Dense Suspension Flows: A Mathematical Model Consistent With Thermodynamics

Abstract

We address the flows of dense suspensions of particles within the framework of two-velocity continuum. Thermodynamics of such a continuum is developed by the method suggested in the papers of L. D. Landau and I. M. Khalatnikov. As an application, we consider the convective settling problem. We capture the Boycott effect and prove that the enhanced sedimentation occurs in a 10 tilted vessel due to vortices. We do not call on additional interphase forces like the Stokes drag, the virtual mass force, the Archimedes force, the Basset-Boussinesq force and etc. Instead, we apply a generalized Fick's law for the particle mass concentration flux vector.

Recursive Settling of Particles in Shear Thinning Polymer Solutions: Two Velocity Mathematical Model

“…A weak formulation of the problem and a detailed description of the algorithm are given in Ref. [ 10 ]. The ParaView open-source package visualization application is used to visualize the results.…”

“…Forces were even used that obviously depended on time and on prehistory, such as the Basset–Boussinesq force [ 27 ]. In our recent work [ 10 ], the Boycott effect was explained without the use of additional hydrodynamic forces, but only due to the gravitational component of the concentration flux in Fick’s law. As far as we know, the issue of particle settling in non-Newtonian fluids has not been considered theoretically and experimentally in the case of inclined vessels.…”

“…As a result, the entire suspension becomes a two-velocity continuum, with the fluid and the solid phases enjoying some rheological constitutive laws. Such a method was validated in the recent paper concerning the Boycott sedimentation effect, which stated that enhanced sedimentation occurs in a tilted vessel [ 10 ].…”

“…The principle goal of the present paper is to adjust the method of [ 10 ] for the description of particles settling in a polymer solution. To this end, particles are assumed to be suspended in a non-Newtonian power-law fluid, in contrast to [ 10 ], where such a fluid is considered to be Newtonian.…”

“…The principle goal of the present paper is to adjust the method of [ 10 ] for the description of particles settling in a polymer solution. To this end, particles are assumed to be suspended in a non-Newtonian power-law fluid, in contrast to [ 10 ], where such a fluid is considered to be Newtonian. One more rheological feature of this work is that the gravitational mobility in Fick’s law is chosen in such a way that the numerical results on sedimentation are consistent with experiments on particles settling in polymer solutions [ 4 ].…”