On the movement of two layers of viscous liquids on the outer surface of a horizontal rotating cylinder

The plane motion of thin layers of viscous immiscible liquids on the outer surface of a horizontal cylinder rotating at a constant angular velocity in a field of gravity and inertia is explored. In the case of sufficiently slow motion, neglecting the inertial terms of the Navier-Stokes equations, circumferential and radial velocity components were obtained, as well as an interrelated system of evolution equations for the inner and outer layers in a gravitational field. The problem of determining the type of surfaces of two layers in the case of unsteady motion of liquids on the outer surface of a rotating cylindrical shell is solved. (paper)