Sinking bubbles in a fluid under vertical vibration

The special nonlinear effect of sinking bubbles is observed when the container partially filled with a liquid is excited by vibration. This paper is concerned with this interesting phenomenon in an incompressible viscous fluid under vertical vibration. We construct the theoretical model from the view of vibration mechanics and fluid mechanics. According to theoretical analysis, we derive the accurate model of the bubble moving in the liquid and the added mass caused by it. After that, the control equation of the bubble is given by the force analysis and the differential equation of variable-mass systems. Besides, the critical depth of the sinking bubble is derived based on the method of direct separation of motions. We further explore and analyze the specific reasons why the bubbles sink. At the same time, the conditions where the variable mass has a significant influence on the motion of the object are given. The main factors affecting the sinking of bubbles, density, frequency, and amplitude are numerically simulated and analyzed with different conditions. To prevent or weaken the effect of sinking bubbles in the oscillating fluid, feasible approaches are proposed. Meanwhile, the theory is validated experimentally.