Kinematics of Bulkley–Herschel fluid flow with a free surface during the filling of a channel

The non-Newtonian fluid flow with a free surface occurring during the filling of a plane channel in the gravity field is modeled. The mathematical formulation of the problem using the rheological Bulkley–Herschel model is presented. A numerical finite-difference algorithm for solving this problem is developed. A parametric investigation of the main characteristics of the process as functions of the control parameters is performed. The effect of the rheological parameters of the fluid on the distribution of the quasisolid motion zones is demonstrated.