Predicting the Characteristics of Defect Transitions on Curved Surfaces

The energetically optimal position of lattice defects on intrinsically curved surfaces is a complex function of shape parameters. For open surfaces, a simple condition predicts the critical size for which a central disclination yields lower energy than a boundary disclination. In practice, this transition is modified by activation energies or more favorable intermediate defect positions. Here it is shown that these transition characteristics (continuous or discontinuous, first or second order) can also be inferred from analytical, general criteria evaluated from the surface shape. A universal scale of activation energy is found, and the criterion is generalized to predict transition order as symmetries such as that of the shape are broken. The results give practical insight into structural transitions to disorder in many cellular materials of technological and biological importance

Rectified inertial forces on spherical particles in oscillatory fluid flows near interfaces

Inertial microfluidics has become an indispensable tool in engineering science, materials science, health and medicine, among other fields, to precisely control and manipulate particles, cells and vesicles without the need for charges or chemistry. Despite its ubiquitous prevalence, describing effects of small but finite inertia is a fundamental fluid dynamical problem that has not been solved in full generality. One of the most efficient and powerful ways to exploit inertia in low Reynolds number settings is through the use of oscillatory flows, which can be utilized to exert remarkably consistent and controllable forces on fluid-borne objects over millisecond time scales. Particle manipulation in fast oscillatory flows is now a major tool in lab-on-a-chip processing as well as in diagnostic and biomanufacturing applications. While there are several studies that have successfully exploited inertia in experiments, a theoretical understanding of inertial forces on particles in oscillatory flows, crucial for the systematic design of practical lab-on-a-chip applications, has lagged behind. Due to the inherent non-linearity of fluid dynamics, a large class of oscillating flows set up by localized oscillating objects gives rise to irreversible steady motion even at low Reynolds number. It has recently been shown that particle transport in such flows leads to differential displacement and efficient sorting of microparticles. In the first part of the dissertation, we describe inertial forces and their effect on particle motion by incorporating the leading order viscous and inviscid effects near localized oscillating interfaces. Resulting in direct predictions for displacement on steady time scales, the model predicts a richer and qualitatively different behavior from that expected from earlier, simplified radiation-force formalisms. Depending on experimental control parameters, the net effect of interfacial oscillation can be either an attraction to or a repulsion from the interface, and particles can be captured at a fixed distance or released. These results are also verified in comparison with experiments. While this model captures available experimental data well in the low and high frequency limits, it has shortcomings in the intermediate range, important for applications. We revisit the low Reynolds number assumption inherent to the Maxey--Riley (MR) equation, the main theoretical foundation for fluid forces on particles, and find that for particles in flows generated by localized oscillating objects, this assumptions is easily violated and the nonlinear inertial terms can no longer be neglected. Thus, it is precisely the use of localized oscillations in modern microfluidics that is now pushing the envelope of the MR equation, exposing its limits in predicting the emergence and magnitude of observed significant and persistent forces. Based on insights from both experiments and direct numerical simulations of the full Navier--Stokes equations, we systematically quantify inertial forces on particles in general background flows from first-principles, employing a generalized reciprocal-theorem-based approach. Our formalism can be adapted to manifold flow situations typically encountered in inertial microfluidics. Because of their paramount importance in the arsenal of modern microfluidics, we specialize our general theory to oscillatory flows. Through a systematic analytical modeling approach we derive, isolate, and understand these inertial forces and find that they naturally emerge from a combination of particle inertia and spatial oscillatory flow variation, and that they can be quantified through a generalization of the Maxey--Riley equation to cases where that theory has been unable to describe observations. Our formalism predicts additional attractive contributions towards oscillating boundaries even for density-matched particles, a previously unexplained experimental phenomenon. The accuracy of the theory is demonstrated against full scale, three-dimensional direct numerical simulations throughout its range. Having developed a rigorous description of inertial forces on particles in oscillatory flows, the last part of this work focuses on practical utility. The theory is extended to account for the presence of interfaces and arbitrary flows in two dimensions. Using time-scale separation, we derive a system of overdamped ODEs for particle motion on time scales of rectified motion that yields fundamental physical insight and is efficient to compute. We study the transport of finite-sized inertial microparticles under a superposition of streaming and transport flows, focusing on the use of oscillating microbubbles for continuous, high-throughput size or density-based manipulation of microparticles. Our computationally efficient and rigorous model accurately quantifies the magnitude of displacement of particles across streamlines in comparison to experiments. Thus, the proposed formalism offers a systematic and practical approach that augments physical understanding and enables precise model predictions, potentially spurring more compact, reliable, and efficient forms of particle manipulation