Viscometry of Nonhomogeneous Flows and the Behavior of a Titanium‐Crosslinked Hydroxypropyl Guar Gel in Couette Flow

Abstract

This work shows that when standard homogeneous fluid viscometry relations are applied to fluids which form rheologically distinct regions during flow (i.e., nonhomogeneous flows), the measured “viscosities” are actually some function of the rheology and geometry of each of these regions. Formulations for these apparent “viscosities” are developed for nonhomogeneous Couette flows, and the analogous formulations for Poiseuille and steady‐slot flows are presented. Explicit formulations are given for fluid regions having power‐law rheology, and predicted trends with assumed region rheology and geometry are shown. Testing of a hydroxypropyl guar (HPG) solution crosslinked with titanium acetylacetonate showed this gel to flow as a nonhomogeneous fluid in Couette flow. This conclusion is based on flow visualization studies and on the difference in the apparent experimental “viscosity” measured when using wide and narrow gap Couette viscometers. For this gel a dramatic reversible change in rheology occurs when the angular velocity is increased to some critical level. At this critical angular velocity, the flow changes from a low shear‐stress apparent‐slip flow to a high shear‐stress nonhomogeneous flow. Apparent‐slip flow data were modeled using a three‐layer nonhomogeneous model.