Creeping flow analysis of an integrated microfluidic device for rheometry

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.