Simulations of extensional flow in
microrheometric devices

Mónica S. N. Oliveira, Lucy E. Rodd, Gareth H. McKinley, Manuel A. Alves

We present a detailed numerical study of the flow of a Newtonian fluid through
microrheometric devices featuring a sudden contraction-expansion. This flow configuration is
typically used to generate extensional deformations and high strain rates. The excess pressure
drop resulting from the converging and diverging flow is an important dynamic measure to
quantify if the device is intended to be used as a microfluidic extensional-rheometer. To
explore this, we examine the effect of the contraction length, aspect ratio and Reynolds
number on the flow kinematics and resulting pressure field. Analysis of the computed velocity
and pressure fields show that, for typical experimental conditions used in microfluidic
devices, the steady flow is highly three-dimensional with open spiraling vortical structures in
the stagnant corner regions. The numerical simulations of the local kinematics and global
pressure drop are in good agreement with experimental results. The device aspect ratio is
shown to have a strong impact on the flow and consequently also on the dimensionless excess
pressure drop, which is quantified in terms of the dimensionless Couette and Bagley
correction factors. We suggest an approach for calculating the Bagley correction which may
be especially appropriate for planar microchannels with a contraction followed by an
expansion and which may present a significant improvement in the approach presently used to
analyze experimental data.