Integrated Calendar

Multicomponent systems are ubiquitous in nature and industry. While the physics of binary and ternary liquid mixtures is well-understood, the thermodynamic and kinetic properties of N-component mixtures with N>3 have remained relatively unexplored. Inspired by recent examples of intracellular phase separation, we investigate equilibrium phase behavior and morphology of N-component liquid mixtures within the Flory-Huggins theory of regular solutions. In order to determine the number of coexisting phases and their compositions, we developed a new algorithm for constructing complete phase diagrams, based on numerical convexification of the discretized free energy landscape. Together with a Cahn-Hilliard approach for kinetics, we employ this method to study mixtures with N=4 and 5 components. In this talk I will discuss both the coarsening behavior of such systems, as well as the resulting morphologies in 3D. I will also mention how the number of coexisting phases and their compositions can be extracted with Principal Component Analysis (PCA) and K-Means clustering algorithms. Finally, I will discuss how one can reverse engineer the interaction parameters and volume fractions of components in order to achieve a range of desired packing structures, such as nested "Russian dolls" and encapsulated Janus droplets.

Saturn rings are composed of water-ice particles and traces of rocky materials whose sizes may vary from micro meters to a few meters. A model that describes the observed size distribution considers aggregation and fragmentation of ring particles upon collision and the distribution can be calculated analytically by solving the steady state Smoluchowski equation.

In writing down the deterministic Smoluchowski equation, it is assumed that the total mass is infinite. We try to understand the behavior of the system when the total mass is finite and the effects of Stochasticity becomes important.

Further, it has been observed that the steady state in these systems becomes unstable and shows oscillations for non-local reaction Kernels. We will also discuss the role of non-locality for the case of finite total mass when Stochasticity becomes relevant and see whether oscillations would survive or not.