Chaotic Advection for Thermal Mixing

Abstract Mixing at macroscopic scales is very common in various industrial applications. Industrial processes can bring into play highly viscous or shear-sensitive fluids, and the mixing operation is seldom carried out alone. Often, heating or cooling operations are required before starting another step of the process. Many industrial fluids have non-Newtonian rheological behavior, and their physical properties can also depend on the temperature. These conditions are favorable for the use of the chaotic advection phenomenon to enhance both laminar mixing and heat transport throughout the fluid in a mixing device. The objective of this numerical study was to show how, for an archetypal mixing device (the two-rod mixer), chaotic advection can enhance thermal mixing for three different rheological fluid behaviors: shear-thinning, Newtonian and shear-thickening. The fluid is heated by the walls, and the walls are able to rotate. Two wall boundary conditions are investigated: a fixed wall temperature and a constant wall heat flux. The effects of different parameters (flow configurations, stirring protocols, and periods of modulation) have been studied to promote wall heat transfer by chaotic mixing. To quantify the degree of thermal mixing in the two-rod mixer, we use statistical indicators that characterize the mean value of the time-evolving fluid temperature and its variance. Probability distribution functions of the temperature are also calculated and followed through time to evaluate the quality of the thermal mixing. We show that thermal chaotic mixing is controlled by the topology of the flow near the moving or nonmoving parietal walls. Complex recurrent temperature patterns may arise that reveal the presence of thermal strange eigenmodes. We have found that chaotic advection can improve thermal mixing for both shear-thinning and shear-thickening fluids with an efficiency that is strongly dependent on the choice of the stirring protocol imposed on the walls. Temperature dependence of the fluid viscosity may also alter the flow and thus induce a nonnegligible effect on the thermal chaotic mixing.