Обоснование математической модели многослойного сдвигового течения бетонной смеси по наклонной поверхности откоса канала

Abstract

In assessing the hydrodynamic parameters of concrete mixtures placed in monolithic channel linings, the most important point is the development of mathematical models that describe the processes of concrete mixture slippage, taking into account the dynamics of speed reduction and increase in the viscosity of the concrete mixture over time. The main regularities of the hydrodynamic multilayer shear flow of a concrete mixture on the surface of a flat channel slope, where a multilayer plane-parallel viscous flow moves under the action of gravity, are investigated. The boundary value problem of a two-layer flow of a concrete mixture is solved, a system of two layers of viscous incompressible liquids is considered with the properties of each, respectively, the thickness of the bottom and upper layers, taking into account the sliding velocity of particles of a viscous liquid located one above the other. The obtained analytical solution of the problem in the stationary regime of a two-layer shear flow of two different immiscible viscous fluids with different properties makes it possible to formulate the main laws of such flows and describe the processes of sliding of a multilayer concrete mixture, taking into account the dynamics of speed reduction and increase in the viscosity of the concrete mixture over time. A mathematical model has been developed where the dynamic and kinematic structures of a multilayer shear flow in both viscous layers are presented separately.