Prediction of onset of Taylor-Couette instability for shear-thinning fluids

The definition of Reynolds number (Re) in a Taylor-Couette flow for a shear-thinning fluid is discussed in this paper. Since the shear-thinning property causes spatial distribution of fluid viscosity in a Taylor-Couette flow reactor (TCFR), a method to determine Re by using a numerical simulation is suggested. The effective viscosity (η eff) in Re was the average viscosity using a weight of dissipation function $$ {\eta}_{\mathrm{eff}}={\displaystyle \sum_{i=1}^N{\overset{\cdot }{\gamma}}_i^2{\eta}_i\Delta {V}_i}/{\displaystyle \sum_{i=1}^N{\overset{\cdot }{\gamma}}_i^2\Delta {V}_i}, $$ where N is the total mesh number, η i (Pa·s) is the local viscosity, $$ {\overset{\cdot }{\gamma}}_i $$ (1/s) is the local shear-rate, and ΔV i (m3) is the local volume for each cell. The critical Reynolds number, Re cr, at which Taylor vortices start to appear, was almost the same value with the Re cr obtained by a linear stability analysis for Newtonian fluids. Consequently, Re based on η eff could be applicable to predict the occurrence of Taylor vortices for a shear-thinning fluid. In order to understand the relation between the rotational speed of the inner cylinder and the effective shear rate that resulted in η eff, a correlation equation was constructed. Furthermore, the critical condition at which Taylor vortices appear was successfully predicted without further numerical simulation.