Profiles of Static Liquid–Gas Interfaces in Axisymmetric Containers with Different Accelerations

Abstract

Second-order perturbation solutions of profiles of bubbles suspended in liquid and liquid−gas interfaces when liquid all sinks in the bottom with different accelerations are derived. Six procedures are developed based on these solutions, and they are divided into two types. One type takes the coordinates of end points of profiles as input, and the other type takes liquid volume or gas volume as input. Numerical simulations are performed with the Volume of Fluid method, and numerical results are in good agreement with the predictions of these procedures. The greater the acceleration, the flatter the bubble until all liquid sinks to the bottom. Effects of acceleration on bubble shape must be considered; otherwise, it will cause a volume prediction error of up to 10%. When all liquid sinks to the bottom, predictions of liquid volume with the same liquid meniscus height as inputs differ considerably for different accelerations. The most significant change in liquid volume occurs when the bond number Bo ≪ 1. Effects of acceleration and liquid contact angle on the liquid−gas interfaces must be considered when evaluating liquid residue. These findings should be quite helpful for liquid residue measurement and fine management in spacecraft.