Filtration process of a nanofluid with particles size less than 100 nm through a porous medium is analyzed theoretically on the base of direct numerical simulation. Mathematical description of this process is fulfilled using the MIM model and Darcy's law, which are modified to take into account the nonlinear reverse reaction of sorption properties of the material on the intensity of pore velocity. A new parameter, which characterizes this nonlinearity, is introduced into the model. In fact, it represents the value of critical velocity for particle separation from the pore walls by the flow. The values of permeability and porosity decrease in dependence on time during the saturation of porous medium with nanoparticles. These parameters are related with each other by the Kozeny–Carman equation. The results of calculations show that the variation of the critical velocity for particle separation significantly affects on the dynamics of redistribution of the mobile and immobile impurity in porous material.
Numerical Simulation of Deformable Particle Behavior at Crossflow Filtration Process