We present quantitative experimental data on colloidal laning at the single-particle level. Our results demonstrate a continuous increase in the fraction of particles in a lane for the case where oppositely charged particles are driven by an electric field. This behavior is accurately captured by Brownian dynamics simulations. By studying the fluctuations parallel and perpendicular to the field we identify the mechanism that underlies the formation of lanes.Far from thermodynamic equilibrium, a wealth of fascinating selforganization processes can emerge along with unusual pattern formation and novel transport properties. 1,2 One of the simplest prototypes of non-equilibrium pattern formation is lane formation, exhibited by dusty plasmas, 3,4 granular matter, 5 pedestrian dynamics, 6,7 and army ants. 8 In this paper, we characterize the patterning and dynamical signatures of lane formation in a colloidal system experimentally and with computer simulations. Our results may find use in electronic ink, which also contains oppositely charged colloids that are driven by electric fields. 9,10 A fundamental and microscopic understanding of non-equilibrium phenomena requires resolving the underlying dynamical processes on the scale of the individual particles. For this, colloidal dispersions are excellent model systems since they can be brought out of equilibrium in a controlled way by external fields and the trajectories of the individual particles can be tracked in real space using confocal microscopy, which allows unparalleled comparison with computer simulation and particle-level theory. 11-13 Here, we first study the formation of lanes in driven colloidal mixtures as a function of the driving strength using both experiments and Brownian dynamics computer simulations. Lane formation in this 3D system is found to be a continuous process as a function of driving field. Starting from an initial mixed state, the dynamical mechanism behind the formation of lanes is identified: there is an enhanced lateral mobility of particles induced by collisions with particles driven in the opposite direction, which sharply decreases once lanes are formed. Therefore, particles in a lane can be regarded as being in a dynamically 'locked-in' state.In our experiments, we used a binary dispersion of sterically stabilized, nearly equal sized, but oppositely charged polymethylmethacrylate (PMMA) spheres inside a rectangular capillary. The particles were synthesized by dispersion polymerization, 14 and fluorescently labeled with either 7-nitrobenzo-2-oxa-1,3-diazole (NBD) or rhodamine isothiocyanate (RITC). The two species are color-coded as 'green' (s green ¼ 1.06 mm, polydispersity 6%, NBDlabeled) and 'red' (s red ¼ 0.91 mm, polydispersity 7%, RITC-labeled). The overall volume fraction of the suspension f green (0.090) + f red (0.090) was 0.18.To match the density and refractive index of the particles with the solvent, the particles were dispersed in a mixture of 27.2 w% cisdecahydronaphthalene and cyclohexylbromide containing 75 mM tetrabut...

A dynamical density functional theory (DDFT) for translational Brownian dynamics is derived which includes hydrodynamic interactions. The theory reduces to the simple Brownian DDFT proposed by Marconi and Tarazona (U. Marini Bettolo Marconi and P. Tarazona, J. Chem. Phys. 110, 8032 (1999); J. Phys.: Condens. Matter 12, A413 (2000)) when hydrodynamic interactions are neglected. The derivation is based on Smoluchowski's equation for the time evolution of the probability density with pairwise hydrodynamic interactions. The theory is applied to hard-sphere colloids in an oscillating spherical optical trap which switches periodically in time from a stable confining to an unstable potential. Rosenfeld's fundamental measure theory for the equilibrium density functional is used and hydrodynamics are incorporated on the Rotne-Prager level. The results for the time-dependent density profiles are compared to extensive Brownian dynamics simulations which are performed on the same Rotne-Prager level and excellent agreement is obtained. It is further found that hydrodynamic interactions damp and slow the dynamics of the confined colloid cluster in comparison to the same situation with neglected hydrodynamic interactions.

A density functional theory for colloidal dynamics is presented which includes hydrodynamic interactions between the colloidal particles. The theory is applied to the dynamics of colloidal particles in an optical trap which switches periodically in time from a stable to unstable confining potential. In the absence of hydrodynamic interactions, the resulting density breathing mode, exhibits huge oscillations in the trap center which are almost completely damped by hydrodynamic interactions. The predicted dynamical density fields are in good agreement with Brownian dynamics computer simulations.

We generalize the formalism of dynamical density functional theory for translational Brownian dynamics toward that of anisotropic colloidal particles which perform both translational and rotational Brownian motion. Using a mean-field approximation for the density functional and a Gaussian-segment model for the rod interaction, the dynamical density functional theory is then applied to a concentrated rod suspension in a confined slab geometry made by two parallel soft walls. The walls are either expanded or compressed and the relaxation behavior is investigated for an equilibrated starting configuration. We find distinctly different orientational ordering during expansion and compression. During expansion we observe preferential parallel ordering of the rods relative to the wall while during compression there is homeotropic ordering perpendicular to the wall. We find a nonexponential relaxation behavior in time. Furthermore, an external field which aligns the rods perpendicular to the walls is turned on or switched off and similar differences in the relaxational dynamics are found. Comparing the theoretical predictions to Brownian dynamics computer simulation data, we find good agreement.

A binary mixture of oppositely charged colloids which is driven by an external electric field is studied by extensive Brownian dynamics computer simulations, ignoring hydrodynamic interactions. The particle interaction is modeled via a screened Coulomb potential together with a steric repulsion. A strong electric field leads to lane formation of oppositely driven lanes. Each lane comprises particles of the same charge. A nonequilibrium "phase diagram" classifying different steady states is obtained as a function of the colloidal volume fraction and the Coulomb coupling. Different steady states are characterized by structural correlations perpendicular and parallel to the applied field. We find a variety of different phases involving lane chains at small volume fraction and low screening, and lanes with two-dimensional crystalline order perpendicular to the field at high volume fraction. The lateral crystalline order can be a square, triangular, or rhombic lattice. In between there is a lateral network structure. These predictions can be verified in real-space experiments on oppositely charged colloids.