An experimental study of transitions and instabilities in shear banding fluids using wormlike micellar solutions as model fluids and measurements of velocity fields and critical conditions is proposed. While shear banding, i.e. discontinuities in the velocity gradient in a flowing material, has been reported in a broad range of important materials, including suspensions, emulsions, foams, granular materials, and liquid crystalline polymers, wormlike micellar solution provide a convenient paradigm for studies of shear banding fluids for many reasons. Wormlike micellar solutions show simple viscoelastic behavior that is characterized by a single relaxation time, are easy to prepare, and, in contrast to polymers, are not susceptible to shear-degradation or chain scission. Recent theoretical and experimental work suggests that both interfacial and purely elastic instabilities may occur in these systems. Inertial instabilities are also likely, and these systems thus promise incredibly rich dynamics.
Intellectual Merit : The intellectual merit of the proposal lies in understanding these interactions and scaling in shear banding materials. A Taylor-Couette (TC) flow apparatus, where the flow occurs between concentric, rotating cylinders, will be the model flow for these experimental studies. The TC problem offers a number of unique features that make it ideal for teasing apart the forces that drive instability. First, the role of inertial destabilization for Newtonian fluids has been well-studied, and inertial (centrifugal) destabilization can be completely eliminated if the flow is generated through rotation of only the outer cylinder. Counter-rotation of the cylinders leads to a nodal surface in the base flow where the angular velocity is zero and leads to essentially an "inner" TC geometry bounded by the rotating inner cylinder and the stationary nodal surface, and an "outer" TC geometry bounded by the stationary nodal surface and the rotating outer cylinder. Counter-rotation thus provides a convenient mechanism for introducing both a free (rather than hard, no slip) boundary and a continuously variable length scale for the gap between the cylinders. Purely elastic instabilities in the TC problem are also well-understood and progress has been made in understanding the combination of inertia and elasticity. Shear banding fluids introduce two additional wrinkles: the new length scale introduced by the shear band, and the potential for interfacial instabilities associated with the discontinuity in properties across the shear band. In contrast to elastic instabilities, interfacial instabilities are stabilized by increased curvature. Thus, the TC problem provides a platform for systematically isolating the effects of these three competing instability modes, for understanding the scaling of the modes with curvature, kinematic, and fluid parameters, and for understanding the role of rigid versus free boundary conditions.
Broader Impacts : The broader impacts of the study lie in processing of shear banding materials, which is relevant to a range of industrially important systems, including powders, suspensions, oil sands, and foams. A postdoctoral scientist will receive training and mentoring, as will approximately 6 undergraduates who will be recruited to participate in this research. This research will also be integrated into graduate coursework on transport phenomena and complex fluids at Berkeley.
