(318c) Rayleigh-Taylor Waves in Viscoelastic Fluids- an Unintuitive Result

An unintuitive result is obtained when the Rayleigh-Taylor (R-T) instability of a viscoelastic fluid overlying a passive gas is considered. Unlike the case of a non-elastic fluid it is shown that the instability need not lead to an overturning of the interface. Saturated waves can be obtained if the shear modulus is within practical values. Even more interesting is that the instability leads to such saturated waves when the side walls are far apart but leads to overturning if the walls are closely spaced and are of the order of the capillary scale. This theoretical result has experimental evidence and is shown by weak nonlinear analysis. If the special case of an infinitely deep viscoelastic layer is considered, a simple expression is obtained from which the transition between steady saturated waves and subcritical behavior can be determined in terms of the leading dimensionless groups. This expression reveals that the supercritical saturation of the free surface is due to the influence of the normal elastic stresses, while the subcritical rupture of the free surface is attributed to the influence of capillary effects. In short, depending upon the magnitude of the scaled shear modulus, there exists a wavenumber at which a transition from saturated waves to subcritical breakup occurs.

Acknowledgment: The authors gratefully acknowledge funding from the National Science Foundation (NSF) via grant number CBET-2025117 and NASA via grant number NNX17AL27G.