Rodrigo Soto

Self-assembly of catalytically active colloidal molecules: Tailoring activity through surface chemistry

A heterogeneous and dilute suspension of catalytically active colloids is studied as a nonequilibrium analogue of ionic systems, which has the remarkable feature of action-reaction symmetry breaking. Symmetrically coated colloids are found to join up to form self-assembled molecules that could be inert or have spontaneous activity in the form of net translational velocity and spin depending on their symmetry properties and their constituents. The type of activity can be adjusted by changing the surface chemistry and ambient variables that control the surface reactions and the phoretic drift.

Segregation induced by inelasticity in a vibrofluidized granular mixture.

We investigate the segregation of a dense binary mixture of granular particles that only differ in their restitution coefficient. The mixture is vertically vibrated in the presence of gravity. We find a partial segregation of the species, where most dissipative particles submerge in the less dissipative ones. The segregation occurs even if one type of the particles is elastic. In order to have a complete description of the system, we study the structure of the fluid at microscopic scale (few particle diameters). The density and temperature pair distribution functions show strong enhancements with respect to the equilibrium ones at the same density. In particular, there is an increase in the probability that the more inelastic particles group together in pairs (microsegregation). Microscopically the segregation is buoyancy driven, by the appearance of a dense and cold region around the more inelastic particles.

Statistical mechanics of fluidized granular media: Short-range velocity correlations

A statistical mechanical study of fluidized granular media is presented. Using a special energy injection mechanism, homogeneous fluidized stationary states are obtained. Molecular dynamics simulations and theoretical analysis of the inelastic hard-disk model show that there is a large asymmetry in the two-particle distribution function between pairs that approach and separate. Large velocity correlations appear in the postcollisional states due to the dissipative character of the collision rule. These correlations can be well-characterized by a state dependent pair correlation function at contact. It is also found that velocity correlations are present for pairs that are about to collide. Particles arrive at collisions with a higher probability that their velocities are parallel rather than antiparallel. These dynamical correlations lead to a decrease of the pressure and of the collision frequency as compared to their Enskog values. A phenomenological modified equation of state is presented.

Temperature inversion in granular fluids under gravity

We study, via hydrodynamic equations, the granular temperature profile of a granular fluid under gravity and subjected to energy injection from a base. It is found that there exists a turn-up in the granular temperature and that, far from the base, it increases linearly with height. We show that this phenomenon, observed previously in experiments and computer simulations, is a direct consequence of the heat flux law, different form Fouriers, in granular fluids. The positive granular temperature gradient is proportional to gravity and a transport coefficient μ0, relating the heat flux to the density gradients, that is characteristic of granular systems. Our results provide a method to compute the value μ0 for different restitution coefficients. The theoretical predictions are verified by means of molecular dynamics simulations, and the value of μ0 is computed for the two-dimensional inelastic hard sphere model. We provide, also, a boundary condition for the temperature field that is consistent with the modified Fouriers law.

Sudden Chain Energy Transfer Events in Vibrated granular Media

In a mixture of two species of grains of equal size but different mass, placed in a vertically vibrated shallow box, there is spontaneous segregation. Once the system is at least partly segregated and clusters of the heavy particles have formed, there are sudden peaks of the horizontal kinetic energy of the heavy particles, that is otherwise small. Together with the energy peaks the clusters rapidly expand and the segregation is partially lost. The process repeats once segregation has taken place again, either randomly or with some regularity in time depending on the experimental or numerical parameters. An explanation for these events is provided based on the existence of a fixed point for an isolated particle bouncing with only vertical motion. The horizontal energy peaks occur when the energy stored in the vertical motion is partly transferred into horizontal energy through a chain reaction of collisions between heavy particles.

Run-and-tumble dynamics in a crowded environment: persistent exclusion process for swimmers.

The effect of crowding on the run-and-tumble dynamics of swimmers such as bacteria is studied using a discrete lattice model of mutually excluding particles that move with constant velocity along a direction that is randomized at a rate α. In stationary state, the system is found to break into dense clusters in which particles are trapped or stopped from moving. The characteristic size of these clusters predominantly scales as α(-0.5) in both one and two dimensions. For a range of densities, due to cooperative effects, the stopping time scales as T(1d)(0.85) and as T(2d)(0.8), where T(d) is the diffusive time associated with the motion of cluster boundaries. Our findings might be helpful in understanding the early stages of biofilm formation.

Fluctuation-Induced Casimir Forces in Granular Fluids

We numerically investigate the behavior of driven noncohesive granular media and find that two fixed large intruder particles, immersed in a sea of small particles, experience, in addition to a short-range depletion force, a long-range repulsive force. The observed long-range interaction is fluctuation-induced and we propose a mechanism similar to the Casimir effect that generates it: The hydrodynamic fluctuations are geometrically confined between the intruders, producing an unbalanced renormalized pressure. An estimation based on computing the possible Fourier modes explains the repulsive force and is in qualitative agreement with the simulations.

Self-assembly of active colloidal molecules with dynamic function.

Catalytically active colloids maintain nonequilibrium conditions in which they produce and deplete chemicals and hence effectively act as sources and sinks of molecules. While individual colloids that are symmetrically coated do not exhibit any form of dynamical activity, the concentration fields resulting from their chemical activity decay as 1/r and produce gradients that attract or repel other colloids depending on their surface chemistry and ambient variables. This results in a nonequilibrium analog of ionic systems, but with the remarkable novel feature of action-reaction symmetry breaking. We study solutions of such chemically active colloids in dilute conditions when they join up to form molecules via generalized ionic bonds and discuss how we can achieve structures with time-dependent functionality. In particular, we study a molecule that adopts a spontaneous oscillatory pattern of conformations and another that exhibits a run-and-tumble dynamics similar to bacteria. Our study shows that catalytically active colloids could be used for designing self-assembled structures that possess dynamical functionalities that are determined by their prescribed three-dimensional structures, a strategy that follows the design principle of proteins.

Nonlinear analysis of the shearing instability in granular gases

It is known that a finite-size homogeneous granular fluid develops a hydrodynamiclike instability when dissipation crosses a threshold value. This instability is analyzed in terms of modified hydrodynamic equations: first, a source term is added to the energy equation which accounts for the energy dissipation at collisions and the phenomenological Fourier law is generalized according to previous results. Second, a rescaled time formalism is introduced that maps the homogeneous cooling state into a nonequilibrium steady state. A nonlinear stability analysis of the resulting equations is done which predicts the appearance of flow patterns. A stable modulation of density and temperature is produced that does not lead to clustering. Also a global decrease of the temperature is obtained, giving rise to a decrease of the collision frequency and dissipation rate. Good agreement with molecular dynamics simulations of inelastic hard disks is found for low dissipation.

A two-sphere model for bacteria swimming near solid surfaces

We present a simple model for bacteria like Escherichia coli swimming near solid surfaces. It consists of two spheres of different radii connected by a dragless rod. The effect of the flagella is taken into account by imposing a force on the tail sphere and opposite torques exerted by the rod over the spheres. The hydrodynamic forces and torques on the spheres are computed by considering separately the interaction of a single sphere with the surface and with the flow produced by the other sphere. Numerically, we solve the linear system which contains the geometrical constraints and the force-free and torque-free conditions. The dynamics of this swimmer near a solid boundary is very rich, showing three different behaviors depending on the initial conditions: (1) swimming in circles in contact with the wall, (2) swimming in circles at a finite distance from the wall, and (3) swimming away from it. Furthermore, the order of magnitude of the radius of curvature for the circular motion is in the range 8-50μm, ...