Rigid bodies formulation arising from visco-plastic flows with some numerical illustrations

This work reveals a weak formulation of rigid bodies motion arising from free boundaries evolution in visco-plastic flows. This phenomena could modelize the cooling of blood-plasma in thin arteries. The fluid motion is governed by the incompressible Norton-Hoff operator in the non-cylindrical quasi-static case coupled with the time-dependent convection system. We supply the existence of an interface between two non-miscible fluids by the use of the non-smooth evolution theory. We prove that the fluid's flow is transformed to a rigid body when its consistency is very large. The established result is, in some sense, an extension of the existing formulations. We supply some numerical illustrations to validate our results.