Modeling interfacial mass transfer driven bubble growth in supersaturated solutions

Kurian J Vachaparambil,Kristian Etienne Einarsrud

doi:10.1063/5.0020210

Kurian J Vachaparambil, Kristian Etienne Einarsrud

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https://doi.org/10.1063/5.0020210

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Abstract

A commonly encountered phenomenon in chemical processes is bubble evolution driven by supersaturation. On the continuum scale, this essentially involves interfacial mass transfer resulting in the growth of bubbles and their subsequent detachment from a surface. Analytical approaches to study this phenomenon typically involve estimating the driving force for interfacial mass transfer based on Sherwood number (Sh) correlations and the bulk concentration of dissolved gas. This is often not practical since the bulk concentration is often unknown and Sh correlations are sometimes not available to provide an accurate description of the associated flow fields. With the use of interface-resolved simulations to model these processes, the local distribution of dissolved gas can be obtained by solving for the concentration field. The driving force for interfacial mass transfer can be computed based on Sh correlations (which can be adopted for specific flows and are typically used in “engineering” applications) or the universally applicable Fick’s first law. This paper compares the predictions of these approaches for the well-studied case of a two-dimensional bubble growing in an unbounded supersaturated solution for three different levels of supersaturation. The equivalent two-dimensional simulations are run in a previously developed volume of fluid framework on OpenFOAM® [K. J. Vachaparambil and K. E. Einarsrud, Appl. Math. Model. 81, 690–710 (2020)]. The results show that the choice of an appropriate Sh correlation can provide a reasonable estimate of bubble growth. In a more universal approach, which is relevant when the flow being simulated cannot be captured by a single Sh correlation (e.g., bubble growth/coalescence and detachment) or when existing Sh correlations are not applicable, Fick’s first law can be used to compute the driving force for bubble growth, provided that the concentration boundary layer can be resolved.

Highlights

Bubble evolution in supersaturated solutions is a process initiated by nucleation, followed by interfacial mass transfer driven growth and eventually detachment from the surface.1 This phenomenon is relevant to processes such as electrolysis of water and electrolytic reduction of alumina, as well as to the opening of champagne bottles
As an analytical solution is available for this flow scenario, the results of simulations with the driving forces computed based on Fick’s first law and on two Sherwood number (Sh) correlations have been compared with the theoretical results to assess the predictions of bubble growth
● If a Sh correlation that is appropriate for the specific flow being simulated is chosen to compute the driving force for interfacial mass transfer, a reasonably accurate prediction of bubble growth can be obtained

Summary

Introduction

Bubble evolution in supersaturated solutions is a process initiated by nucleation, followed by interfacial mass transfer driven growth and eventually detachment from the surface. This phenomenon is relevant to processes such as electrolysis of water and electrolytic reduction of alumina, as well as to the opening of champagne bottles. Bubble evolution in supersaturated solutions is a process initiated by nucleation, followed by interfacial mass transfer driven growth and eventually detachment from the surface.. The bubble growth can be divided into two main regimes: inertial (which lasts for less than a second for very small bubbles of the order of tens of micrometers in size) and diffusion-controlled (the interfacial mass transfer driven regime relevant for continuum scale bubbles).. The bubble growth can be divided into two main regimes: inertial (which lasts for less than a second for very small bubbles of the order of tens of micrometers in size) and diffusion-controlled (the interfacial mass transfer driven regime relevant for continuum scale bubbles).2 Apart from these two regimes, in electrochemical systems, the heterogeneous reactions that result in supersaturation of the liquid can affect the bubble growth.. The bubble growth can be divided into two main regimes: inertial (which lasts for less than a second for very small bubbles of the order of tens of micrometers in size) and diffusion-controlled (the interfacial mass transfer driven regime relevant for continuum scale bubbles). Apart from these two regimes, in electrochemical systems, the heterogeneous reactions that result in supersaturation of the liquid can affect the bubble growth. the continuumscale bubble growth driven by interfacial mass transfer in supersaturated solutions is an important topic that has been investigated using analytical, numerical, and experimental approaches

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