Simple criterion for vortex formation in the channel flow of power-law fluids

Vortices can have negative effects on the processing of various flows in industrial engineering. Thus, there have been many attempts to seek vortex-free operating conditions. This study explores the feasibility of applying the flow reversal condition in the Couette-Poiseuille (C-P) flow of power-law fluid to the prediction of vortex birth. In previous studies, flow reversal conditions are explicitly expressed only in terms of the pressure gradient. In certain industrial flows, which involve various traits of C-P flows such as slot coating, the flow rate is the key operating parameter, which needs to be precisely controlled. Therefore, in this work, we analytically derived a critical flow-rate condition for the flow reversal to occur in planar C-P flows. The critical condition was compared with the computationally-predicted vortex formation conditions in the slot coating flow. The flow reversal condition, despite its simplicity, successfully predicted the onset of vortex birth in the downstream slot coating flow for power-law fluids. Moreover, the result suggested that stronger shear-thinning effect allows a wider range of vortex-free operating conditions.