Abstract
The spectral element marker particle (SEMP) method is a high-order numerical scheme for modelling multiphase flow where the governing equations are discretised using the spectral element method and the (compressible) fluid phases are tracked using marker particles. Thus far, the method has been successfully applied to two-phase problems involving the collapse of a two-dimensional bubble in the vicinity of a rigid wall. In this article, the SEMP method is extended to include a third fluid phase before being applied to bubble collapse problems near a fluid-fluid interface. Two-phase bubble collapse near a rigid boundary (where a highly viscous third phase approximates the rigid boundary) is considered as validation of the method. A range of fluid parameter values and geometric configurations are studied before a bioengineering application is considered. A simplified model of (micro)bubble-cell interaction is presented, with the aim of gaining initial insights into the flow mechanisms behind sonoporation and microbubble-enhanced targeted drug delivery. Results from this model indicate that the non-local cell membrane distortion (blebbing) phenomenon often observed experimentally may result from stress propagation along the cell surface and so be hydrodynamical in origin.
Highlights
The dynamics of bubble collapse has received substantial attention in the literature over the past 100 years
This article employs a similar non-dimensionalisation as used in Lind and Phillips (2012): distances are scaled with respect to initial bubble radius R, densities are scaled with respect to the initial bubble density ρb,0, pressures are scaled with respect to ρb,0V2, where V is a reference speed of sound, and stresses are scaled with respect to ρb,0V2
As a high-order spatial approximation is employed in this article, it can be seen from Eq (7), that the overall error in the scheme is dominated by the backward integration step
Summary
The dynamics of bubble collapse has received substantial attention in the literature over the past 100 years. Lind / International Journal of Multiphase Flow 90 (2017) 118–143 interpolating through bubble surface marker points using cubic splines They found good agreement with experimental results for the incompressible phase of the dynamics but concluded that compressibility and thermal effects may be required for the compressible phase (bubble rebound). It is likely that the secondary collapse phase required an amount of compressibility which is beyond the scope of the BEM model In their boundary element study, (Lee et al, 2007) took a different approach and approximated compressible effects by incorporating a loss in energy (provided by experimental data) during the bubble rebound and found very good agreement with experimental results, including the capture of the elusive counterjet.
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