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Conflict of Interest: In relation to this article, we declare that there is no conflict of interest.

Publication history: Received August 20, 2022
Revised October 10, 2022

Acknowledgements: This research was supported by the 2022 scientific promotion program funded by Jeju National University

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Onset and growth of gravitational instability in an isolated porous medium: Linear and nonlinear analyses

Min Chan Kim^†

Department of Chemical Engineering, Jeju National University, Jeju 63243, Korea

mckim@cheju.ac.kr

Korean Journal of Chemical Engineering, May 2023, 40(5), 1045-1054(10), 10.1007/s11814-022-1315-9

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Abstract

Linear and nonlinear analyses were conducted to study the onset and growth of gravitational instability in an isolated porous medium. By considering the dissolution capacity of the isolated system, base concentration profiles were obtained analytically. Based on this base concentration field, linear stability equations were derived under the linear stability theory. The present stability analysis predicts that an isolated system is more stable than the conventional open system. In addition, the dissolution capacity of the isolated system suppresses the onset of instability. Unlike the previous study, the minimum Darcy-Rayleigh number to induce gravitational instability exists and it is a strong function of the dissolution capacity. However, the critical conditions for the high Darcy-Rayleigh number system are insensitive to the dissolution capacity. Based on the results of the linear analysis and the analytically obtained base concentration profile, fully nonlinear numerical simulations were also conducted for the case of Ra=103 . The vertical development of the instability motion and the dissolution flux are significantly suppressed in the high dissolution capacity systems.

Keywords

Gravitational Instability Isolated System Dissolution Capacity Linear Stability Analysis Numerical Simulation

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