## Final Report Summary - DYCOCOS (Dynamics of Confined Complex Suspensions)

“Soft Matter” is a research area denoting the study of a broad range of materials including polymers, liquid crystals, colloidal suspensions and soft biological materials. Typically in these materials a hydrodynamic flow is directly connected to the steady state behavior of these soft deformable materials. This is especially the case with colloidal particles (typically micrometer sized spheres) suspended in a Newtonian fluid such as water. Here any external or internal stimuli can lead to complex reorganization, owing to both local interactions between particles and long-range hydrodynamic interactions. Another example is provided by liquid crystals (LCs) which are typically anisotropic molecules which can exhibit mesophases with both fluid and cristalline characteristics. Finally, a third example where hydrodynamic interactions are important, is provided by so called self-propelling particles, which are out-of-equilibrium even in steady state. This document provides an example of all three of these different cases.

The overall goal of the project is to study the hydrodynamics of confined complex fluids (both colloidal suspensions and liquid crystals) in the means of the large scale hydrodynamic simulations using lattice Boltzmann (LB) method. The project had two main parts: (1) hydrodynamics of driven colloidal suspensions and (2) out-of-equilibrium states in confined liquid crystals.

The main part of (1) concentrated on colloidal sedimentation in cylindrical confinement. This interfaced strongly with an experimental work in the host laboratory, where it was experimentally observed that in a reasonably tight confinement the overall sedimentation speed of initially uniform particle distribution could be signifigantly increased, and even to exceed previous theoretical expectations. We carried out an extensive simulation study, where the results suggest that the hydrodynamically induced fluctuations are not strong enough to lead to a large enough microphase separation to explain the experimentally observed increase of sedimentation velocity in cylindrical capillaries. Further on, the simulations have lead to critical review of the experimental protocol used and possibly could lead to further improved experiments in the future.

These simulations were subsequently expanded to study the effects of the initial particle distribution and confining geometry. Here the extensive simulations have been carried out concentrating on "plug-configuration" (an initial configuration where all the particles are tightly packed in top of the container and quiescent fluid below) and systematically varying the confinement ratio d/D (where d is the particle diameter and D is the diameter of the confining cylinder). The simulations have shown the initial dynamics crucially depends on the ratio d/D, thus highlighting the importance of the confining geometry. Corresponding experiments are undergoing in the host laboratory.

Finally the simulations were extended to so called active particles. Here we considered two different models: so called squirming model for truly hydrodynamic microswimmer and rod-like active Brownian particles in a circular confinement. The squirmer model was used to study the experimentally observed trapping of swimmers at surfaces. This is a standard experimental observation, however the exact theoretical details remains unsolved. We used hydrodynamic simulations to show, that the coupling between hydrodynamics and short-range repulsive interactions between the swimmer and the surface can lead to hydrodynamic trapping of both pushers and pullers at the wall, and to hydrodynamic oscillations in the case of a pusher. It was further shown that the presence of a wall can signifigantly increase the swimming speed compared to bulk or lead to a dynamic standstill depending on the range of the repulsive interactions and the nature of the swimmer.

Recently we also developed a model for a rod-like active Brownian particle, based on Langevin dynamics. This work is a recent collaboration with the university of Bordeaux, where experimental work is undergoing on dry granular active particles. It is anticipated that inertia will play an important role in these systems, thus the newly developed computational model could be instrumental in understanding these systems in greater detail.

The second part of the project concerned out-of-equilibrium liquid crystals. These are are complex fluids with some kind of order. This can be either orientational or translational as well as a combination of these. In the simplest case with only orientational order, the system is called nematic, where all the molecules, on average, point in the same direction, characterized by a nematic director. When chiral molecules are mixed with the nematic liquid crystal, the system adopts a state with a helical twist of the director.

