A direct theory of viscous fluid flow in channels
In this paper the authors continue their studies of fluid flow in channels using their theory of directed fluid sheets. To do this it is necessary to develop a procedure for expressing the conservation laws arising in the theory in an Eulerian form. This done they obtain local equations in Eulerian form by postulating two-dimensional conservation laws for a Cosserat surface of order K, that is one comprising a material surface with K directors. The theory is worked out for application to incompressible, linear viscous fluid flow in a channel whose principal boundaries have given velocities. Examples considered include effects of a time-dependent pressure gradient on flow in a channel with fixed boundaries symmetric about a middle plane, aspects of lubrication theory of flow in a general channel when one channel boundary is a fixed plane and the other moves with constant velocity and flow of a layer of viscous fluid over a fixed boundary.
scientific article; zbMATH DE number 3945655