Non-equilibrium assembly and phase behavior of colloidal particles in active liquids

Abstract

The thesis explores the complex interactions and phase behavior of colloidal particles in active liquids, focusing particularly on systems where large, non-Brownian colloids are dispersed in suspensions of Escherichia coli. The non-equilibrium assembly of colloids has recently gained significant attention due to its potential to create novel structures with properties unattainable in equilibrium systems.\\

Our research combines both experimental and numerical approaches to explore the dynamic clustering phenomena that arise from the interplay between the activity of the system and the effective attractive potential among colloids. The strength of this effective potential can be tuned by varying the size ratio of passive to active particles. A larger size ratio results in stronger effective interactions, which in turn leads to the formation of larger clusters of passive particles. Simulations also show that at sufficiently large size ratios, macroscopic phase separation can occur.\\ Further investigation into the phase separation of colloids reveals novel coarsening features. Similar to a binary mixture in equilibrium systems undergoing phase separation via spinodal decomposition, our system exhibits a spinodal-like route to phase separation. A homogeneous mixture of colloids and swimmers is unstable, leading the colloidal particles to form clusters that grow in size over time. The spatial correlations of a suitable scalar order parameter exhibit dynamic scaling, similar to equilibrium systems. However, the length scale of the clusters grows as $L(t)\sim t^{1/4}$ over the experimental time scales, suggesting slower growth than predicted by the Lifshitz-Slyozov law. The nature of the interfaces and the effect of activity on these interfaces is explored by closely examining the correlation functions.\\ An interesting aspect of our systems is the chirality of microswimmers. E. coli cells break their chiral symmetry when swimming close to solid boundaries. The interaction between these chiral swimmers and colloidal particles gives rise to chiral colloidal rotors. Furthermore, their assembly due to effective interactions results in dynamic clusters with persistent rotations, which markedly differ from those formed in equilibrium systems. At sufficiently high densities, our system exhibits several hallmark features of a percolation transition. A closer examination of the critical exponents associated with cluster size distribution, the average cluster size, and the correlation length near the critical density reveals deviations from the predictions of the standard continuum percolation model. Consequently, our experiments reveal a richer phase behavior of colloidal assemblies in active liquids.\\ In addition to studying collective behaviors, this thesis also examines the dynamics of individual colloidal particles in active media. Unlike Brownian particles, which display a Gaussian distribution in displacement, the colloids in active media show deviations from this form. These deviations depend on the size of the colloidal particles. We have characterized these deviations and interpreted the results using the concept of superstatistics. Finally, the dynamic clustering of colloids in the steady state was analyzed using aggregation and fragmentation models, by constructing a transition matrix and applying a monomer approximation.\\