Our research is of theoretical and computational nature, and focuses on mesoscale theories of nonequilibrium phenomena in extended systems, with applications to Materials Science and Soft Matter Physics. The evolution of systems outside of thermodynamic equilibrium generically involves unstable boundaries and moving topological defects. The mesoscale offers a convenient platform in which to bridge traditional microscopic theory and atomistic simulation of non equilibrium and fully macroscopic descriptions of transport models that need to accommodate discontinuities at moving boundaries and singular fields at defects. We develop mesocale models, analyze their multiple scale asymptotics, and obtain their non equilibrium properties through large scale computation. Our research is currently motivated by the study of microstructure evolution in materials science, and fluid flows of topological origin in nematic suspensions.
Mesoscale theory of defected materials
A current objective in Materials Science, “reversing the arrow: materials by design”, calls for the development of theoretical and computational inverse methods to design materials that have specified properties and function. Such an inverse optimization problem requires robust solutions to the forward problem involved in the determination of macroscopic properties as a function of the nano and mesoscopic properties and composition of the material. Although great progress has been achieved in the inverse design of materials close to thermodynamic equilibrium, most materials, specially soft solids, are rarely uniform, but rather exhibit complex and often evolving microstructure. Therefore the standard tools of Solid State Physics and equilibrium Statistical Mechanics do not generally apply. In fact, the strong response of non equilibrium phases to external stresses and perturbations means that their properties strongly depend on interactions with boundaries, preparation methods, and prior history. The aim of our work is to establish the theoretical framework within which to predict structure evolution in non-equilibrium solids, and thus to develop the foundation of reliable forward models of processing-structure-property relationships.
Soft solids present an important class of materials for the study and eventual manipulation of defects in the design of material systems with tailored properties. Their elastic softness presents qualitatively and quantitatively different challenges for the study of collective defect equilibria and dynamics as compared to hard solids. In this sense, they hold great promise to become a practical avenue for allowing the resolution of new qualitative and quantitative questions in the field of defects and nonlinear elasticity theory. The larger size of the effective molecular units that constitute the soft solid not only lowers characteristic energies by several order of magnitude, but also characteristic distances (e.g., size of the unit cell) are much larger (hundreds of nm and above) so that they become accessible by conventional optical diagnostics. Decreases in characteristic energies also lead to shorter characteristic times for defect motion, and hence allow the study of their kinetics and their manipulation. Our research seeks to address key questions about the topological description of the kinematics of a defected solid, the appropriate constitutive laws for dissipative motion of defects, and to develop the theory in parallel with high resolution experiments and numerical analysis of mesoscale models.
Topology driven flows in nematic suspensions
The study of of liquid crystal based suspensions is motivated by applications in materials science as well as in biological systems. At a fundamental level, and in contrast with normal suspending fluids, nematic order in a liquid crystalline matrix leads to long range elastic interactions either among colloidal particles or with bounding walls, resulting in a variety of unexpected phenomena. Furthermore, long range order in the matrix is distorted by the suspended particles, resulting in unavoidable topological defects that must move with the particles. On the one hand, the existence of structure in the liquid matrix affords new opportunities for flow control, processing, and suspension stability. At the same time, and for the same reasons, efficient engineering of these systems requires major advances to our current understanding of simple fluid colloids. From proposals for new display technologies and nanofluidic devices to more fundamental questions about the mechanisms of clustering and de-clustering in systems of particles, new experimental findings call for major modeling and analysis efforts. For example, studies of electrophoresis in structured media can facilitate related efforts in biology to model and control nano-fluidic transport as well as contribute towards understanding of motion of cancer cells and their clustering in tumor metastasis.
The figure above (left) shows the spatial charge distribution induced by a (+1, -1) disclination pair under a uniform but oscillatory electric field normal to the line joining the defects. A (+1) disclination represents a suspended particle with homeotropic anchoring, and the (-1) disclination is the associated hyperbolic hedgehog. Both defects lead to spatial charge separation which, in turn, results in streaming flows (figure on the right), resulting in transport normal to the direction of the applied field. Thus a nematic matrix allows nonlinear anisotropic hydrodynamic mobilities. Effects like this one are being developed to engineer designer flows for use in microfluidic devices, including particle sorting and aggregation (including cell sorting), and stirring and the micro scale.