| Complex fluids are liquid mixtures that exhibit unique macroscopic properties when deformed due to the interaction between the suspending fluid and its microstructural components. These components may consist of polymer molecules, solid particles, immiscible drops, or bubbles. Current understanding and modeling of complex fluid behavior is limited due to the difficulty of describing collective hydrodynamic interactions between the suspended media; in the past, dilute or mean-field approximations were required to achieve progress. In this work, we employ numerical simulations to study non-equilibrium phase transitions in polymer solutions and suspensions of slender, rigid fibers. Such non-equilibrium phase transitions occur on the microstructural level in the presence of an external forcing and result in a fundamental shift in macroscopic behavior.;We first study the coil-to-stretch phase transition in dilute solutions of long chain polymer molecules subject to mixed linear flows. In these systems, the coupling between the molecular drag from the imposed flow and thermal motion create unique polymer unraveling dynamics which depend on flow type. Specifically, we show that the effect of increasing flow vorticity is to create configurational fluctuations in polymers, which increase the coil-stretch transition rate. Using a combination of Brownian dynamics simulation and newly developed analytic theory, we show that in extension-dominated mixed flows, the coil-stretch transition can be understood in terms of a Taylor dispersion analysis. We also evaluate the effect of the flow type on the coil-stretch hysteresis observed by Schroeder et al. (2006).;In addition to those of polymers, this work investigates the non-equilibrium phase transitions of suspensions of rigid fibers. Two different transitions are studied: the instability of fiber suspensions in sedimentation and the development of non-uniform concentration profiles in pressure driven flow. The sedimentation instability is driven by interparticle hydrodynamic interactions which amplify concentration fluctuations as particles settle, resulting in densification and particle streamer formation. We begin by using a mean field analysis and Brownian dynamics simulation to evaluate the effect of thermal motion on the instability formation. We find that suspensions with large thermal energy (as compared to gravitational energy) resist phase transition and remain well-mixed. Additionally, we probe the ability of electric fields to stabilize suspensions of polarizable Brownian fibers by inducing orientation in the particle microstructure. Interestingly, we discover a unique region of phase behavior where thermal motion can induce instability and phase transition by mitigating the stabilizing effects of the electric field.;This thermally induced instability, which we have named Brownian demixing, is then shown to be a universal phenomenon in suspension mechanics and will occur whenever Brownian motion couples with an externality that induces orientation in the suspension microstructure. Again, we employ a general mean field theory and Brownian dynamics simulation to demonstrate the importance of demixing in wall-bound particulate suspensions such as those contained within microfluidic devices. Finally, we examine suspensions of Brownian fibers subject to pressure-driven channel flow. We find that steady, non-uniform concentration profiles develop in the wall-normal direction due to shear-induced alignment effects. Because the concentration profiles are length-dependent, we provide a preliminary study on the efficacy of using pressure-driven nanochannels to drive length-based particle separation. |
