Parametric analysis of the transient back extrusion flow to determine instantaneous viscosity

Abstract

Rotational rheometers are extremely sensitive instruments that are able to provide very accurate measurements of low values of different material functions, such as viscosity and viscoelastic moduli, under certain ideal flow conditions. Nevertheless, they fail in providing reliable data for the viscosity when measured at short time scales due to either instrument or fluid inertia. In 1948, Bikerman [“A penetroviscometer for very viscous liquids,” J. Colloid Sci. 3, 75 (1948)] proposed the penetroviscometer device as an instrument to measure the viscosity of highly viscous (102–104\u2009Pa · s) Newtonian fluids under steady shear conditions. In the penetroviscometer, the fluid sample undergoes a kind of flow, which is currently known as back extrusion flow, and it is nowadays used to characterize the rheological properties of foodstuff under steady flow conditions. In this study, we perform a parametric analysis (blockage ratio, initial position, velocity profile of the inner cylinder, and viscosity of Newtonian fluids) of the back extrusion flow to determine its potential to provide reliable viscosity measurements at short time scales. Three-dimensional numerical simulations including free surface effects and inertial terms allowed us to determine its limits of operation. We additionally provide an analytical expression to calculate the time-resolved viscosity, relating the force and velocity of the inner cylinder by means of a geometric factor.