This paper analyzes flow of a power-law fluid in a microfluidic device for the purpose of discovering an algorithm for rheometry. Previous investigations have shown that measurement of the velocity field or the pressure field and the inlet flow rate in a microfluidic T-junction allow determination of rheological parameters uniquely. However, the range of shear induced within the flow domain was limited by the constant pressure drop applied across the micro-device. To avoid this control restriction and further develop our inverse technique, a constant flow rate system was investigated. With this configuration, the flow rate can be set appropriately to achieve a desired shear range and the rheological parameters can be inferred from the measurement of mean pressure at the inlet and at the junction. By assuming creeping flow conditions and the existence of a Hagen-Poiseuille-like law for the relationship between the pressure drop and the volumetric flow rate, the analysis produces an algorithm that is self-consistent (demonstrates the Hagen-Poiseuille law) and permits the inference of the power-law parameters from the ratio of any two field variables measured over a region (averaged), the pressure drop, and the volumetric flow rate.

The main purpose of this study is to model non-Newtonian fluid flows in microgeometries. Velocity fields of dilute xanthan gum solutions in a microfluidic T-junction have been measured for pressure- driven flow using micron resolution particle image velocimetry (mu-PIV). Xanthan gum at a fixed concentration is a power-law fluid. Varying the concentration changes the rheology, effectively altering the power-law parameters reflecting the changes in the fluid's shear response since viscoelasticity and extensional viscosity are negligible for dilute solutions of this substance. As the flow is forced to turn the corner of the T-junction, a range of shear rates, and hence viscosities, is produced. If this feature could be incorporated into a viscometer, then potentially the constitutive parameters of a complex fluid could be ascertained from a single experiment. A mathematical model based on a finite element technique has been developed to simulate the fluid flow in the experimental system. Model predictions of the velocity field are found to agree well (less than 5% error) with observations, thus validating the model.