Power law fluid viscometry through capillary filling in a closed microchannel

Abstract

In this work we analyze the capillary filling dynamics of non-Newtonian fluids that can be modeled with a power law constitutive equation. We solve the Poiseuille equations for an hydrophilic closed channel where capillary pressures drives the fluid in until a rest position given by the barometric pressure is reached. We show that this dynamics can be used to measure both the coefficient k and exponent n, that describes the power law fluid viscosity and we ran tests on Soda Lime Glass microchannels. Using a simple experimental setup with a USB Microscope and a custom image processing software we were able to measure the power law parameters of whole blood, wall varnish and DI water. The exponents were also obtained from the velocity profiles inside the microchannel using a custom μPIV setup matching both results with those measured with a standard Brookfield Rotational Microviscometer.