Hydrodynamics of Flow in a Flat Slot with Boundary Change of Viscosity

Abstract

The laminar flow of viscous incompressible fluid in a flat slot is considered with allowance for the boundary change of viscosity near a solid surface. The model of the stepwise distribution of the dynamic viscosity over the cross section of the channel with its abrupt increase near the slot walls was adopted. In the general case, the different viscosity jumps near the solid surface are introduced into consideration. Also, the dimensions of the boundary layers, where the change of viscosity appears, are considered different. For the accepted dynamic viscosity distribution, integration of the equation for laminar fluid motion was performed. The dependences for calculating the velocity profile in a flat slot are obtained. The researches on the effect of viscosity jump on flow velocity have been conducted. The examples of calculating the velocity distribution along the height of a flat slot are presented. The flows with symmetric and asymmetrical distribution of dynamic viscosity are considered. Based on the obtained velocity distribution, dependences for calculating the flow rate in the flat slot were established. The researches of the influence on the flow rate in a slot of the parameters for the distribution of dynamic viscosity along the cross section of the channel have been conducted. The received result analysis showed that the boundary increase of the dynamic viscosity unambiguously leads to the drop of the throughflow capacity for the flow section. The boundaries of applicability of the traditional approach to calculating the laminar flow of viscous fluid in a flat slot are estimated.