ABSTRACT Electret monolith filters have the advantage of low pressure drop and high filtration efficiency. In such filters, the filtration of submicron aerosol particles occurs as air passes through millions of microchannels. This article investigates the flow and filtration mechanisms in a representative rectangular microchannel of an electret monolith filter. An improved incompressible lattice Boltzmann method with Bhatnagar–Gross–Krook (traditionally shortened as LBGK) and lattice velocity D3Q15 model is employed to simulate no-slip and slip flows in the rectangular microchannels of a monolith filter. We considered mono-disperse submicron particles and one-way coupling (particle motion was affected by the flow, but the presence of particles did not affect the flow). Based on flow computations, the effects of key dimensionless parameters (Reynolds number, Knudsen number, Stokes number and the dimensionless length of the channel) on the total capture efficiency of mono-disperse submicron particles were investigated. Our results indicate that the optimal monolith filter should be characterized by a Knudsen number between 0.022 and 0.044, and that the dimensionless length of the channel should be between 4 and 8. Copyright © 2016 American Association for Aerosol Research