Microbubble or pendant drop control described by a general phase diagram

Abstract

Controlling states and growths of a microscale bubble (or pendant drop) in a static liquid on a solid surface (or orifice) can be achieved by introducing general dimensionless phase diagrams provided in this work. Nowadays, microbubbles are often used to control transport phenomena in various micro- and nano-technologies. This work parametrically presents general three-dimensional phase diagrams of a microbubble on a solid surface by applying perturbation solutions with accuracy to the second power of Bond number of Young–Laplace equation in the literature. The phase diagrams are found to be divided into three regions, depending on if the microbubble surface contains the inflection point or neck. The general growth, departure and entrapment of a microbubble thus can be described by path lines on diagrams by adjusting two of three dimensionless parameters governing the apex and base radii, and contact angle to satisfy the desired requirement. The initial condition is Bond number, defined as the ratio of hydrostatic and capillary pressures at an initial or critical state. Validity of this model is confirmed by comparing with available theoretical data, agreed with experimental results in the literature.