Experimental observations and mathematical description of micellar fluid flow

by Handzy, Nestor Zenon.

iii We present results from a study of wormlike micellar fluids which includes experimental data and a theoretical mathematical model. Experimentally we examined the effects of air bubbles rising through solutions of wormlike micelles. A previous study of this problem reported oscillations in the speed of the rising bubble. Our experiments revealed two distinct types of oscillations, which we have called “type I” and “type II”. By mapping the oscillatory instability to a temperature-concentration phase plane we found that type I oscillations occur when the equilibrium average length of micelles is larger than a critical value. Experimental rheology was performed on the same fluids as well, which identified a transition in equilibrium micellar morphology as concentration increases. This transition is found to occur in the same concentration range as the transition from type I to type II oscillations. The rheological results indicate that type I oscillations occur in fluids which consist of entangled wormlike micelles, while the fluids which give type II oscillations consist of wormlike micelles in a “fused” or crosslinked network state. The rheological data also suggest that shear induced structures (SIS) may form in the fluids in which rising bubbles oscillate, and the oscillatory instability is attributed to the formation and subsequent destruction of SIS in the wake of a rising bubble. Birefringent images taken during the free rise of an air bubble support this hypothesis. The experimental results motivate the inclusion of SIS in a constitutive model for wormlike micellar fluids. We consider a wormlike micellar fluids to consist of three types iv of wormlike micelles: short, long, and “bundles” which represent SIS. The concentrations of these three species are coupled to each other through three ordinary differential equations. The ODE’s are then coupled to the Maxwell constitutive model for viscoelastic fluids to yield a new “weighted Maxwell model”. With a detailed examination of the physical meaning of the weighted Maxwell model, we find that further modifications are necessary in order to remain faithful to the physical properties of wormlike micelles. These considerations lead us to develop a new “memory kernel” to include in our weighted Maxwell model. We explain how the modification works and what it means physically. With numerical simulations, we find that our model is capable of capturing the rheological properties of wormlike micellar fluids.