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.