Bubble wall and bubble pair interaction using potential flow theory M. Moctezuma R. Zenit R. Lima Instituto de Investigaciones en Materiales Universidad Nacional Autonoma de Mexico Abstract In this study the motion and interaction of a bubble with a vertical wall is analyzed in the high Reynolds and low Weber number limit. On this dual limit the inertial effects dominate, and bubbles remain spher- ical. There are experiments that confirm that this approach is valid. The velocity of the fluid was ob- tained by expanding the potential in a series of spher- ical harmonics. The motion equations were obtained using an energy approach. 1 Introduction We study the motion and interaction of a bubble with a vertical wall in the high Reynolds number limit. We consider small Weber number, for which the deforma- tion of the bubble is negligible. The motion of a pair of bubbles has been investigated by several author [3, 1]. In this study, Laplace’s equation is solved in terms of spherical harmonics with a method similar to that used by [1]. In figure (1) photographs of ex- periments are shown. Bubbles moving near a wall, for the same regime as that considered in the the- ory, move to the wall and bounce repeatedly as they move upwards. We want to analyze this effect with potential flow theory. 2 Theoretical framework We have to solve the problem of two spheres in mo- tion with velocity U 1 and U 2 , moving in a nearly in- viscid fluid. The velocity is decomposed in two com- ponents, one mean velocity V=U1+U2, and a differ- ence of velocities component W=W1-W2. Laplace’s Figure 1: Photographs of experiments of a bubble moving near a wall. The bubble positions for different instants were superimposed into the same plate to show the bubble trajectory equation must be solved: ∇ 2 φ =0 (1) The potential can be expanded in a double series of harmonical spherics centered in each sphere: Φ V k = n  i=1 V k · a 1 {g 1 mn  R r 1  n+1 Y k n (cos θ 1 ,μ)(2) +g 2 mn  R r 2  n+1 Y k n (cos θ 1 ,μ)} (3) The next step was to calculate the multipole coeffi- cients using the boundary conditions. This was done equating the normal velocity of the fluid in the sphere surface with the normal velocity of the spheres. The coefficients g mn and f mn were obtained in terms of 1 Mechanics of 21st Century - ICTAM04 Proceedings