Viscous flow through microfabricated hyperbolic contractions

We study the flow of a Newtonian fluid through microfabricated hyperbolic contractions followed by a sudden expansion, with the aim of investigating the potential of this geometry to serve as an extensional microrheometer. A set of planar converging geometries, with total Hencky strains ranging from 1.0 to 3.7, were fabricated in order to produce a homogeneous extensional flow field within the contraction. The velocity field in various planes of the hyperbolic contraction was quantified by means of microparticle image velocimetry (mu PIV) and the pressure drop across the converging geometry was also measured and found to vary approximately linearly with the flow rate. Additionally, an extensive range of numerical calculations were carried out using a finite-volume method to help assess the performance of this geometry as a microfluidic elongational rheometer. The measured velocity fields in the contraction and associated pressure drops compare very well (to within 10%) with the numerical predictions. For the typical dimensions used in the microfluidic devices, the steady viscous flow through the contraction is shown to be three-dimensional and it is demonstrated that regions with nearly constant strain rate can only be achieved using geometries with large total Hencky strains under Hele-Shaw (potential-like) flow conditions.