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Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell

Part II: Stability

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Abstract

Here, we extend the analysis of Part I to determine the linear stability of a bubble in a Hele-Shaw cell analytically. Only the solution branch corresponding to the largest possible bubble velocity U for given surface tension is found to be stable, while all the others are unstable, in accordance with earlier numerical results.

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References

  • Combescot, R., and Dombre, T., 1988, Selection in the Saffman-Taylor bubble and assymmetrical finger problem submitted.

  • Tanveer, S., 1986, The effect of surface tension on the shape of a Hele-Shaw cell bubble, Phys. Fluids, 29, 3537.

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Authors and Affiliations

  1. Mathematics Department, Virginia Polytechnic Institute and State University, 24061, Blacksburg, VA, USA

    S. Tanveer

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  1. S. Tanveer
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Communicated by M.Y. Hussaini

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Tanveer, S. Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. Theoret. Comput. Fluid Dynamics 1, 165–177 (1989). https://doi.org/10.1007/BF00417918

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  • DOI: https://doi.org/10.1007/BF00417918

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