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An Instability Phenomenon in Hele-Shaw Displacements

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  • Gelu Pasa

Abstract

We study the linear instability of the displacement of an Oldroyd-B fluid by air in a Hele-Shaw cell, motivated by possible applications in Secondary Oil Recovery (SOR) process. Most numerical methods have usually failed when the Weissenberg numbers $W_i$ (appearing in the constitutive relations) are near 1. We get an approximate formula of the growth rate with a blow-up for some particular $W_i =O(1)$. Therefore the instability at large Weissenberg numbers is due to the model, and not to the computational methods. Our growth rate is quite similar to Saffman-Taylor's formula (obtained when a Newtonian liquid is displaced by air) if $W_1=W_2$.

Suggested Citation

  • Gelu Pasa, 2017. "An Instability Phenomenon in Hele-Shaw Displacements," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(6), pages 14-23, December.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:6:p:14
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    More about this item

    Keywords

    Oldroyd-B fluids; Hele-Shaw displacement; linear stability;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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