Unstable miscible displacements in radial flow with chemical reactions

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dc.contributor.author Kin, Min Chan
dc.contributor.author Pramanik, Satyajit
dc.contributor.author Sharma, Vandita
dc.contributor.author Mishra, Manoranjan
dc.coverage.spatial United Kingdom
dc.date.accessioned 2021-05-14T05:18:43Z
dc.date.available 2021-05-14T05:18:43Z
dc.date.issued 2021-06
dc.identifier.citation Kin, Min Chan; Pramanik, Satyajit; Sharma, Vandita; Mishra, Manoranjan, "Unstable miscible displacements in radial flow with chemical reactions", Journal of Fluid Mechanics, DOI: 10.1017/jfm.2021.257, vol. 917, Jun. 2021. en_US
dc.identifier.issn 0022-1120
dc.identifier.issn 1469-7645
dc.identifier.uri https://doi.org/10.1017/jfm.2021.257
dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/6432
dc.description.abstract The effects of the A + B ? C chemical reaction on miscible viscous fingering in a radial source flow are analysed using linear stability theory and numerical simulations. This flow and transport problem is describ d by a system of nonlinear partial differential equations consisting of Darcy?s law for an incompressible fluid coupled with nonlinear advection-diffusion-reaction equations. For an infinitely large Peclet number (Pe), the linear stability equations are solved using spectral analysis. Further, the numerical shooting method is used to solve the linearized equations for various values of Pe including the limit Pe ? �. In the linear analysis, we aim to capture various critical parameters for the instability using the concept of asymptotic instability, i.e. in the limit � ? �, where � represents the dimensionless time. We restrict our analysis to the asymptotic limit Da? (= Da� ) ? � and compare the results with the non-reactive case (Da = 0) for which Da? = 0, where Da is the Damk�hler number. In the latter case, the dynamics is controlled by the dimensionless parameter RPhys = ?(RA ? ?RB). In the former case, for a fixed value of RPhys, the dynamics is determined by the dimensionless parameter RChem = ?(RC ? RB ? RA). Here, ? is the ratio of reactants? initial concentration and RA, RB and RC are the log-viscosity ratios. We perform numerical simulations of the coupled nonlinear partial differential equations for large values of Da. The critical values RPhys,c and RChem,c for instability decrease with Pe and they exhibit power laws in Pe. In the asymptotic limit of infinitely large Pe they exhibit a power-law dependence on Pe (RChem,c ? Pe?1/2 as Pe ? �) in both the linear and nonlinear regimes.
dc.description.statementofresponsibility by Min Chan Kin, Satyajit Pramanik, Vandita Sharma, and Manoranjan Mishra
dc.format.extent vol. 917
dc.language.iso en_US en_US
dc.publisher Cambridge University Press en_US
dc.subject fingering instability en_US
dc.subject porous media en_US
dc.title Unstable miscible displacements in radial flow with chemical reactions en_US
dc.type Article en_US
dc.relation.journal Journal of Fluid Mechanics

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