Numerical study of single bubble rising dynamics using the phase field lattice Boltzmann method

In this paper, the rising dynamics of a two-dimensional single bubble in the duct is systematically studied by using an improved phase field lattice Boltzmann (LB) multiphase model. This model enables to handle multiphase flows with mass conservation and high density ratio, up to the order of O(103), which are unavailable in the LB community. The model is first validated by simulating bubble rising problem with the density ratio of 1000 and numerical solutions for bubble shape and position agree well with the previous literature data. Then, it is used to study single bubble rising through a quiescent liquid. The dynamic behavior of the bubble and rising velocity are shown, and the influences of several important physical quantities, including the Eotvos number, Reynolds number, density ratio, viscosity ratio, bubble size and initial bubble shape, are investigated in detail. The numerical results show that the bubble undergoes a great deformation with the increase of the Eotvos number or Reynolds number, and even could break up into multiple satellite bubbles at a sufficiently large value of Eotvos number or Reynolds number. Several classic terminal bubble shapes are also successfully produced in the system. The terminal rising velocity of bubble at equilibrium shows to present an initial increase with the Eotvos number and finally decreases with it, while increasing the Reynolds number could enhance the bubble rising velocity. Both the density ratio and viscosity ratio have less influence on the terminal shape of the bubble, while a greater influence on the rising velocity is reported for the density ratio smaller than 20 and it seems to be independent of the viscosity ratio. At last, we discuss the effects of the bubble size and initial bubble shape. It is found that bubble size has little influence on terminal bubble shape, but decreasing the bubble size can improve the bubble terminal velocity. On the other hand, both the deformation and terminal velocity of the bubble are found to no longer change much with its initial shape.