Modeling of the stage of development of the flow of a viscoplastic medium along an inclined plane

Andreichenko Dmitry Konstantinovich, Safronchik Maria Ilyinichna

The development of the flow of a viscoplastic medium along an inclined plane under the influence of gravity from a state of rest is considered. The flow zone grows gradually, its boundary is unknown in advance and is determined in the process of solving the problem. The angle of inclination is chosen in such a way that the so-called "slipping" effect along the solid wall appears over time. The problem is posed within the framework of the five – parameter Slibar-Paslay model, which allows taking into account the difference in the behavior of the material during loading and unloading, and the possible "slipping" of the material along a solid wall is taken into account using a model of a smooth transition from sticking to slipping similar to the hypothesis of prof.N. P. Petrov for a viscous liquid. The solution of the problem is constructed using the Galerkin projection method using orthogonal Chebyshev polynomials of the first kind as basis functions.

Keywords:unsteady flow; mathematical and computer modeling; non-Newtonian fluids; viscoplastic materials; multiphase flows.