INFLUENCE OF VIBRATION ON POISEUILLE FLOW OF A NON-NEWTONIAN FLUID .2.

An incompressible, isotropic, non-Newtonian fluid undergoes plane Poiseuille flow between two parallel plates, or through a pipe of circular cross-section, as a result of a uniform time-independent pressure gradient. The effect is studied of superposed vibrations of the boundaries, which are not necessarily purely sinusoidal, on the mean rate of discharge of the fluid. The calculations are carried out in detail for a particular constitutive equation of the Rivlin-Ericksen type, with the assumption that the fluid is slightly non-Newtonian. It is seen that in addition to a change in the mean rate of discharge which arises as an interaction of the vibration with the pressure gradient, there may also occur a change in the mean rate of discharge which arises from the interaction of the harmonic components of the vibration and may be independent of the pressure gradient. © 1979 Dr. Dietrich Steinkopff Verlag.