The Stokes–Brinkman Flow Field and Diffusion Deposition of Nanoparticles in a Layer of Hollow Permeable Grains

Abstract

The diffusion deposition of point particles from a Stokes–Brinkman transverse stationary flow in a model monolayer membrane composed of contacting spherical hollow grains (capsules) with porous permeable shells formed from nanoparticles, is calculated. Monolayers with square and hexagonal packings of the grains are considered. Approximation equations are constructed for the dependences of grain drag force on shell thickness, Brinkman permeability parameter S, and internal shell radius ξ. Efficiencies of point particle collection on the grains are calculated as depending on the Peclet number, S, and ξ, and it is shown that layers of hollow permeable grains possess the highest filtration performance criterion among layers of impermeable and permeable uniform porous grains provided that the zero-concentration boundary condition is fulfilled at the outer radius of the grain.