Mutual interaction of a collapsing bubble and a nearby viscoelastic solid

Abstract

The interaction between a microscale collapsing bubble and a nearby viscoelastic solid is investigated numerically. The bubble initiates rapid expansion with high initial pressure, and the stand-off parameter is set to be near 1.0. The viscoelastic properties of the solid are described using the Kelvin-Voigt model, with its elastic modulus E and viscosity eta, varying several orders of magnitude (E = 20-2000 kPa and eta = 2-1000 Pa s). The influence of solid viscoelasticity on bubble behavior and solid deformation are analyzed throughout the entire life cycle of the bubble, from its initial expansion to the moment of liquid jet impingement. The Deborah number, which quantifies the relative timescales of solid deformation and bubble expansion, is employed to characterize the bubble-solid interaction. As the Deborah number increases from the order of 10-2 to 102, the dynamics of the bubble converge toward those observed in the cases of a rigid solid; while the solid deformation displacement reduces to a value close to zero, the maximum expansion radius of the bubble increases by up to 8%, and the speed of the liquid jet decreases by approximately 80%. The temporal distribution of energy components within the fluid domain reveals that the maximum expansion radius of the bubble and the kinetic energy of the liquid jet are inversely related to the energy transferred from the fluid to the solid. The imbalance in pressure surrounding the contracting bubble and the narrow region of the liquid jet are responsible for the enhancement of the liquid jet speed for small solid viscosity. Upon the impingement of the liquid jet onto the solid surface, the width and depth of the crater formed by the jet become greater for large jet speed and small solid viscosity.