johnson,

37

L.J.

Oerzansky

and

38

C-Y.

Chang

J.A.

Macquin

A.f.Ch.E.J.

and

39

S. Srininasan

40

T-K.

42

P.L.T.

42

T.K_

Sherwood,

43

bl.N.

Gill

44

M.C.

Porter,

45

A,S,

Michaels,

46

If-F. Blatt,

and

Sherwood,

Press,

4.I.Ch.E.J_ and

F.A.

15 (1969)

!'illiams,

872-884.

Ind.

Eng.

Chem.

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276-279.

36

Fundam.

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1046-1054. 287-301.

I. Oresner,

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Chem-

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Cambridge, tlass. (1966) Chem.

Eng.

M.

Scher,

Tnd.

Eng.

Chem.

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24

Desalination

Brian,

Desalination

and

966-974.

A.1.Ch.E.J.

C. Tien,

4 (1965)

(79fQ)

Gill,

Guin,

P.L_T.

Brian,

20

Dravid,

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Ser.

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7 (1961)

Prod.

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U. Merten

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Progr.

Eng.

Osmosis.

Res.

64

Develop.

(19681

Michaefs

No.

and

25

(~~~g~

71.

61. 11

234-248.

(1972)

31-43.

L. Nelson,

Ilembrane

Science

and

Technology, Plenum Press, Kew York (1970) 47-97. 47

D.R.

48

A-A_

Kozinski

49

R.L.

Goldsmith,

Ind.

Eng.

50

J.U_

Carter

P.G.

Vewick,

frettin

purity

and and

znd

51

P.

and

De,jmek,

52

H.

53

blelinder,

A.R. Table

them.

D.G.

56

H, Lolachi,

H. Lolachi,

Thomas,

thesis,

tyngby and

of Paper

~~3~-1~~~.

1 (1971) product

113-120.

flux

presented

August

6th

21-25

(1978).

of macro-

(1975).

0.S.l;. Res. Chem.

Its

Eouipment

in ultrafiltration

Unrverslty

and

to the

Chemical

Czechoslovakia,

Dept.

507-522.

Rev. Ind.,

ProSr.

Rent

Technical

727

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Acrivos,

ibid.

Res.

Ind.

9 (1970)

!!.L. Griffith 0.S.M.

18 (1972)

Engineering,

Lund

correction,

55

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polarization

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Q (1979)

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orediction

Ph.D.

Tekn.lic.

Johnson

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of Chemical Praha,

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The

flow

Eng,

Concentration

and

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of Denmark, 54

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molecules,

Chem,

Lightfoo~,

E.N.

in ultrafiltration

International Design

Doshi,

M_R.

Dev.

and

Ertg, Cehm.

Fundam.

8

(lQ7(?) 359,

304. R.M.

Rept

Keller,

843,

U.S.

Cesalination Cleat

of

the

9 (1971) Interior

23. (1973)

_

100

EWTTHIASSOM

57

E . !4. Pitera

and

(1973)

52.

5g

E.A.G.

l-lamer,

59

E.A.C.

Hamer

J. Csurny, C.G.

S.L.

1970.

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van

and

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Food, Lai,

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P.M.

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the

and

I!.P!.

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T-J_

Kennedy,

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59

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67

T.J.

Sennedy,

68

\!.L. Thager,

P.L.

O-S.\!.

Symo.

on

2nd

I’.G.

the

Sisso~

aeriod 270,

l5/3 Oak

and 1968

Ridqe

(1973).

(1977)

Koning,

C.A.

Smolders

and

465-483. of milk

and

International

whey

b_v reverse

Congress

Bozeman, Cesalination

Gill, in

ftonge. 6-J.

(1973)

for

J.

University,

Ultrafilrration

12

OF

Encineerinn

(1979).

State

Delucia

Velden, 22

Il. Looez-Leiva,

2nd

Cr. (Eds.)p.

Concentration

27-31

!lontana

the

Philips,

ReDort

Tennessee

der

at

Develop.

(1969). at

H-0.

Johnson

Ridge,

R. de Boer,

Thesis,

J.S.

van

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Kraus,

Progress

and

Oak

Waal,

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osmosis,

Moore

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Des.

SIVIK

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K.A.

Biennial

G.E.

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N.P.M.

Jr,

Febr.

562-4,

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425,

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van

Ind,

3,

Flimi,

J.S.

J. Hiddink

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and

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l!estmoreland,

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J.

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U.S.

Osmosis,

Reverse

60

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AND

rotary

R.L.

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11 (1972) flow,

annular

I*lcCoy and

Yontana,

Merson,

lo!?-2@5.

Ph.!?. thesis,

Enn.

Chem.

Pro?.

El. Nerson

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29

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(1975)

a22-c26. 60_.

H.L.

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A.1.Ch.E.J. removal

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Ileetinq,

20,

No.

2 (1974)

in ultrafiltration.

!'ash. C.C.

E. !?t-ioli and

C-. Capobianco, (1977)

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C.

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Trans-

XATTHIXSSON

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85

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29

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71-go_ 91

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93

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29

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T.H.

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