Simulation of an unstable delayed flow of a viscoplastic fluid along an inclined plane, taking into account the effect of wall sliding

Safronchik Mariya Ilinichna, Andreichenko Dmitry Konstantinovich

The stages of unsteady flow of a "retarded" viscoplastic medium along an inclined plane under the influence of gravity are modeled, taking into account the effect of slippage along a solid wall. The boundary of the flow zone at the stages of development and attenuation of the flow is not known in advance and is determined in the process of solving the problem. The angle of inclination is chosen in such a way that, over time, the so-called "slip" effect along the solid wall appears. The problem is posed within the framework of the five-parameter Slibar-Paslay model, which makes it possible to take into account the difference in the behavior of the material under loading and unloading. The possible "slip" of the material along the 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 the basis functions.

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