Effect of Péclet number on miscible rectilinear displacement in a Hele-Shaw cell.
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It is observed that, depending on various flow parameters, a fluid system with a larger Pe exhibits a lower instantaneous growth rate than a system withA smaller Pe, which is contrary to the results when such stresses are absent.Abstract:
The influence of fluid dispersion on the Saffman-Taylor instability in miscible fluids has been investigated in both the linear and the nonlinear regimes. The convective characteristic scales are used for the dimensionless formulation that incorporates the Peclet number (Pe) into the governing equations as a measure for the fluid dispersion. A linear stability analysis (LSA) is performed in a similarity transformation domain using the quasi-steady-state approximation. LSA results confirm that a flow with a large Pe has a higher growth rate than a flow with a small Pe. The critical Peclet number (Pec) for the onset of instability for all possible wave numbers and also a power-law relation of the onset time and most unstable wave number with Pe are observed. Unlike the radial source flow, Pec is found to vary with t0. A Fourier spectral method is used for direct numerical simulations (DNS) of the fully nonlinear system. The power-law dependence of the onset of instability ton on Pe is obtained from the DNS and found to be inversely proportional to Pe and it is in good agreement with that obtained from the LSA. The influence of the anisotropic dispersion is analyzed in both the linear and the nonlinear regimes. The results obtained confirm that for a weak transverse dispersion merging happens slowly and hence the small wave perturbations become unstable. We also observ that the onset of instability sets in early when the transverse dispersion is weak and varies with the anisotropic dispersion coefficient, e, as ∼√[e], in compliance with the LSA. The combined effect of the Korteweg stress and Pe in the linear regime is pursued. It is observed that, depending on various flow parameters, a fluid system with a larger Pe exhibits a lower instantaneous growth rate than a system with a smaller Pe, which is contrary to the results when such stresses are absent.read more
Citations
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Wavelength selection of fingering instability inside Hele-Shaw cell
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Stable and unstable miscible displacements in layered porous media.
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References
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The Penetration of a Fluid into a Porous Medium or Hele-Shaw Cell Containing a More Viscous Liquid
TL;DR: In this paper, it was shown that a flow is possible in which equally spaced fingers advance steadily at very slow speeds, such that behind the tips of the advancing fingers the widths of the two columns of fluid are equal.
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Viscous fingering in porous media
TL;DR: Mecanisme de digitation visqueuse. as discussed by the authors : Deplacements non miscibles en cellules de Hele Shaw. Butteau et al. describe a set of ecoulements in a cellule.
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Stability of miscible displacements in porous media: Rectilinear flow
C. T. Tan,George M. Homsy +1 more
TL;DR: In this article, a theoretical treatment of the stability of miscible displacement in a porous medium is presented, where the base state of uniform velocity and a dispersive concentration profile is time dependent, leading to predictions of the growth rate.
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Channeling in packed columns
TL;DR: In this paper, the existence or absence of a tendency towards channeling is shown to depend upon the linear velocity of flow, defined in terms of the viscosities and densities of the two fluids.
Journal ArticleDOI
Simulation of nonlinear viscous fingering in miscible displacement
C. T. Tan,George M. Homsy +1 more
TL;DR: In this article, a Fourier spectral method is used as the basic scheme for numerical simulation of viscous fingering in miscible displacements, and it is shown that at short times, both the growth rate and the wavelength of fingers are in good agreement with predictions from our previous linear stability theory.