Universal Force Diagrams of a Microbubble in Static Fluid on a Surface

Universal dimensionless three-dimensional universal lift force diagrams for a microbubble (or pendant drop) in a static liquid on a solid surface (or orifice) are presented in this work. Studying microbubble dynamics is important due to its controlling mass, momentum, energy and concentration transfer rates in many micro- and nano-sciences and technologies. In this study, dimensionless force diagrams are introduced by applying the solutions for microbubble shape for small Bond number in literature. A parametric study reveals that two dimensionless independent parameters, Bond number and contact angle (or base radius), are required to specify force diagrams. Each diagram can be divided into three regions, depending on if the microbubble surface contains the inflection or neck point. The total life force includes hydrostatic buoyancy, difference in gas and hydrostatic pressures at the base, capillary pressure, as well as surface tension induced by the variation of circumference which has not been treated in literature. In the absence of viscous stress, the total lift force equals surface tension induced by the variation of circumference.