Unstable miscible displacements in radial flow with chemical reactions

Kim, Min Chan; Pramanik, Satyajit; Sharma, Vandita; Mishra, Manoranjan

doi:10.1017/jfm.2021.257

Cited by 13 publications

(9 citation statements)

References 49 publications

(70 reference statements)

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“…The above stability equations (3.32)–(3.34) are to be solved by employing the outward shooting scheme (Kim et al. 2021).…”

Section: Linear Stability Analysissupporting

confidence: 79%

“…The variation of viscosity depending on concentration is modelled by (2.5), which has been widely used in related fields (Nijjer, Hewitt & Neufeld 2018; Kim et al. 2021). The given initial and boundary conditions are where is the position of dissolution front, is the concentration at the solid salt–liquid interface and is the velocity of the liquid phase at the interface, which will be discussed below.…”

Section: Governing Equations and Base Fieldsmentioning

confidence: 99%

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Theoretical and numerical studies on dissolution of horizontal salt body and pattern formation incorporated with a dynamic moving interface

Hong

Kim

2023

J. Fluid Mech.

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The dissolution of a horizontal salt body is theoretically and numerically investigated by considering the coupled dynamics of the dissolution reaction and the diffusive and convective mass transfer at the salt surface. To take into account the nature of the recessing salt surface and the dissolution-driven convection, a dynamic moving boundary condition coupled with a dissolution reaction are employed By employing a newly derived moving interface condition and parameters, a theoretical analysis predicts the onset of gravitational instability, suggesting scaling relationships between parameters to describe the onset of instability (in transport-dominant (Damkholer number $Da \to \infty $ and Rayleigh number $Ra > {10^5}$ ), onset time ${\tau _d}\sim R{a^{ - 2/3}}$ and ${\tau _d}\sim (RaDa)^{1/4}$ for reaction-dominant regimes $(Da \to 0)$ ). The scaling relationships on dissolution (the average height change, $\Delta {h_{avg}}\sim \sqrt \tau $ for the diffusion-dominant regime and $\Delta {h_{avg}}\sim R{a^{0.79/3}}{\tau ^{0.86}}$ for the convection-dominant regime) are also suggested to explain the pattern formation. Under a convective mass transfer condition, the concentration gradient of the solute developed during the recession of the salt surface results in an adverse density gradient, which causes gravitational instability motion and finally determines the formation of a dissolution pattern. In addition, two-dimensional and three-dimensional numerical simulations visualize dissolution-driven convective flow fields, the recession of the liquid-solid interface and pattern formation on the dissolving interface. Theoretical and numerical analyses of the dissolution process suggest that the control of gravitational instability is important to prevent or enhance dissolution pattern formation. This systematic parameter study provides a deep understanding of the effect of gravitational instability on convection-driven dissolution in a horizontal geometry.

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“…The above stability equations (3.32)–(3.34) are to be solved by employing the outward shooting scheme (Kim et al. 2021).…”

Section: Linear Stability Analysissupporting

confidence: 79%

Section: Governing Equations and Base Fieldsmentioning

confidence: 99%

Theoretical and numerical studies on dissolution of horizontal salt body and pattern formation incorporated with a dynamic moving interface

Hong

Kim

2023

J. Fluid Mech.

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“…Another important controlling parameter that has been the focus of the earlier experimental [23,41,42] and numerical studies [24][25][26][27][28]32,33] of product C increases with it, that creates more non-monotonicity in the viscosity profile. The same phenomenon is also noticed here, for both positive and negative R c (figure 7a,b).…”

Section: Resultsmentioning

confidence: 99%

“…Another important controlling parameter that has been the focus of the earlier experimental [23,41,42] and numerical studies [24–28,32,33] in Hele–Shaw cell flows is the Damköhler number Da. An increase in the Damköhler number increases the growth of instability as the maximum of product C increases with it, that creates more non-monotonicity in the viscosity profile.…”

Section: Resultsmentioning

confidence: 99%

“…A chemical reaction can trigger or control hydrodynamic instabilities, which are known as chemo-hydrodynamic instabilities. Rayleigh–Taylor [22–24], viscous fingering (VF) [25–28], convective dissolution [29] and double-diffusive instabilities [30,31] are identified as chemo-hydrodynamic instabilities in porous media flows. In particular, a simple chemical reaction of A+Bfalse→C type can trigger all these instabilities by actively modifying Darcy’s flow through a change in density or viscosity of underlying fluids locally at the reactive zone.…”

Section: Introductionmentioning

confidence: 99%

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Stability of a layered reactive channel flow

2023

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We analyse the linear stability of a reactive plane Poiseuille flow, where a reactant fluid A overlies another reactant B in a layered fashion within a two-dimensional channel. Both reactants are miscible and have the same viscosity, while upon reaction, they produce either a less or more-viscous product fluid C . The reaction kinetics is of simple A + B → C type, and the production of C occurs across the initial contact line of reactants A and B in a mixed zone of small and finite width. All three fluids have the same density. We demonstrate the effects of various controlling parameters such as the log-mobility ratio, Damköhler number, Schmidt number, Reynolds number, position and thicknesses of the reactive zone on the stability characteristics. We show that a tiny viscosity stratification by the reaction destabilizes the flow at a moderate (10–1000) and even at low Reynolds numbers (0.01–1). The maximum growth occurs for shorter waves than for the Tollmien–Schlichting eigenmode, and the ranges of unstable wavenumbers are wider than that known for non-reactive channel flow systems. In most cases, the instability occurs due to the overlap of the critical layer with the viscosity-stratified layer. Surprisingly for some parameters, it is observed that the reaction can make σ M decrease with increasing Reynolds number.

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Computational framework for complex flow and transport in heterogeneous porous media

Icardi

Pescimoro

Municchi

et al. 2023

Engineering with Computers

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We present a flexible scalable open-source computational framework, named , based on the finite-volume library OpenFOAM®, for flow and transport problems in highly heterogeneous geological media and other porous materials. The framework combines geostatistical pre- and post-processing tools with specialised partial differential equations solvers. Random fields, for permeability and other physical properties, are generated by means of continuous or thresholded Gaussian random fields with various covariance/variogram functions. The generation process is based on an explicit spectral Fourier decomposition of the field which, although more computationally intensive than Fast Fourier Transform methods, allows a more flexible choice of statistical parameters and can be used for general geometries and grids. Flow and transport equations are solved for single-phase and variable density problems, with and without the Boussinesq approximation, and for a wide range of density, viscosity, and dispersion models, including dual-continuum (dual permeability or dual porosity) formulations. The mathematical models are here presented in details and the numerical strategies to deal with heterogeneities, equation coupling, and boundary conditions are discussed and benchmarked for the heterogeneous Henry and Horton–Rogers–Lapwood problems, and other test cases. We show that our framework is capable of dealing with large permeability variances, viscous instabilities, and large-scale three-dimensional transport problems.

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Unstable miscible displacements in radial flow with chemical reactions

Abstract: Abstract

Cited by 13 publications

References 49 publications

Theoretical and numerical studies on dissolution of horizontal salt body and pattern formation incorporated with a dynamic moving interface

Theoretical and numerical studies on dissolution of horizontal salt body and pattern formation incorporated with a dynamic moving interface

Stability of a layered reactive channel flow

Computational framework for complex flow and transport in heterogeneous porous media

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