Pressure laminar flow of a Brownian suspension in a flat channel

Based on two-fluid concepts of the hydrodynamics of heterogeneous media, liquid (gas)-solid particles without phase transitions and in the absence of mass forces with the Newtonian rheological law of continuous incompressible components, a model of pressure laminar flow of a Brownian suspension is proposed, taking into account the pressure of particles in the equation for the dispersion phase. The pressure of particles is estimated through their energy expended to maintain the stability of the homogeneity of the suspension. The procedure for linearizing the pressure gradient in the dispersed phase was carried out with the introduction of a parameter indicating the existence of a transverse coordinate in which the phase velocities are equal. A system of model differential equations with boundary conditions for ``sticking'' of phases to the channel walls and axial symmetry of the velocity field is formulated and analytically solved in a 2-D geometric format, assuming unidirectional suspension flow in a flat horizontal channel. It has been established that an increase in the flow velocity leads to a greater advance of the particle velocity near the wall and a greater lag in the flow core, and the maximum phase velocity on the channel axis is greater than the velocity of the liquid without a dispersive phase. A comparative analysis of the results of calculating the resistance coefficient with known experimental data confirmed the correctness of the proposed model and confirmed the decrease in the resistance to flow of Brownian suspensions compared to a homogeneous liquid medium.