Interactions between two bubbles on a ho

This study investigates the interactions between two bubbles on a heated or cooled surface, focusing on the resulting motion and aggregation driven by thermal gradients. The objective is to extend existing theoretical frameworks concerning bubble dynamics by analyzing two bubbles simultaneously, rather than relying on single bubble models. We employed quasi-steady equations to solve for the temperature and velocity fields, allowing us to quantitatively assess the relative velocity between bubbles influenced by their proximity to each other and the wall. Our findings reveal a counterintuitive increase in approach velocity as the bubbles near each other, despite the presence of hydrodynamic resistance. The asymptotic analysis indicates that the thermocapillary force becomes singular as bubble separation decreases. The results align reasonably well with experimental data, although there is a slight overestimation of bubble velocities. This research enhances understanding of bubble behaviors under temperature gradients, with implications for various industrial and environmental processes.