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Micropolar medium in a funnel-shaped crusher

Fomicheva, Mariia; Vilchevskaya, Elena N.; Bessonov, Nikolay; MĂĽller, Wolfgang H.

In this paper, the solution to a coupled flow problem for a micropolar medium undergoing structural changes is presented. The structural changes occur because of a grinding of the medium in a funnel-shaped crusher. The standard macroscopic equations for mass and linear momentum are solved in combination with a balance equation for the microinertia tensor containing a production term. The constitutive equations of the medium describe a linear viscous material with a viscosity coefficient depending on the characteristic particle moment of inertia, the so-called microinertia. A coupled system of equations is presented and solved numerically in order to determine the distribution of the fields for velocity, pressure, viscosity coefficient, and microinertia in all points of the continuum. The numerical solution to this problem is found by using the implicit finite difference method and the upwind scheme.
Published in: Continuum Mechanics and Thermodynamics, 10.1007/s00161-021-00973-w, Springer Nature