Oscillatory Behaviour in Statically Stressed Viscoelastic Inflation Flow
AbstractThe influence of fluid elasticity is investigated by examining the biaxial inflation of a spherical shell of a viscoelastic fluid subject to a constant and a linearly ramped change of pressure. In contrast to the monotonic growth of a Newtonian fluid, that of a viscoelastic fluid is found to be oscillatory under conditions of large Deborah number, for a thick shell, and for sudden inception. Although this type of non‐monotonic behaviour has been predicted in other similar flow configurations of viscoelastic fluids, there is no evidence of it occurring experimentally. The current calculations, in the case of a bubble growing in an infinite viscoelastic medium, show that, if a ramped rather than a sudden pressure is applied initially, the amplitude of the oscillations decreases as the rate of pressure decreases. This may explain why oscillations have not been observed in experiment, since a sudden initial driving pressure is difficult to realize.