Air Bubble Collapse in Non-Newtonian Medium with an Application in Biology

An unsteady compressible multiphase flow solver is developed and used to simulate shockbubble interaction in a non-Newtonian fluid. A five-equation multiphase model that accounts for capillary and viscous effects is employed and discretized by finite volume methodology. Harten-Lax-Van Leercontact Riemann solver is invoked to compute the convective fluxes and tangent of hyperbola for interface capturing interface sharpening scheme is applied to reduce the excessive diffusion at the interface. Multiple benchmark problems such as air-helium shock tube, shock cavity interaction, Rayleigh-Taylor instability and underwater explosion are probed to evaluate the performance and accuracy of this method. The results obtained compare well with the available experimental and numerical data. The developed solver is then used to study shock-interface interaction in both Newtonian and non-Newtonian mediums. Non-Newtonian liquid is resembling the blood modeled by Carreau-Yasuda constitutive equation. The obtained results show an expedition of bubble-collapse with a higher jet tip velocity in non-Newtonian medium compared to that in the Newtonian surrounding liquid. Moreover, a third phase adjacent to the bubble collapse is considered and the penetration depth of the re-entrant jet in the neighboring phase is studied as a measure of tissue injury. Our results show that by increasing post shock pressure, the re-entrant jet velocity and thus the penetration depth increases. Furthermore, increasing the adjacent phase viscosity results into less penetration depth in the tissue..