The linear stability of double-diffusive miscible rectilinear displacements in a Hele-Shaw cell
Pritchard, D. (2009) The linear stability of double-diffusive miscible rectilinear displacements in a Hele-Shaw cell. European Journal of Mechanics - B/Fluids, 28 (4). pp. 564-577. ISSN 0997-7546 (https://doi.org/10.1016/j.euromechflu.2009.01.004)
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Abstract
We investigate the viscous instability of a miscible displacement process in a recti-linear geometry, when the viscosity contrast is controlled by two quantities whichdiuse at dierent rates. The analysis is applicable to displacement in a porousmedium with two dissolved species, or to displacement in a Hele-Shaw cell with twodissolved species or with one dissolved species and a thermal contrast. We carry outasymptotic analyses of the linear stability behaviour in two regimes: that of smallwavenumbers at intermediate times, and that of large times.An interesting feature of the large-time results is the existence of regimes in whichthe favoured wavenumber scales with t−1/4, as opposed to the t−3/8 scaling foundin other regimes including that of single-species ngering. We also show that theregion of parameter space in which the displacement is unstable grows with time,and that although overdamped growing perturbations are possible, these are neverthe fastest-growing perturbations so are unlikely to be observed. We also interpretour results physically in terms of the stabilising and destabilising mechanisms actingon an incipient nger.
ORCID iDs
Pritchard, D. ORCID: https://orcid.org/0000-0002-9235-7052;-
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Item type: Article ID code: 13796 Dates: DateEventAugust 2009Published5 February 2009Published OnlineSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Mrs Mary McAuley Date deposited: 16 Dec 2009 16:01 Last modified: 22 Nov 2024 18:10 URI: https://strathprints.strath.ac.uk/id/eprint/13796