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Understanding the Collective Behaviour of Catalytically-Driven, Self-Propelled Colloids: From Fine-Grained Hydrodynamic Simulations to Effective Field-Theoretical Descriptions

Periodic Reporting for period 1 - HydroCat (Understanding the Collective Behaviour of Catalytically-Driven, Self-Propelled Colloids: From Fine-Grained Hydrodynamic Simulations to Effective Field-Theoretical Descriptions)

Reporting period: 2015-11-16 to 2017-11-15

Microscopic particles have been used to achieve many industrial goals. For example, they form the basis for cosmetics, and cement. In addition, investigating such particles has a strong biomedical relevance, think blood. Suspensions of passive particles obey the laws of statistical physics, which have been successfully applied to describe a wide range of equilibrium phenomena. However, when taken out of equilibrium, there is an unprecedented richness of dynamics, e.g. the patterns formed by flocks of birds or growing bacterial colonies.

Researchers strive to incorporate the richness of living dynamics into traditional equilibrium systems to create new products. Of technological interest is the enhanced microfluidic mixing that can be achieved by the incorporation of motile (self-propelled) components. Central to the implementation of such features is the development of artificial self-propelled particles. These achieve motion by generating chemical gradients through catalytic surface reactions. Artificial swimmers are preferred over biological ones, because they do not bring any evolutionary baggage into the mix.

Yet, despite artificial self-propelled particles being around since the mid 2000’s, many aspects of the way they achieve motion are poorly understood. This is problematic from an implementation perspective, as better understanding of these particle’s propulsion mechanism will enable the exploration of new propulsion routes that employ non-toxic fuels. Currently, hydrogen peroxide is widely used to fuel the motion of these particles, but this chemical is not biocompatible. Attempts to produce swimmers powered by less harmful chemical fuels have been unsuccessful, thus far.

Finally, full understanding of the nature of the propulsion mechanism of man-made swimmers will facilitate their use as simple model systems to understand out-of-equilibrium systems. Physicist wish to use these particles to study the origin of the complex dynamics observed in living systems, without having the added complications that biological functions such as reproduction and decision-making skills bring about. Artificial swimmers seem ideally suited for the task, as they only self-propel. However, to truly understand the dynamics in these systems one must disentangle the various contributions that are present: fluid flow, chemical fields, contact interactions, etc. Since the presence of chemical gradients is intimately linked with their motion, one must understand the latter fully to be able to extract how the former influences the collective motion of such particles.
In this action, the mechanism by which artificial particles achieve self-propulsion was investigated by theoretical and numerical means. This modeling is necessary to exclude certain self-propulsion mechanisms based on available experimental data. The researcher has developed the numerical methods necessary to model chemically self-propelled swimmers. The main finding of this research is that ions play an important role in the motion of these swimmers. Not just those ions generated by the surface reactions on the swimmer, but also those ions involved in reactions in the bulk. That is, neutral polar molecules are in equilibrium with the ions that they can dissociate into, and these ionic species can modulate the concentration gradients induced by the surface reactions. Such bulk reactions are commonplace, for instance, the reason why pure water has a pH of 7 is because of autocatalysis of water into hydronium and hydroxide ions.

The research into the presence of bulk chemical reactions involving ions is not only relevant to self-propulsion, but it has significant implications for studies into the catalytic properties of substrates. Namely, measuring species concentrations far away from the surface, is not a good means to extract the properties of the surface catalytic processes. This is because bulk reactions can screen the effects of surface reactions and modify the nature of the produced species. Properly accounting for the chemistry in the bulk will provide new insight into the chemistry taking place at the surface. This is crucial to improving many industrial processes that rely on aqueous catalytic reactions.

These results were already exploited to describe the way an ion-exchange resin achieves microfluidic pumping in thoroughly deionized water, in collaboration with the experimental group of Prof. Dr. T. Palberg (Mainz). Surprisingly, the trace amounts of ions present in this system are sufficient to generate strong fluid flows over millimetric ranges, with the ion exchange resin only measuring 50 microns across. This further underpins the importance of ions in the generation of out-of-equilibrium flow fields and has significant implications for the description of many colloidal systems, for which fluid flow was traditionally modeled as originating through the presence of neutral gradients. It may be, that in many instances, the presence of small amounts of ions, in fact, dominates the physics of the system.

The researcher has also elucidated effect of pure hydrodynamic flow on the interaction between particles and swimmers, as well as the effect of typical boundary conditions, such as confining walls and periodic simulation domains, on this interaction. This is a necessary step towards disentangling the components that lead to the onset of collective motion in chemical swimmers. In addition, this research has suggested a new approach to characterize the hydrodynamic properties of micro swimmers. Traditionally, the flow field generated by a swimming organism is mapped by putting many small tracer particles in the fluid and tracking their motion. This is a difficult process. The research performed during the action shows that alternatively, one could simply analyze the trajectory of a single swimmer between two microscope slides and fit the hydrodynamic characteristics of the swimmer directly from that.

The above results were published in peer-reviewed journals including, Soft Matter, The Journal of Chemical Physics, The Journal of Fluid Mechanics, Physical Review E, and Macromolecular Theory and Simulations. In addition, the researcher engaged with the public through the “Bacterial Circus” outreach event at the National Museum of Scotland for the Edinburgh Science Festival 2016. Together with Dr. A. Brown, the researcher developed a model bacterial swimmer to explain elementary school students the difference between swimming on our length scale and that of microorganisms, also see this YouTube video:
The major new pieces of research resulting from the project is the development of an electrokinetic lattice Boltzmann algorithm that includes moving boundary conditions. This numerical method enables the study of fluid systems with solvated ions in the presence of electric field, including moving colloidal and nanoscopic particles. However, this algorithm has a much wider application than the scope of the action, which specifically targeted self-propelled particles. It has already been applied to study the rectification of current and fluid flow in a nanopore ‘diode’ as well as the translocation of a nanoparticle through such a pore. Beyond this, it may also be employed to study the flow of electrolytes through porous materials, which has application in the oil industry and modeling of flow in the human body.
Shape-anisotropic model hydrodynamic swimmers.
Swimming trajectories of a swimmer between two plates.
The effect of bulk association-dissociation reactions on self-electrophoretic swimmers.
Comparison between theoretical and lattice-Boltzmann results for self-electrophoretic swimmers.