Emergent Colloidal Dynamics Far From Equilibrium
CECAM-HQ-EPFL, Lausanne, Switzerland
A generic out-of-equilibrium dissipative system subjected to a time-dependent energy injection develops nontrivial collective dynamics and large-scale coherent structures, which are far more complex than their equilibrium counterparts [1-24]. The main source of such emergent behavior is the many body dissipative interactions among colloids (steric [2,3], electrostatic , magnetic [5,6]), external (or internal in the case of active self-propelled particles) energy injection, and coupling of particles dynamics to the fluid flow around them. Self-propelled "active colloids" (synthetic swimmers or living microorganisms) are intrinsically out-of-equilibrium, which gives rise to various emergent phenomena, e.g. collective motility, swarming or active clustering of “living crystals” . Dynamics and self-assembly in out-of-equilibrium driven colloidal systems is a rapidly growing area of research aiming towards prediction and discovery of novel multifunctional dynamic architectures that are not generally available at equilibrium . Understanding interactions and emergent dynamics in complex nonequilibrium dissipative system presents a significant theoretical and computational challenge.
Alternating magnetic, electric and hydrodynamic fields have successfully been used to force colloidal systems out of equilibrium and thus to promote new self-organized dynamic structures [9-18]. Static electrical fields in combination with the electro-hydrodynamic convective flows create emergent structures like toroidal vortices and pulsating rings when applied to metallic microparticles immersed in a poorly conducting liquid . AC electric fields and patterned electrodes have been exploited to achieve dynamic templating of 3D colloidal patterns , and the polarization of electric double layers of colloidal rods due to an external alternating electric field is found to give rise to rich phase behavior . Biaxial rotating electric/magnetic fields are a versatile tool to direct colloidal assembly . A variety of low dimensional structures like chains, foams, membranes and clusters exhibiting viscoelastic properties [5, 12, 14, 15] have been observed. Unusual dynamic advection lattices have recently been reported in a suspension of magnetic platelets subjected to a time dependent biaxial magnetic field with a prescribed frequency or phase relation . Magnetic colloidal particles suspended at a liquid–air interface and energized by alternating magnetic fields self-assemble into complex structures and swimmers exhibiting remarkable dynamic behavior due to the additional coupling of particles to liquid through the interface excitations [6, 13, 23, 24]. Coupling via the fluid flow enables synchronization of the dynamics of flagella and cilia on microorganisms and thus plays a crucial role in self-propulsion of such microorganisms at low-Reynolds numbers. Synchronization has been recently exploited also as a tool towards dynamic self-assembly  where magnetic Janus particles assembled in dynamic microtubes in the precessing magnetic field . Finally, the observation of low-Reynolds number turbulence in two meso-scale experimental systems – one living  and one electric-field-driven  – further highlights the close conceptual relationship between driven, dissipative systems and living systems.
Theoretically, some features of the emergent dynamics in driven colloids can be understood in the framework of the amplitude equation (Ginzburg-Landau type equation) [13, 16, 25] coupled to the conservation law equation describing the evolution of the particle density and the Navier-Stokes equation for hydrodynamic flows. Nevertheless, the fundamental microscopic mechanisms leading to the dynamic self-assembly and their relations to the emergent behavior often remain unclear. Computer simulations are practically the only method to theoretically investigate such questions. However, modeling the nonequilibrium self-assembly presents a huge computational challenge due to the complex many-body interactions and collective dynamics on very different time scales. One of the main challenges is to properly account for the particle-fluid coupling. In very confined geometries the structure of the fluid (usually water) governs the dynamics: to properly describe this one needs to resort to atomistic simulations with proper description of hydrogen bonds etc. . Naturally, the length- and time scales accessible are then very limited. On a more coarse grained level, the fluid flow around colloids is modeled by molecular dynamics methods like Lattice-Boltzmann  and Multi Particle Collision Dynamics [28,29]. Flow around a single colloid is characterized by low Reynolds number, which simplifies the treatment of hydrodynamic interaction in these models, however, it becomes difficult to describe collective dynamics of self-assembled structures, which have a larger effective Reynolds number implying that inertial hydrodynamic terms become important. Alternative approach is to describe the colloidal dynamics by molecular dynamics simulations coupled to the Navier-Stokes equations describing large-scale time-averaged hydrodynamic flows generated by the colloids . In all of the coarse grained approaches, exact accounting of the particles-fluid coupling in response to external periodical excitations is computationally challenging and usually simplifying assumptions have to be made. Nevertheless, such models still provide vital information on the mechanisms governing out-of-equilibrium dynamics and self-assembly in colloidal systems. The planned workshop will be an ideal opportunity to create a constructive discussion between researches in the field of non-equilibrium self-assembly on the role of the fluid-particle coupling in the process of dynamic self-assembly and to define appropriate simulation methods to treat this coupling.
Anand Yethiraj (Memorial University) - Organiser & speaker
Jure Dobnikar (Chinese Academy of Sciences) - Organiser
Alexey Snezhko (Argonne National Laboratory) - Organiser & speaker