Prediction of Spherical Bubble-Chain-Induced Liquid Flow through Far-Wake Superposition Based on Bubble-Chain Hydrodynamics

Abstract

Recent experimental observations revealed that clean spherical bubble chains generate a nearly uniform upward liquid flow. The physical origin of this liquid flow, however, remains unclear. Hydrodynamic interactions in aligned bubble chains were therefore investigated using high-accuracy embedded-boundary simulations that resolve the interfacial boundary layer while capturing long-range interactions among multiple clean spherical bubbles. The simulations were used to quantify the evolution of hydrodynamic interactions within bubble chains and to identify the conditions under which bubble-induced liquid flow can be represented by the superposition of isolated-bubble far wakes. Based on these findings, a reduced-order model was developed and applied to experimentally measured bubble trajectories. The model successfully reproduced the nearly uniform upward liquid flow observed in the experiments. To clarify the role of bubble dispersion, the predictions were compared with those for a uniformly dispersed bubble arrangement having the same overall dispersion width. While the uniformly dispersed arrangement produced a center-peaked velocity distribution, only the experimentally observed bubble trajectories reproduced the nearly uniform upward liquid flow. These results demonstrate that the liquid flow is governed not simply by the dispersion width but by the bubble trajectories that establish the spatial distribution of far wakes. The present study provides a physical framework linking hydrodynamic interactions among bubbles, bubble dispersion, and bubble-induced liquid flow, together with a reduced-order model for predicting the liquid flow generated by bubble chains.