On hyperbolicity and solution properties of the continual models of micro/nanoparticle aggregation and sedimentation in concentrated suspensions

Abstract

In continual mechanics sedimentation of aggregating particles in concentrated suspensions are determined by the mass and momentum conservation laws for each component of the suspension. The resulting quasilinear system of differential equations governing the flow could be hyperbolic, strongly strictly or weakly hyperbolic depending on the model accepted. The type and Eigenvalues of the matrix influence the characteristics of the pattern formation during the sedimentation that is essential for the model application in modern medical, microbiological and nanofluidic technologies. In this paper the hyperbolicity of the three-phase model of aggregation and sedimentation of micro/nanoparticles is studied.

A study of a quasilinear model of the particles of a suspension that are aggregated and settled in an inhomogeneous field

“…For the case of the aggregating particles in inclined tubes in an inhomogeneous external field, it was shown that other variants of the arrangement of families of characteristics can be added to the possible patterns of characteristics (Figs. 1a-d), which is also confirmed by numerical calculations based on the initial hyperbolic system of the continuum model [8,20] by the finite volume method [21]. Since the settling of the particles in inclined tubes at certain angles of inclination leads to a significant acceleration of settling and separation of mixtures (Boycotte effect) and is widely used in oil and gas industry [22], biological [14,23,24] and nanotechnology [3,5], the study of such sort of problems is of interest not only for the theory of hyperbolic differential equations, but also for many applied problems.…”