Liquid Crystals (LCs) are orientationally ordered fluids. In a broader sense, LCs can be thought of as soft matter with orientational order, an emerging class of complex fluids. There are many experiments which show interesting flow phenomena in liquid crystals. We focus on two of these, where vorticity, driven by external sources, creates material flow. In the Janossy effect, dye molecules under photoexcitation in a liquid crystal host act as rotors of molecular motors, and generate vorticity and subsequent flow. In the Yokoyama-Tabe experiment, chiral molecules in a Langmuir monolayer are caused, by a transverse current of water vapor, to rotate and give rise to flow. This award will support work aimed at understanding such phenomena, where local torques, acting essentially as point sources of vorticity, give rise to macroscropic translation and flow. The work will be carried out through an interdisciplinary collaboration involving applied mathematics and physics, with the goal of developing a sound mathematical model which is capable of predicting the dynamical behavior of orientationally ordered systems where flow plays an essential role; and building robust computational tools that will capture the essential features of the interplay between flow and microstructure. The mathematical model we propose has two important components. First, it is the use of the full orientational probability density function, rather than a few of its moments to characterize orientational order. Second, the flow dynamics is included in the model. It is known that inhomogeneous flows play important roles in forming transient microstructures, thus the orientational state must be coupled with the macroscopic flow field. This will lay the framework for the study and design of other complex soft matter systems where flow and local vorticity play important roles. A novel aspect is the exploration of the effectiveness of peer mentoring by graduate students from applied mathematics and physics collaborating on this project.
In the rapidly advancing field of materials science, complex fluids are emerging as an increasingly important class of materials. They are capable of exhibiting a remarkably broad range of behavior in response to excitations, leading to a wide variety of applications. This rich responsivity originates in physical processes which are made possible by complex internal structure. Complex fluids range today from liquid crystals to micro- and nanocolloids, virus suspensions and active biofluids. A key component of many of these systems is orientational order of the constituents. Remarkable and unexpected behavior can result from the coupling between orientational order and translation; this includes rubber lasers and light driven plastic motors. This award will support work aimed at understanding such phenomena, with the goal of building computational tools to describe and to help to understand and utilize the responsible mechanisms. The broader impacts of the proposed work are the usefulness of the developed tools to the larger community in the design of photo-responsive soft matter, metamaterials for transformation optics and strategies for biological transport. They include contributions to science and mathematics education at the graduate level. The two graduate students, one in applied mathematics and one in chemical physics, participating in this project will gain expertise in various aspects of this multifaceted work and will benefit from interactions with more senior members of the research team and each other. A vigorous effort will be made to encourage the participation of women and members of underrepresented groups in this project.
