Vibration-induced interfacial instabilities in viscoelastic fluids

Vertically vibrated interfaces between viscoelastic fluids may arise in contexts as diverse as ultrasonic emulsification, microgravity materials processing, and geophysics. If the vibration amplitude is large enough at a given frequency, the interface can become unstable and give rise to standing waves. The present work provides a linear analysis of this phenomenon for the cases where either or both of the fluids are viscoelastic. The fluids are assumed to be laterally unbound, and Floquet theory is used to develop a recursion relation between the temporal modes of the interfacial deformation. Conversion of this relation into a matrix eigenvalue problem allows determination of the critical vibration amplitude needed to excite the standing waves and the corresponding critical wave number. Using a single-mode Maxwell model to describe the viscoelasticity and considering infinite fluid depths, we present calculations for three cases: bottom fluid viscoelastic/top fluid Newtonian, bottom fluid Newtonian/top fluid viscoelastic, and both fluids viscoelastic. When only one of the fluids is viscoelastic, the interfacial waves can respond harmonically to the forcing. The waves may also be excited more easily than in the case where both fluids are Newtonian. When both of the fluids are viscoelastic, it appears possible to excite Stoneley-like waves at the interface.