Exact solution of the problem of flow of a polymer solution in a plane channel

One‐dimensional flow of polymer solutions in a plane channel under the action of the pressure gradient has been considered. To describe the rheological properties of the solutions we have selected: 1) generalization of the Jeffreys phenomenological model with an objective time derivative Fabc with six arbitrary material constants; 2) the differential vector model proposed by Remmelgas, Harrison, and Leal and that is the approximation of the Doi–Edwards–Marrucci–Grizzuti model. Exact analytical solutions of the problem of flow in a plane channel have been obtained for them. In the two cases the problem can have both a unique solution and a nonunique solution. The velocity profiles are either smooth nearly parabolic or have weak tangential discontinuities. Criterial conditions for the appearance of ambiguous flow regimes have been obtained.