A STEADY FLOW OF A VISCOUS MULTI-LAYER FLUID IN A TOROIDAL TUBE WITH SMALL RADIUS

The steady flow of a multi-layer viscous incompressible fluid is considered in a toroidal tube. Each layer has a viscosity coefficient of its own. The velocity vector has one nonzero circular component not depending on the circular coordinate. The inertial terms in the Navier-Stokes equations are neglected or, in other words, the system of Stokes equations is considered under the following boundary contact-conditions: the nonslip conditions are given on the toroidal surface, hydrostatic pressure values are given at the tube ends, and the contact conditions are given on the interface between the layers. An inhomogeneous equation is obtained for the rate component and its analytic solution is found. The results obtained are used to study the blood flow in narrow curvilinear vessels, to determine the blood flow parameters, the distribution of erythrocytes over the vessel cross-section and also to determine the hydrodynamic resistance to the flow.