[Zurück]

W. Schneider:
"On basic equations and kinematic-wave theory of separation processes in suspensions with gravity, centrifugal and Coriolis forces";
Acta Mechanica, 228 (2017), 16 S.

Neglecting inertial and viscosity effects in the bulk flow is a common assumption in the analysis
of separation processes in suspensions under the action of gravity or centrifugal and Coriolis forces. While
there is a number of examples of particular solutions, the general form of the basic equations for three space
dimensions, together with the appropriate boundary and initial conditions, is still uncertain and, with regard to
certain aspects, even controversial. An essential point is a proper choice of the variables. Here it is proposed to
introduce the mass density of the mixture, the mean mass velocity of the mixture and the total volume flux as a
set of dependent variables. After some manipulations, a complete set of basic equations is obtained. It consists
of two continuity equations, a generalized drift-flux relation, and two linearly independent components of a
vector equation describing the total body force as irrotational. Then, by eliminating the mean mass velocity of
themixture from the set of unknowns, a generalized kinematic-wave equation is derived. It describes kinematic
waves that are embedded in a bulk flow that may be one-, two- or three-dimensional. Concerning boundary
conditions at solid walls, one has to ascertain whether the total body force at the wall points into the suspension
or out of it. In the former case, a thin boundary layer of clear liquid is formed at the wall, whereas in the latter
case a thin sediment layer may either stick at the wall or slide along it. Each of those three possibilities leads
to a particular boundary condition for the bulk flow in terms of the dependent variables. In addition, initial
conditions and kinematic shock relations are briefly discussed. Finally, the application of the kinematic-wave
theory to the settling process in rotating tubes is outlined.

This paper is dedicated to the memory of Franz Ziegler

kinematic-wave theory

http://dx.doi.org/10.1007/s00707-017-1998-x

http://publik.tuwien.ac.at/files/publik_267883.pdf

Projektleitung Wilhelm Schneider:
AIC Androsch International Management Consulting GmbH Forschung auf dem Fachgebiet Strömungsmechanik und Thermodynamik