Extensional effects in viscoelastic fluid flow through a micro-scale double cross-slot

Abstract

The flow of viscoelastic fluids through a microfluidic flow-focusing device was studied numerically. The conceived device is shaped as a double cross-slot with three entrances and three exits, in a symmetric configuration, aiming to achieve a constant extensional rate (<(epsilon) over dot>) at the centerline. The two-dimensional numerical simulations using the upper-convected Maxwell (UCM) model allow us to analyze the effect of Deborah number (De) on the flow patterns under creeping flow conditions. As a consequence of the small length scales and high deformation rates associated with the micro-channel flow, strong viscoelastic effects are observed, including purely elastic asymmetries. The double cross-slot geometry enables the generation of a region of converging flow, with the added advantage of keeping the flow region of interest away from walls, thus minimizing shear effects. The imposed Hencky strain can be controlled by varying the ratio of the flow rates in the inflowing branches. The shape of the streamlines defining the converging region is strongly influenced by the velocity ratio and by the geometric parameters of the device (e.g. the relative size of the entrance branches). By tuning these parameters, we are able to generate a region of nearly constant t at the centerline.