tailieunhanh - Generalized diffusion theory of hydrodynamical particle migration in suspensions part 1: the case of equal densities

This paper is concerned with using the simplest model from developed general theory for modeling of particle migration in suspensions- one of the most important and complicated aspects of particle-- liquid two- phase flows, that has been observed and studied by many authors. For this purpose it is considered the motion of Newtonian fluid- rotating rigid spherical particles two- phase continuum with specialized nonlinear constitutive equations, when the particle and fluid have equal densities. | T~J? chf Ccr hqc Journal of Mechanics, NCNST of Vietnam T. XIX, 1997, No 2 (9- 14) GENERALIZED DIFFUSION THEORY OF HYDRODYNAMICAL PARTICLE MIGRATION IN SUSPENSIONS Part 1: The case of equal densities NGUYEN VAN D!EP Instt."t-ute of Mechanz'cs, Hano1.' y,·etnam Abstract. The general continuum theory has been developed for two- phase flows of fluid with deformable particles, where the micro- deformation of particles and the relative motion between phases have been taken into account [1-3]. This paper is concerned with using the simplest model from developed general theory for modeling of particle migration in suspensions- one of the most important and complicated aspects of particle-- liquid two- phase flows, that has been observed and studied by many authors. For this purpose it is considered the motion of Newtonian fluid- rotating rigid spherical particles two- phase continuum with specialized nonlinear constitutive equations, when the particle and fluid have equal densities. The obtained equation system has used for studying quantitatively particle migration problem in the circular Couette flow. Introduction One of the most important and complicated aspects of particle- liquid two- phase flows is problem of particle migration. For example, many experiments show that for up- flow in a circular test section the bubbles tend to migrate toward the wall and thus the void fraction profile has a distinct peak near the wall. In contract, for down- How the bubble tend to migrate toward the center of the pipe [4, 5]. The particle migration is observed also in gas- solid particle fiow [6], and in concentrated suspensions [7, 8]. Several mechanisms have been proposed to explain theoretically the lateral migration phe~ nomena. For examples, the particle migration in two- phase flows explained by the lift force due to shear stress was analytically derived by Saffman [9] and the lift force due to particle rotation derived by Rubinow and Keller [10]. These forces are .