Using a large-scale simulation model we studied a binary fluid system consisting of a simple fluid component (such as oil or water) and a complex fluid component (a chiral liquid crystal in our case). The simulations revealed very rich behavior, where the isotropic fluid could be distributed in spherical droplets arrested by the LC matrix, akin to solid particles, or for example distributed on tubes spanning the whole sample, in which case the topology of the simple fluid would be set by the liquid crystalline host. In the inverse case, when the chiral liquid crystal was confined into droplets surrounded by the isotropic phase, we observed multitude of different topological states. These could be very important for next generation energy saving device applications for example.

The overall goal of the project is to study the hydrodynamics of confined complex fluids (both colloidal suspensions and liquid crystals) in the means of the large scale hydrodynamic simulations using lattice Boltzmann (LB) method. The project had two main parts: (1) hydrodynamics of driven colloidal suspensions and (2) out-of-equilibrium states in confined liquid crystals.

The main part of (1) concentrated on colloidal sedimentation in cylindrical confinement. This interfaced strongly with an experimental work in the host laboratory, where it was experimentally observed that in a reasonably tight confinement the overall sedimentation speed of initially uniform particle distribution could be signifigantly increased, and even to exceed previous theoretical expectations. We carried out an extensive simulation study, where the results suggest that the hydrodynamically induced fluctuations are not strong enough to lead to a large enough microphase separation to explain the experimentally observed increase of sedimentation velocity in cylindrical capillaries. Further on, the simulations have lead to critical review of the experimental protocol used and possibly could lead to further improved experiments in the future.

These simulations were subsequently expanded to study the effects of the initial particle distribution and confining geometry. Here the extensive simulations have been carried out concentrating on "plug-configuration" (an initial configuration where all the particles are tightly packed in top of the container and quiescent fluid below) and systematically varying the confinement ratio d/D (where d is the particle diameter and D is the diameter of the confining cylinder). The simulations have shown the initial dynamics crucially depends on the ratio d/D, thus highlighting the importance of the confining geometry. Corresponding experiments are undergoing in the host laboratory.

Finally the simulations were extended to so called active particles. Here we considered two different models: so called squirming model for truly hydrodynamic microswimmer and rod-like active Brownian particles in a circular confinement. The squirmer model was used to study the experimentally observed trapping of swimmers at surfaces. This is a standard experimental observation, however the exact theoretical details remains unsolved. We used hydrodynamic simulations to show, that the coupling between hydrodynamics and short-range repulsive interactions between the swimmer and the surface can lead to hydrodynamic trapping of both pushers and pullers at the wall, and to hydrodynamic oscillations in the case of a pusher. It was further shown that the presence of a wall can signifigantly increase the swimming speed compared to bulk or lead to a dynamic standstill depending on the range of the repulsive interactions and the nature of the swimmer.

Recently we also developed a model for a rod-like active Brownian particle, based on Langevin dynamics. This work is a recent collaboration with the university of Bordeaux, where experimental work is undergoing on dry granular active particles. It is anticipated that inertia will play an important role in these systems, thus the newly developed computational model could be instrumental in understanding these systems in greater detail.

The second part of the project concerned out-of-equilibrium liquid crystals. These are are complex fluids with some kind of order. This can be either orientational or translational as well as a combination of these. In the simplest case with only orientational order, the system is called nematic, where all the molecules, on average, point in the same direction, characterized by a nematic director. When chiral molecules are mixed with the nematic liquid crystal, the system adopts a state with a helical twist of the director.

Using a large-scale simulation model we studied a binary fluid system consisting of a simple fluid component (such as oil or water) and a complex fluid component (a chiral liquid crystal in our case). The simulations revealed very rich behavior, where the isotropic fluid could be distributed in spherical droplets arrested by the LC matrix, akin to solid particles, or for example distributed on tubes spanning the whole sample, in which case the topology of the simple fluid would be set by the liquid crystalline host. In the inverse case, when the chiral liquid crystal was confined into droplets surrounded by the isotropic phase, we observed multitude of different topological states. These could be very important for next generation energy saving device applications for example.

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**Record Number**: 192287 /

**Last updated on**: 2016-12-08