ISSN 0015-4628, Fluid Dynamics, 2018, Vol. 53, No. 2, pp. 255–269. c  Pleiades Publishing, Ltd., 2018. Original Russian Text c  A.A. Gavrilov, A.V. Shebelev, 2018, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2018, No. 2, pp. 84–98. Single-Fluid Model of a Mixture for Laminar Flows of Highly Concentrated Suspensions A. A. Gavrilov 1* and A. V. Shebelev 2** 1 Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia 2 Siberian Federal University, Krasnoyarsk, Russia Received January 27, 2017 Abstract—A model of laminar flow of a highly concentrated suspension is proposed. The model includes the equation of motion for the mixture as a whole and the transport equation for the particle concentration, taking into account a phase slip velocity. The suspension is treated as a Newtonian fluid with an effective viscosity depending on the local particle concentration. The pressure of the solid phase induced by particle-particle interactions and the hydrodynamic drag force with account of the hindering effect are described using empirical formulas. The partial-slip boundary condition for the mixture velocity on the wall models the formation of a slip layer near the wall. The model is validated against experimental data for rotational Couette flow, a plane-channel flow with neutrally buoyant particles, and a fully developed flow with heavy particles in a horizontal pipe. Based on the comparison with the experimental data, it is shown that the model predicts well the dependence of the pressure difference on the mixture velocity and satisfactorily describes the dependence of the delivered particle concentration on the flow velocity. DOI: 10.1134/S0015462818020064 Channel flows of a “liquid-solid particle” mixture are commonly encountered in engineering practice in many branches of industry. At low flow velocities in horizontal channels, the particles are deposited on the bottom wall, forming a dense layer of particles. Laminar flows of mixtures, which occur at low velocities and often with the formation of a layer of settled particles, have not been well understood. In laminar pipe flows of suspensions, an effective resuspension of particles is observed, caused by a transverse migration of particles (see, for instance, the review [1]). In a shear flow at small but finite particle Reynolds numbers, a slow migration of single particles from the wall is attributable to the onset of the Saffman lift force exerted on a spherical particle by the shear flow [2, 3]. In dense suspensions, the effect of particle migration in the direction of reduced shear rate and particle concentration is detected in [4]. The particle migration effect explains the particle resuspension phenomenon observed when a shear stress is applied to a particle layer, with the subsequent removal of the particles in the carrier flow and erosion of the layer. The migration of particles caused by the particle-particle interactions was first described for non- colloidal suspensions in paper [5], devoted to experimental studies of long-term transient processes in a Couette viscometer. Then, the effect of particle migration induced by shear was confirmed experimentally in a plane-channel [6] and a circular-pipe flow [7, 8]. The first closed mathematical model of suspension flow with account of the particle migration effect, called the diffusion model, was proposed in [9]. The model describes the appearance of a particle drift in a shear flow in the direction of decrease in the effective viscosity of the mixture and decrease in the shear rate. In a recent paper [10], a regularization of the diffusion model was proposed to resolve the singularities in the region with a vanishingly small shear rate, and a parametric study of suspension flow in an inclined plane channel was performed, but no comparison with experiment was provided. The second class of empirical models uses the hypothesis of the onset of particle migration under the action of nonuniform normal stresses in the solid phase, with the isotropic part of these stresses, called the particle pressure, being associated with the energy of particle chaotic velocities. The Suspension * E-mail: gavand@yandex.ru. ** E-mail: aleksandr-shebelev@mail.ru. 255