An Analytical Method to Estimate Supersaturation in Gas–Liquid Systems as a Function of Pressure-Reduction Step and Waiting Time

Abstract

When the concentration of a gas exceeds the equilibrium concentration in a liquid, the gas–liquid system is referred as a supersaturated system. The supersaturation can be achieved by either changing the pressure and/or temperature of the system. The gas from a supersaturated liquid escapes either through bubble nucleation that usually occurs on solid surface and/or gas diffusion through the gas–liquid interface. The bubble nucleation requires a minimum threshold supersaturation. A waiting time is required to observe whether the applied supersaturation is sufficient to initiate bubble nucleation. When the supersaturation is not sufficient to cause bubble nucleation, some or all of the supersaturated gas may diffuse out from the liquid through the gas–liquid interface before further reducing the pressure in order to increase the supersaturation. In this article, using Fick’s second law of diffusion and Henry’s law, an analytical method is proposed to estimate the level of supersaturations generated in three gas–liquid systems at different step-down pressures. Characteristic times of the gas–liquid systems were estimated to validate whether the waiting times used in this study are in accordance with the semi-infinite diffusion model used to estimate the supersaturations generated.

Keywords

• bubble nucleation
• gas-liquid systems
• supersaturation
• step-down pressure
• Fick’s second law diffusion
• characteristic time