The dynamic behavior of a collapsing bubble in a magnetic fluid

Abstract In this article it is investigated the nonlinear response of an oscillatory bubble suspended in an incompressible magnetic fluid. After an appropriate non-dimensionalization of the governing equation, it is found that the most relevant physical parameters of the system are: the Reynolds number, the Weber number, the magnetic pressure coefficient and the magnetic permeability ratio bubble-fluid governing equation. The integration of the nonlinear differential equation governing the bubble motion is performed analytically by using a regular expansion and numerically by using a fourth-order Runge–Kutta scheme. Unstable configurations of the bubble motion are shown for different values of the magnetic pressure coefficient. An important consequence of magnetic colloidal particles in the flow is that it may drastically attenuate instabilities, avoiding bubble against collapse. The present findings have implications for acoustic cavitation in cryogenic liquids.