European Journal of Mechanics B/Fluids 25 (2006) 164–171 Injection and coalescence of bubbles in a quiescent inviscid liquid ✩ F.J. Higuera ∗ , A. Medina 1 E. T. S. Ingenieros Aeronáuticos, Pza. Cardenal Cisneros 3, 28040 Madrid, Spain Received 11 October 2004; received in revised form 17 March 2005; accepted 27 June 2005 Available online 1 September 2005 Abstract Time periodic generation and coalescence of bubbles by injection of a gas at a constant flow rate through an orifice at the bottom of a quiescent inviscid liquid is investigated numerically using a potential flow formulation. The volume of the bubbles is determined for different values of a Weber number and a Bond number. Single bubbling and different regimes of coalescence are described by these computations. The numerical results show qualitative agreement with well-known experimental results for liquids of low viscosity, suggesting that bubble interaction and coalescence following gas injection is to a large extent an inviscid phenomenon for these liquids, many aspects of which can be accounted for without recourse to wake effects or other viscosity- dependent ingredients of some current models.  2005 Elsevier SAS. All rights reserved. Keywords: Bubble generation; Coalescence; Potential flow 1. Introduction The generation of bubbles by injection of a gas into a liquid at rest is an important and much studied problem. Extensive research has been summarized in a variety of models that address the many facets of the problem with different levels of detail; see Refs. [1–5] for reviews. The conceptually simplest models are based on a balance of the forces acting on a bubble of assumed shape (Refs. [6–8], among others). These models clearly show the existence of a regime of low gas flow rate in which the effect of the inertia of the liquid is negligible and the volume of the bubbles is a constant independent of the gas flow rate, and a regime of high gas flow rate in which the effect of the surface tension is negligible and the volume of the bubbles increases as the 6/5 power of the gas flow rate and is independent of the size of the injection orifice. The original models of Davidson and Schuler [6] and Ramakrishna et al. [7], which served to establish these results, have been extended to include a variety of effects such as the viscous drag of the bubbles, the flow left by the viscous wake of the preceding bubble, the momentum flux of the injected gas, and the different shapes and apparent masses of the bubble at different stages of its growth. Extensions also include a set of ad hoc criteria to account for the interference, collision and coalescence of bubbles [9], which are observed to occur at high flow rates and eventually ✩ This work was supported by the Spanish Ministerio de Ciencia y Tecnología under project DPI2002-4550-C07-5. * Corresponding author. E-mail address: higuera@tupi.dmt.upm.es (F. Higuera). 1 On sabbatical leave from IMP, Mexico. 0997-7546/$ – see front matter  2005 Elsevier SAS. All rights reserved. doi:10.1016/j.euromechflu.2005.06.001