An Instability Phenomenon in Hele-Shaw Displacements

Gelu Pasa

Journal of Mathematics Research, 2017, vol. 9, issue 6, 14-23

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 $W_1=W_2$.

Keywords: Oldroyd-B fluids; Hele-Shaw displacement; linear stability (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:9:y:2017:i:6:p:14

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