Modeling cross-flow ultrafiltration of permeable particle dispersions

Cross-flow ultrafiltration is a pressure-driven separation and enrichment process of small colloidal particles where a colloidal feed dispersion is continuously pumped through a membrane pipe permeable to the solvent only. We present a semi-analytic modified boundary layer approximation (mBLA) metho...

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Bibliographic Details
Published in:The Journal of chemical physics 2020-11, Vol.153 (20), p.204110-204110
Main Authors: Park, Gun Woo, Nägele, Gerhard
Format: Article
Language:English
Subjects:
Advection-diffusion equation
Approximation
Axial flow
Boundary layers
Colloiding
Computational fluid dynamics
Concentration gradient
Cross flow
Diffusion coefficient
Dispersions
Finite element method
Hollow fiber membranes
Mathematical analysis
Microgels
Permeability
Physics
Reference systems
Similarity solutions
Solvents
Stokes flow
Ultrafiltration
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Summary:Cross-flow ultrafiltration is a pressure-driven separation and enrichment process of small colloidal particles where a colloidal feed dispersion is continuously pumped through a membrane pipe permeable to the solvent only. We present a semi-analytic modified boundary layer approximation (mBLA) method for calculating the inhomogeneous concentration-polarization (CP) layer of particles near the membrane and the dispersion flow in a cross-flow filtration setup with a hollow fiber membrane. Conditions are established for which unwarranted axial flow and permeate flow reversal are excluded, and non-monotonic CP profiles are observed. The permeate flux is linked to the particle concentration on the membrane wall using the Darcy–Starling expression invoking axially varying osmotic and trans-membrane pressures. Results are discussed for dispersions of hard spheres serving as a reference system and for solvent-permeable particles mimicking non-ionic microgels. Accurate analytic expressions are employed for the concentration and solvent permeability dependent dispersion viscosity and gradient diffusion coefficient entering into the effective Stokes flow and advection–diffusion equations. We show that the mBLA concentration and flow profiles are in quantitative agreement with results by a finite element method. The mBLA results are compared with predictions by an earlier CP layer similarity solution, showing the higher precision of the former method.
ISSN:0021-9606
1089-7690
DOI:10.1063/5.0020986