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Two-layer flow in a corrugated channel

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Abstract

The flow of two superposed viscous fluid layers in a two-dimensional channel confined between a plane and a wavy or indented wall is studied by analytical and numerical methods at arbitrary Reynolds numbers. The interface between the two fluids may exhibit constant or variable surface tension due to an insoluble surfactant. The flow is computed from a specified initial condition using the immersed-interface method on a curvilinear grid constructed by conformal mapping. The numerical simulations illustrate the effect of geometrical nonlinearity and reveal that inertia may increase or decrease the amplitude of the interface profile at steady state depending on the flow parameters. Increasing either the Reynolds number or the wall amplitude above a certain threshold value provokes flow instability and overturning of the interface. In the Appendix, a linear perturbation analysis is performed for arbitrary Reynolds numbers on the assumption of small-amplitude sinusoidal undulations, and results for the amplitude and phase shift of the interfacial and surfactant concentration wave are documented for a broad range of flow conditions. It is found that inertia may have a mixed effect on the deformation and phase shift, while the surfactant promotes the deformation of the interface under most conditions.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, George Washington University, Suite T739, 801 22nd St. NW, Washington, DC, 20052, USA

    H. Luo

  2. School of Mathematics, University of East Anglia, Norwich, England, NR4 7TJ, UK

    M. G. Blyth

  3. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, 92093-0411, USA

    C. Pozrikidis

Authors
  1. H. Luo
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  2. M. G. Blyth
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  3. C. Pozrikidis
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Correspondence to M. G. Blyth.

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Luo, H., Blyth, M.G. & Pozrikidis, C. Two-layer flow in a corrugated channel. J Eng Math 60, 127–147 (2008). https://doi.org/10.1007/s10665-006-9134-2

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  • DOI: https://doi.org/10.1007/s10665-006-9134-2

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