## Understanding the Dynamics of Complex Fluids Using Microfluidics: Suspensions and Wormlike Micellar Solutions

- Author(s): Hwang, Margaret Yvonne
- Advisor(s): Muller, Susan J
- et al.

## Abstract

Microfluidics are often used to inform the design of applications such as blood additives, high-throughput DNA sequencing, and point-of-care/lab-on-chip diagnostics. The small characteristic length scales in microfluidic systems can be leveraged to maintain low Reynolds numbers Re (ratio of inertial to viscous forces); with a viscoelastic fluid, the length scales can also lead to high elasticity numbers El (ratio of elastic to inertial forces). As a result, flow in microfluidic devices is not turbulent and can be highly elastic, providing a wealth of experimental capabilities. These include multiphase flow manipulation (which can be used to generate monodisperse bubbles and drops), trapping and analysis of single cells, and the development of secondary flows driven by elasticity. This dissertation focuses on three microfluidic studies: 1) microparticle generation and characterization, 2) examination of suspension flow dynamics, and 3) development of elastic instabilities in viscoelastic fluids flowing around a sharp bend.

Microfluidic devices are capable of monodisperse, deformable particle generation, which is advantageous for tuning the specific properties of suspension components. This facilitates the systematic study of individual component properties on suspension flow behavior such as lateral migration and enables the study of suspension flow dynamics. Microfluidics is an ideal platform for studying suspension flow phenomena due to the long entry lengths needed to observe lateral migration. Although these length scales are large in macroscale, potentially on the order of meters, in microscale the entry length can be on the order of centimeters. This work additionally concerns the development of elastic instabilities in wormlike micellar solutions, a class of surfactant-based viscoelastic fluids. Due to the coupling of the elastic nature of wormlike micellar strands and the curvature of the flow streamlines, wormlike micellar solutions in flow can develop secondary flows (vortices). Despite the prevalent use of wormlike micellar solutions in consumer products, in drug delivery, and in drag-reducing agents, their structure and the mechanics of their flow behavior are not well understood. Planar microdevices can be used to investigate purely elastic instabilities that develop from a combination of shear or extensional flows. In contrast to flow in the more commonly studied microfluidic cross slot and contraction geometries, which is predominantly extensional, the flow in a sharp 90-degree bend is shear-dominated.

This dissertation first investigates controlled microparticle generation and characterization. Monodisperse particles of varying size, shape, and deformability were produced using two microfluidic strategies. First, monodisperse emulsion droplets of a crosslinkable polymer solution were generated via a flow-focusing design, in which drops are formed from a central emulsified phase that is focused by adjacent continuous phases, generating well-controlled drop sizes from 45 to 183 µm. Subsequently, droplets were crosslinked either 1) on chip, resulting in spherical particles, or 2) in an external gelation bath, resulting in an assortment of non-spherical, axisymmetric particles. Particle deformability was then quantified using micromechanics in a tapered capillary, where a particle is trapped at the tip of the taper. The shear and compressive moduli were obtained simultaneously by applying a range of hydrostatic pressures on the particle and analyzing the resulting particle deformation. This method allowed for differentiation between shear and compressive moduli and determined an effective modulus for an entire particle rather than a localized modulus. Changing the polymer system, crosslinker concentration, or polymer concentration produced particles with shear moduli (G) ranging over three orders of magnitude, from 0.013 kPa to 26 kPa.

This library of particles was then used for lateral migration studies in long channels. The lower moduli microparticles (G < 0.10 kPa) are sufficiently soft to deform in channel flow, undergoing similar shape transitions as those seen in literature for capsules and vesicles. With increasing viscous shear, initially circular solid elastic particles in confined channel flow form egg-like, triangular, arrowhead, and finally parachute-like shapes. These shapes are distinct from previously reported capsule and vesicle deformation shapes and can be quantified by dimensionless quantities such as circularity, elongation, depth of the dimple at the trailing edge, and radius of curvature at the leading edge of the particle. Correlations were observed between capillary number Ca (ratio of viscous forces to restoring forces, in this case shear modulus) and the deformation as characterized by two parameters: circularity and radius of curvature at the tip. At low Ca, particle deformation is small and circularity is very close to 1; as Ca increases, circularity changes become more significant. Using circularity and radius of curvature at the tip, it is possible to obtain Ca and the corresponding shear modulus for individual particles from their deformation in channel flow.

The final focus of this work is to examine the behavior of wormlike micellar solutions in a shear-dominated flow, particularly considering the flow and instabilities of shear thinning polymeric and wormlike micellar solutions through a microfluidic 90-degree bend. Two wormlike micellar solutions of cetylpyridinium chloride (CPCl) and sodium salicylate (NaSal) in water were investigated. At low NaSal to CPCl ratios, the wormlike micelles were linear; however, at high ratios the wormlike micelles became branched and showed shear banding within a range of shear rates. Microfluidic experiments on all solutions studied revealed unique regimes as secondary flows developed. At a critical Weissenburg number Wi (the ratio of elastic forces to viscous forces in shear), the flow of the polymeric solution transitioned from a steady base flow to a secondary flow that is characterized by the formation of a stationary lip vortex. The wormlike micellar solutions developed intermediate secondary flow behavior as Wi increased before transitioning to a third regime characterized by a time-dependent lip vortex. The linear wormlike micellar solution revealed a second regime similar to the one observed in the polymeric solution, but the branched, shear-banding wormlike micelle solution developed an intermittent outer corner vortex in addition to a time-dependent lip vortex. In contrast, no third regime was apparent in the polymeric solution over the same range of Wi. These differences in flow behavior demonstrate that the stability of elastic flows is a strong differentiator of rheological differences.