Bioprocess Engineering

, Volume 15, Issue 2, pp 99–104 | Cite as

Multistage affinity cross-flow filtration: mathematical modelling and analysis

  • X. -Y. Dong
  • L. -Y. Li
  • Y. Sun


A multistage affinity cross-flow filtration (mACFF) process for protein purification is proposed. The process is mathematically modelled taking into account a case of rapid equilibrium binding of a target protein to its macroligand. The process performance, i.e., dimensionless breakthrough volume (Q b + )and recovery yield (REC) to obtain a desired purity is analysed by computer simulations. The results indicate that Q b + increases with the increase of stage number (n) due to the increase of affinity binding efficiency. In addition, REC also increases with the increase of n, especially for lower affinity systems, even though the feed loading is the same as the corresponding breakthrough volume that increases with n. Thus both feed loading and recovery yield can be enhanced by raising the stage number. Incompletely permeable membranes reject the target and contaminant proteins. So they delay the appearance of the breakthrough point and compromise the contaminant washing efficiency. Hence although Q b + increases with the increase of membrane rejection coefficient (R), REC decreases when the feed loading equals that of Q b + . However, when the feed loading is kept unchanged and equals Q b + at R=0, REC does not decrease, but slightly increases with the increase of R. This result indicates that incompletely permeable membranes may also be employed for the mACFF process. In general, the model gives a predictive evaluation of the mACFF process successfully.


Waste Water Affinity Binding Permeable Membrane Process Performance Protein Purification 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

C mol/l

contaminant concentration

F l/min

flow rate


macroligand volume fraction


index for stage number


dissociation constant


number of stages

P %


Q 1

feeding or washing volume

q mol/l

binding density


binding capacity


membrane rejection coefficient


recovery yield

T mol/l

target protein concentration

t min


V 1

sum of contactor volumes


volume of the jth stage contactor

Subscript and Superscript




contaminant proteins


feeding step


feeding broth into the 1st stage


the jth contactor


out of contactor (filtrate)


target protein


washing step


dimensionless quantity


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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • X. -Y. Dong
    • 1
  • L. -Y. Li
    • 1
  • Y. Sun
    • 1
  1. 1.Department of Chemical Engineering and Research Center for BiotechnologyTianjin UniversityTianjinP.R. China

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