Numerical investigation of the deformation mechanism of a bubble or a drop rising or falling in another fluid

A numerical method for simulating the motion and deformation of anaxisymmetric bubble or drop rising or falling in another infiniteand initially stationary fluid is developed based on the volume offluid (VOF) method in the frame of two incompressible and immiscibleviscous fluids under the action of gravity, taking intoconsideration of surface tension effects. A comparison of thenumerical results by this method with those by other works indicatesthe validity of the method. In the frame of inviscid andincompressible fluids without taking into consideration of surfacetension effects, the mechanisms of the generation of the liquid jetand the transition from spherical shape to toroidal shape during thebubble or drop deformation, the increase of the ring diameter of thetoroidal bubble or drop and the decrease of its cross-section areaduring its motion, and the effects of the density ratio of the twofluids on the deformation of the bubble or drop are analysed boththeoretically and numerically.