Numerical Simulations of Bubble Dynamics Near Viscoelastic Media

Abstract

Cavitation-induced damage occurs in a wide range of applications, including in naval hydrodynamics, medicine, and the Spallation Neutron Source. Local transient pressure decreases in liquid flow may give rise to explosive bubble growth and violent collapse, with shock waves produced at collapse interacting with neighboring solids. Although the mechanisms of erosion to hard, metallic solids can be predicted in relatively simple geometries, damage to soft materials (e.g., elastomeric coatings, soft tissue) or in confined geometries is less well understood. In such problems, the constitutive models describing the medium are non-trivial and include effects such as (nonlinear) elasticity, history (relaxation effects) and viscosity. As a result, the influence of the shock on the material and the response of the material to the shock are poorly understood.

To gain fundamental insights into cavitation-induced damage to both soft objects and rigid materials, we develop a novel Eulerian approach for numerical simulations of wave propagation in heterogeneous viscoelastic media. We extend the five-equations multiphase, interface-capturing model, based on the idea that all the materials (gases, liquids, solids) obey the same equation of state with spatially varying properties, to incorporate the desired constitutive relation. We consider problems in which the deformations are small, such that the substances can be described by linear viscoelastic constitutive relations. One difficulty is the calculation of strains in an Eulerian framework, which we address by using a hypoelastic model in which an objective time derivative (Lie derivative) of the constitutive relation is taken to evolve strain rates. The resulting numerical framework is a solution-adaptive, high-order interface-capturing approach for compressible, multiphase flows involving linear viscoelasticity at all speeds.

We then utilize this numerical framework to gain fundamental insights into cavitation damage (i) in a confined geometry, (ii) in shock wave lithotripsy, and (iii) to rigid objects covered by an elastomeric coating. We examine the maximum stresses, pressures, and temperatures along/in rigid/compliant objects. We quantify the effect of confinement on an inertially collapsing bubble and determine the appropriate scaling governing the maximum pressures can predicted on the surfaces. We investigate the stresses produced to a model kidney stone due to a shock wave by examining the amplification of tensile stresses in the stone when a gas bubble is present. The impact loads on a polymeric coating relevant to naval engineering applications by shock-induced bubble collapse indicate how pitting and coating material ejection may take place by repeated cavitation events near the surface.