Semi-analytical solutions of passive scalar transport in generalized Newtonian fluid flow

Transport during flow of generalized Newtonian fluids (GNFs) appears often in systems that can be treated in a simplified form as either cylindrical tubes or slit openings between parallel plates. Based on the pioneering work of Taylor, analytical solutions for transport in these simplified systems were derived generally. This includes analytical solutions for advection dominated transport, as well as a computation of the enhanced molecular diffusion coefficient in low Peclet number systems. These generally derived solutions were developed without assuming any specific fluid rheology and can predict transport when only a steady velocity field is known. The newly derived general solutions for species transport were applied to Cross and Carreau model fluids using a semi-analytical solution for velocity of these fluids. The semi-analytical solutions derived herein were compared to microscale simulations and showed agreement with the numerical error of those simulations. Because of the general nature of the transport solutions derived herein, these solutions can be applied to other non-Newtonian fluids, such as viscoelastic or viscoplastic fluids, as a straightforward extension of this work.