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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 (µ-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.