Modeling cross-flow ultrafiltration of permeable particle dispersions

Area of Science:

• Colloid and Surface Science
• Chemical Engineering
• Fluid Dynamics

Background:

• Cross-flow ultrafiltration separates particles using membranes, but concentration polarization (CP) complicates the process.
• Accurate modeling of CP is crucial for optimizing filtration efficiency and understanding particle behavior near membranes.

Purpose of the Study:

• To develop and validate a semi-analytic modified boundary layer approximation (mBLA) method for calculating inhomogeneous CP layers.
• To analyze dispersion flow and permeate flux under conditions excluding axial flow and permeate flow reversal.
• To compare mBLA results with finite element methods and previous models.

Main Methods:

• Developed a semi-analytic mBLA method for cross-flow ultrafiltration with hollow fiber membranes.
• Incorporated accurate analytic expressions for concentration and solvent permeability-dependent dispersion viscosity and diffusion.
• Utilized the Darcy-Starling expression to link permeate flux to particle concentration and pressure gradients.

Main Results:

• The mBLA method accurately predicts inhomogeneous concentration polarization (CP) profiles, including non-monotonic ones.
• Quantitative agreement was achieved between mBLA and finite element method results for concentration and flow profiles.
• The mBLA method demonstrated higher precision compared to earlier CP layer similarity solutions.

Conclusions:

• The mBLA method provides a precise and efficient tool for analyzing concentration polarization in cross-flow ultrafiltration.
• The study establishes conditions for excluding unwanted flow phenomena and observes complex CP behaviors.
• Results are validated for hard sphere and microgel-like particle systems, showing broad applicability.