An Instability Phenomenon in Hele-Shaw Displacements


  •  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 $W_1=W_2$.


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