Purely-elastic flow instabilities in a microfluidic cross-slot geometry

Abstract

In this work we demonstrate numerically, using a 3D finite-volume method, that viscoelastic flow in a microfluidic cross-slot geometry can lead to flow asymmetries under perfectly symmetric flow conditions. This supercritical instability is predicted using the upper-convected Maxwell model under creeping flow conditions, thus demonstrating that it is purely elastic in nature. The numerical results obtained agree qualitatively with the recent experimental findings of Arratia et al.[1]. We investigate the effect of the aspect ratio of the geometry, showing the stabilizing effect of the upper and lower walls. In the limit of small depth a Hele-Shaw flow is approached and the onset of asymmetric flow is suppressed. On the other hand, the elastic instability that leads to a periodic flow occurs at increasingly smaller Deborah numbers as the aspect ratio decreases.