42 L. Palacio et al. Journal of Membrane Science 222 2003 41–51
has demonstrated that this fouling is typically caused by the deposition of large protein aggregates on the
membrane surface [7–9]
. However, fundamental stud- ies of membrane fouling have almost always been
limited to solutions of a single protein. These results are very difficult to apply to the microfiltration of
many food products e.g. whey, beverages e.g. beer and wine, and bioprocessing solutions e.g. harvested
cell culture fluid, all of which contain a complex mixture of a wide range of protein molecules.
Güell and Davis [10]
have performed one of the only fundamental studies of fouling during microfil-
tration of protein mixtures. Flux decline data were ob- tained with bovine serum albumin BSA, lysozyme,
and ovalbumin, both alone and in binary and ternary mixtures. Fouling by BSA or lysozyme alone was
dominated by pore blockage internal fouling, while ovalbumin showed a transition between pore blockage
and cake filtration. Ovalbumin showed the greatest flux decline, which was attributed to the greater number
of large aggregates of this protein present in solution. Protein mixtures containing ovalbumin showed a flux
decline similar to that obtained with ovalbumin alone, suggesting that the ovalbumin aggregates dominated
the fouling behavior. The flux decline with mixtures of BSA and lysozyme was mid-way between the fouling
seen with the individual proteins. In contrast, the flux decline for mixtures of ovalbumin and lysozyme was
greater than that observed with either of the pure pro- teins. No quantitative analysis was provided for any
of these observations.
Ho and Zydney [11]
, have recently developed a combined pore blockage and cake filtration model for
protein fouling. This model was shown to provide an excellent fit of flux decline data for bovine serum
albumin [11]
and for a series of four other model proteins
[12] . The objective of this work is to study
the fouling behavior of several well-defined protein mixtures, using this combined pore blockage—cake
filtration model to obtain fundamental insights into the nature of the protein—protein interactions and
their effect on membrane fouling.
2. Theory
The initial flux decline in this model arises from blockage of the membrane pores by physical deposi-
tion of large protein aggregates on the membrane sur- face:
dA
open
dt = −
αQ
open
C
b
1 where A
open
is the area of the open unblocked pores, Q
open
the volumetric flow rate through the open pores, C
b
the bulk protein concentration, and α is equal to the pore area blocked per unit mass of protein con-
vected to the membrane surface. Unlike most prior pore blockage models, these aggregates are assumed
to allow some fluid flow through the blocked pores. The resistance of the protein layer R
p
continues to increase with time as additional protein is convected
to the membrane surface: dR
p
dt =
f
′
R
′
J
blocked
C
b
2 where f
′
is the fraction of protein in the bulk solution that contributes to the growth of the existing deposit, R
′
the specific protein layer resistance, and J
blocked
is the filtrate flux through the previously covered blocked
pores on the membrane surface. The model explicitly accounts for the inhomogeneity in the resistance of
the protein layer that arises because the deposit only grows over the time interval t−t
p
, where t
p
is the time at which that particular region was first covered by a
protein aggregate. R
p
can be evaluated by integration of
Eq. 2 with:
J
blocked
= P
µR
m
+ R
p
3 to give
[11] :
R
p
= R
m
+ R
p0
1 + 2f
′
R
′
PC
b
µR
m
+ R
p0 2
t − t
p
− R
m
4 where
P is the transmembrane pressure, µ the so-
lution viscosity, R
m
the resistance of the clean mem- brane, and R
p0
is the resistance of the first layer of the protein deposit i.e. the initial resistance of the
protein aggregate. The filtrate flow rate through the fouled membrane at any given filtration time can be
expressed as the sum of the flow rates through the open and blocked pores
[11] :
L. Palacio et al. Journal of Membrane Science 222 2003 41–51 43
Q = Q exp
− α
PC
b
µR
m
t +
t
α PC
b
µR
m
+ R
p
exp −α
PC
b
µR
m
t
p
dt
p
5 with R
p
evaluated from Eq. 4
. The integration over t
p
accounts for the time dependent blockage of the membrane surface.
Although Eq. 5
is relatively easy to evaluate nu- merically, Ho and Zydney
[11] have also developed a
much simpler analytical solution for the filtrate flow rate by assuming that the resistance of the protein layer
over the fouled region of the membrane is uniform at its maximum value given by
Eq. 4 with t
p
= 0.
Using this assumption, the coefficient multiplying the exponential in the convolution integral in
Eq. 5 be-
comes a constant and can be pulled outside of the in- tegral to give:
Q = Q exp
− α
PC
b
µR
m
t +
R
m
R
m
+ R
p
1 − exp −
α PC
b
µR
m
t 6
The first term in Eqs. 5 and 6
represents the flow rate through the open pores and is equivalent to clas-
sical pore blockage model. The second term describes the flow through the blocked pores. The flow rate is
thus described by three key parameters: a pore block- age parameter α, the ratio of the initial resistance
of the protein deposit to the membrane resistance β = R
p0
R
m
, and a parameter describing the cake growth γ = 2f
′
R
′
R
m
+ R
p0
. The best fit values of the parameters α, β, and γ
for the different protein mixtures were determined by minimizing the sum of the squared residuals between
the filtrate flow rate data and the model calculations Eq. 5
using the method of steepest descent.
Table 1 Physical characteristics of proteins
Protein Sigma catalog number
Source Molecular weight kDa ku
a
Isoelectric pH Albumin BSA
A7906 Bovine serum
67 4.7
Lysozyme A6876
Chicken egg 14
11.0 Pepsin
P6887 Pig stomach
36 1.0
a
1 kDa = 1 ku.
3. Materials and methods
