Non-viscometric flows of viscoelastic fluids in round tubes driven by transversal boundary waves

The unsteady transversal flow field in the tube flow of a memory integral fluid of order type driven by rotational boundary waves is investigated. A perturbation in terms of the amplitude of the sinusoidal boundary waves is used. Qualitative conclusions are independent of the explicit forms of the constitutive functions. Quantitative results are obtained by assuming Maxwell type of behavior for the latter. It is shown that transversal steady flows is a possibility if several rotational waves with frequencies in a certain ratio are imposed on the boundary. As a result helical steady flows may be possible in the longitudinal direction in a round tube. A parametrical study of the oscillating transversal field is presented for highly elastic and shear thinning liquids.