THE FLOW OF A LIQUID-FILM ON THE INSIDE OF A ROTATING CYLINDER, AND SOME RELATED PROBLEMS

A liquid film flows on the inner surface of a rotating horizontal cyli nder. The simplest lubrication model assumes a force balance between v iscosity and the streamwise component of gravity, and the equation for the film thickness admits a continuous solution only when the average thickness is less than a certain critical value. Above this value, a discontinuous solution is possible but the details are not accessible by means of the simple theory. This behavior can be traced to the grad ual periodic variation of the streamwise component of gravity in the s treamwise direction. We consider also two related problems in which th is variation occurs more or less abruptly: (i) when the moving wall co mprises two straight segments inclined at different angles, and (ii) w hen the dragged film emerges through the free surface of a second, ove rlying liquid. These problems are approached by introducing a smoothin g parameter, namely surface tension, and solving a suitable initial va lue problem. We use the method of lines for this purpose because of th e availability of robust ODE software which can exploit the structure of the problem; however, the periodic conditions of the cylinder probl em necessitate a special approach to the discretization. (C) 1997 Amer ican Institute of Physics.