A multiscale model for particle filtration
Particle filtration using porous membranes is a well-studied industrial process with multiple important applications in the pharmaceutical and biotechnology spaces. As filtration occurs, particles deposit in pores, which causes the filter to clog, resulting in membrane-downtime for cleaning or replacement, which can be expensive.
Experimental observations of the particle-pore interactions that lead to clogging are difficult and destructive, while mathematical approaches that focus on detailed models of the microscale are often too computationally expensive for filter-scale experiments, since membranes consist of billions of continuous, interconnected fibrils.
In this talk, we develop a multiscale model for filtration that couples a dynamical network system on the microscale with a macroscale PDE system. We construct a discrete version of the usual method of multiple scales, and use this to homogenise the problem of flow and deposition of particles through an arbitrarily-connected periodic network of channels, which models the pores in the filtration medium. The result is an effective system that consists of Darcy’s equation coupled with an advection-reaction equation. Microscopic network information enters via the permeability and the deposition rate, which are parameters of this system. These parameters are given in terms of the channel conductances via solution of a simple, low dimensional, linear algebraic problem, thus offering the potential for significantly decreased computational complexity compared to standard approaches.