Exact Poiseuil-type solutions for flows of viscoelastic polymer fluid through a circular pipe

Resolving equations describing stationary flows of an incompressible viscoelastic polymer fluid through a circular pipe are derived on the basis of the rheological mesoscopic Pokrovskii–Vinogradov model. Exact solutions of the equations are obtained, and restrictions on the values of the rheological parameters that ensure their existence are formulated. These results enable one to constructively describe the destruction of Poiseuille-type laminar flow. The size and orientation of the macromolecules of the polymer fluid play a key role in the mechanics of this process. liquids. The mathematical description of the process uses the singular points of the solutions.