Cross Flow Filtration of a Suspension with Arbitrary Concentration Profile in a Microchannel

Microfluidic filtration is applicable to process intensification and other areas where in-process volumes are to be minimized. However, numerous complications are encountered in attempting cross flow filtration of suspensions flowing in thin layers over high-permeability filters. A model for cross flow filtration of a suspension with an arbitrary inlet concentration profile in a microchannel will be presented. Unlike previous authors who have treated only a thin boundary layer at the filter surface, we apply the convective diffusion equation to the entire fluid domain. The steady state solution is shown to depend on an appropriately defined Péclet number and a dimensionless filter length. These parameters constrain when steady-state operation is possible and provide the basis for optimal design.