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.

We consider two systems of active swimmers moving close to a solid surface, one being a living population of wild-type E. coli and the other being an assembly of self-propelled Au-Pt rods. In both situations, we have identified two different types of motion at the surface and evaluated the fraction of the population that displayed ballistic trajectories (active swimmers) with respect to those showing randomlike behavior. We studied the effect of this complex swimming activity on the diffusivity of passive tracers also present at the surface. We found that the tracer diffusivity is enhanced with respect to standard Brownian motion and increases linearly with the activity of the fluid, defined as the product of the fraction of active swimmers and their mean velocity. This result can be understood in terms of series of elementary encounters between the active swimmers and the tracers.

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 $\alpha$. 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 ${\alpha }^{-0.5}$ in both one and two dimensions. For a range of densities, due to cooperative effects, the stopping time scales as ${\mathcal{T}}_{1d}^{0.85}$ and as ${\mathcal{T}}_{2d}^{0.8}$, where ${\mathcal{T}}_d$ is the diffusive time associated with the motion of cluster boundaries. Our findings might be helpful in understanding the early stages of biofilm formation.

The induced diffusion of tracers in a bacterial suspension is studied theoretically and experimentally at low bacterial concentrations. Considering the swimmer–tracer hydrodynamic interactions at low Reynolds number and using a kinetic theory approach, it is shown that the induced diffusion coefficient is proportional to the swimmer concentration, their mean velocity and a coefficient $\beta $ , as observed experimentally. This paper shows that $\beta $ increases as a result of the interaction with solid surfaces. The coefficient $\beta $ scales as the tracer–swimmer cross-section times the mean square displacement produced by single scattering events, which depends on the swimmer propulsion forces. Considering simple swimmer models (acting on the fluid as two monopoles or as a force dipole), it is shown that $\beta $ increases for decreasing swimming efficiencies. Close to solid surfaces, the swimming efficiency degrades and, consequently, the induced diffusion increases. Experiments on wild-typeEscherichia coliin a Hele-Shaw cell, under buoyant conditions, are performed to measure the induced diffusion on tracers near surfaces. The modification of the suspension pH varies the swimmers’ velocity over a wide range, allowing the $\beta $ coefficient to be extracted with precision. It is found that solid surfaces modify the induced diffusion: decreasing the confinement height of the cell, $\beta $ increases by a factor of 4. The theoretical model reproduces this increase, although there are quantitative differences, probably attributed to the simplicity of the swimmer models and to the estimates for the parameters that modelE. coli.

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.

We present an experimental study of density and order fluctuations in the vicinity of the solid-liquid-like transition that occurs in a vibrated quasi-two-dimensional granular system. The two-dimensional projected static and dynamic correlation functions are studied. We show that density fluctuations, characterized through the structure factor, increase in size and intensity as the transition is approached, but they do not change significantly at the transition itself. The dense, metastable clusters, which present square symmetry, also increase their local order in the vicinity of the transition. This is characterized through the bond-orientational order parameter Q4, which in Fourier space shows an Ornstein-Zernike-like behavior. Depending on the filling density and vertical height, the transition can be of first- or second-order type. In the latter case, the associated correlation length $\xi${}4, the relaxation time $\tau${}4, the zero k limit of Q4 fluctuations (static susceptibility), the pair correlation function of Q4, and the amplitude of the order parameter obey critical power laws, with saturations due to finite size effects. Their respective critical exponents are $\nu${}$\perp${}=1, $\nu${}$\parallel${}=2, $\gamma${}=1, $\eta${}=0.67, and $\beta${}=1/2, whereas the dynamical critical exponent z=$\nu${}$\parallel${}/$\nu${}$\perp${}=2. These results are consistent with model C of dynamical critical phenomena, valid for a nonconserved critical order parameter (bond-orientation order) coupled to a conserved field (density).