  Membrane ultrafiltration (UF) is a pressure driven process allowing for the
separation and enrichment of protein solutions and dispersions of nanosized
microgel particles. The permeate flux and the near-membrane
concentration-polarization (CP) layer in this process is determined by
advective-diffusive dispersion transport and the interplay of applied and
osmotic transmembrane pressure contributions. The UF performance is thus
strongly dependent on the membrane properties, the hydrodynamic structure of
the Brownian particles, their direct and hydrodynamic interactions, and the
boundary conditions. We present a macroscopic description of cross-flow UF of
non-ionic microgels modeled as solvent-permeable spheres. Our filtration model
involves recently derived semi-analytic expressions for the
concentration-dependent collective diffusion coefficient and viscosity of
permeable particle dispersions [Riest et al., Soft Matter, 2015, 11, 2821].
These expressions have been well tested against computer simulation and
experimental results. We analyze the CP layer properties and the permeate flux
at different operating conditions and discuss various filtration process
efficiency and cost indicators. Our results show that the proper specification
of the concentration-dependent transport coefficients is important for reliable
filtration process predictions. We also show that the solvent permeability of
microgels is an essential ingredient to the UF modeling. The particle
permeability lowers the particle concentration at the membrane surface, thus
increasing the permeate flux.
