Coupled pulsation and translation of two gas bubbles in a liquid. (Q2767793)

The problem of two interacting bubbles in an incompressible liquid is very old; the authors quote the V. F. K. Bjerknes' paper ``Field of force'' appeared in 1906. Since then, many authors studied the problem from different points of view and obtained numerous results that are presented in the introduction to the paper. The initial problem is completed by an acoustic field influencing the coupled bubble motion in the fluid. Despite of the obtained theoretical and experimental results, many mechanisms of the two-bubble dynamics are not well understood, and many of the possible dynamics for two interacting bubbles are not yet known. The authors ``endeavour to shed new light on these questions by presenting a joint analytical and numerical investigation of two interacting spherical gas bubbles in a liquid to which a sound field is applied''.NEWLINENEWLINEThey begin the study by recalling the initial elements of the motion: two spherical gas bubbles of radii \(R_1(t)\) and \(R_2(t)\) undergo damped and driven radial pulsations in a liquid of density \(\rho\), viscosity \(\mu_{\text{vis}}\) and hydrostatic pressure \(p_0\). The bubbles centres are fixed and \(D\) is the distance between them. They are immersed in an incompressible irrotational fluid under the hypothesis that they remain spherical. Under these conditions, the authors derive the boundary problem for the bubble motion and solve it using a fundamental Oguz-Prosperetti's virial theorem by means of which the radial pulsations and the bubble translation are determined.NEWLINENEWLINE Continuing their theoretical investigations, they add to the above results the influence of a weak acoustic field. In this case, the authors introduce two new parameters, \({\mathcal B}\) and \({\mathcal F}\), very important for the bubble motion analysis, taking in account the four sign combinations of these parameters. The authors continue the investigations by considering a moderately strong forcing regime in which the motion of the bubbles can be dramatically affected. All these new results are presented by means of numerous plots and tables.