Residence time distribution of a purely viscous non-Newtonian fluid in helically coiled or spatially chaotic flows

Abstract

This work is dedicated to an experimental study of residence time distributions (RTD) of a pseudoplastic fluid in different configurations of helically coiled or chaotic systems. The experimental system is made up of a succession of bends in which centrifugal force generates a pair of streamwise Dean cells. Fluid particle trajectories become chaotic through a geometrical perturbation obtained by rotating the curvature plane of each bend of ±90° with respect to the neighboring ones (alternated or twisted curved ducts). Different numbers of bends, ranging from 3 to 33, were tested. RTD is experimentally obtained by using a two-measurement-point conductimetric method, the concentration of the injected tracer being determined both at the inlet and at the outlet of the device. The experimental RTD is modeled by a plug flow with axial dispersion volume exchanging mass with a stagnant zone. RTD experiments were conducted for generalized Reynolds numbers varying from 30 to 270. The Peclet number based on the diameter of the pipe is found to increase with the Reynolds number whatever the number of bends in the system. This reduction in axial dispersion is due to both the secondary Dean flow and the chaotic trajectories. Globally, the flowing fraction, which is one of the characteristic parameters of the model, increases with the Reynolds number, whatever the number of bends, to reach a maximum value ranging from 90% to 100%. For Reynolds numbers less than 200, the flowing fraction increases with the number of bends. The stagnant zone models fluid particles located close to the tube wall. The pathlines become progressively chaotic in small zones in the cross section and then spread across the flow as the number of bends is increased, allowing more trapped particles to move towards the tube center. Results have been compared with those previously obtained using Newtonian fluids. The values of the Peclet number are greater for the pseudoplastic fluid, the local change of apparent viscosity affecting the secondary flow. For pseudoplastic fluids, the apparent viscosity is lower near the wall and higher at the center of the cross section. The maximum axial velocity is flattened as the flow behavior index is reduced, inducing a decrease of the secondary flow in the central part of the pipe and an acceleration of it near the wall, which reduces the axial dispersion. These results are encouraging for the use of this system as continuous mixer for complex fluids in laminar regime, particularly for small Reynolds numbers.