Theoretical modelling for bubble dynamics with migration effects under dynamic Reynolds numbers

Bubble dynamics constitutes a fundamental scientific problem in fluid mechanics. Although the oscillation can be predicted through theories for bubble dynamics in previous studies, the viscous effects on the bubble migration remains difficult to predict accurately. In this study, we establish a theoretical model for bubble migration across the entire cycle. The theoretical model derives a drag coefficient expression under dynamic Reynolds numbers, and incorporates corrections to account for non-spherical bubble dynamics. A key advance is the capability to account for viscous drag without relying on constant empirical drag coefficients. Validation against experimental results demonstrates that the theoretical model effectively predicts the bubble migration. Furthermore, we discuss the correlation between drag coefficient and Reynolds number, and elucidate the effects of viscous domain range and bubble deformation on the drag coefficient of the present model.