  This paper develops a modified version of the Boltzmann equation for
micro-scale particulate flow with capture and diffusion that describes the
colloidal-suspension-nano transport in porous media. An equivalent sink term is
introduced into the kinetic equation instead of non-zero initial data,
resulting in the solution of an operator equation in the Fourier space and an
exact homogenization. The upper scale equation is obtained in closed form
together with explicit formulae for the large-scale model coefficients in terms
of the micro-scale parameters. The upscaling reveals the delay in particle
transport if compared with the carrier water velocity, which is a collective
effect of the particle capture and diffusion. The derived governing equation
generalizes the current models for suspension-colloidal-nano transport in
porous media.
