Existence and uniqueness of solution to unsteady Darcy-Brinkman problem with Korteweg stress for modelling miscible porous media flow

Kundu, Sahil; Maharana, Surya Narayan; Mishra, Manoranjan

doi:10.1016/j.jmaa.2024.128532

Journal of Mathematical Analysis and Applications

2024

DOI: 10.1016/j.jmaa.2024.128532

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Existence and uniqueness of solution to unsteady Darcy-Brinkman problem with Korteweg stress for modelling miscible porous media flow

Sahil Kundu,

Surya Narayan Maharana,

Manoranjan Mishra

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Onset of cabbeling instabilities in superconfined two-fluid systems

Leyrer,

Ulloa,

Ortega

et al. 2024

Physics of Fluids

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Convective-driven mixing in permeable subsurface environments is relevant in engineering and natural systems. This process occurs in groundwater remediation, oil recovery, CO2 sequestration, and hydrothermal environments. When two fluids come into contact in superconfined geometries like open fractures in rocks, complex molecular dynamics can develop at the fluid–fluid interface, creating a denser mixture and leading to cabbeling instabilities that propel solutal convection. Previous studies in superconfined systems have used models based on unstable density distributions—generating Rayleigh–Taylor instabilities—and analog fluid mixtures characterized by nonlinear equations of state—resulting in cabbeling dynamics—yet often neglecting interfacial tension effects, which is also relevant in miscible systems. This study incorporates the Korteweg tensor into the Hele–Shaw model to better understand the combined influence of geometry confinement and interfacial tension on the onset of cabbeling instabilities in two-fluid superconfined systems. Through direct numerical simulations, we investigate the system's stability, revealing that the onset, characterized by the critical time tc, exhibits a nonlinear relationship with the system's nondimensional parameters—the Rayleigh number Ra, the anisotropy ratio ϵ, and the Korteweg number Ko. This relationship is crystallized into a single scaling law tc=F(Ra,ϵ,Ko). Our findings indicate that geometry and effective interfacial tension exert a stabilizing effect during the initial stages of convection, stressing the necessity for further exploration of its influence on fluid mixing in superconfined systems.

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Onset of cabbeling instabilities in superconfined two-fluid systems

Leyrer,

Ulloa,

Ortega

et al. 2024

Physics of Fluids

View full text Add to dashboard Cite

show abstract

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Existence and uniqueness of solution to unsteady Darcy-Brinkman problem with Korteweg stress for modelling miscible porous media flow

Cited by 1 publication

References 52 publications

Onset of cabbeling instabilities in superconfined two-fluid systems

Onset of cabbeling instabilities in superconfined two-fluid systems

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