Under partial confinement, the motion of colloidal particles is restricted to a plane or a line but their dynamics is influenced by hydrodynamic interactions mediated by the unconfined, three-dimensional flow of the embedding fluid. We demonstrate that this dimensionality mismatch induces a characteristic divergence in the collective diffusion coefficient of the colloidal subsystem. This result, independent of the specific interparticle forces in the colloid, is solely due to the kinematical constraint on the colloidal particles, and it is different from the known divergence of transport coefficients in purely one or two-dimensional fluids.

Using Brownian dynamics simulations, density functional theory, and analytical perturbation theory we study the collapse of a patch of interfacially trapped, micrometer-sized colloidal particles, driven by longranged capillary attraction. This attraction is formally analogous to two-dimensional (2D) screened Newtonian gravity with the capillary length^as the screening length. Whereas the limit^! 1 corresponds to the global collapse of a self-gravitating fluid, for finite^we predict theoretically and observe in simulations a ringlike density peak at the outer rim of a disclike patch, moving as an inbound shock wave. Possible experimental realizations are discussed. DOI: 10.1103/PhysRevLett.107.128302 PACS numbers: 82.70.Dd, 47.11.Mn, 47.40.Àx The dynamics of matter under the influence of longranged attractions is studied intensively in several branches of physics [1], in particular, with respect to inherent instabilities. Most prominently, the structure formation in the universe is understood as the consequence of an instability in self-gravitating matter, and cosmological theories in conjunction with numerical simulations have been successfully applied to explain the dynamical formation of clusters, galaxies, or dark matter halos on large scales [2]. More recently, other systems with gravitational-like attractions have been investigated, including seemingly unrelated phenomena like bacterial chemotaxis [3,4] or capillary-driven clustering in colloids trapped at fluid interfaces [5,6]. In these systems the interaction is effectively cut off beyond a finite range, albeit much larger than the mean interparticle separation.In a self-gravitating fluid any homogeneous mass distribution is unstable with respect to small fluctuations on sufficiently large scales [7] (Jeans's instability). In systems with a cutoff gravitational-like attraction, this instability only occurs below a critical temperature [4,5]. As the range of the interaction is scaled [6] from infinity down to a microscopic length like the size of the particles, the dynamical evolution of the instability crosses over from gravitational collapse to spinodal decomposition. A standard theoretical approach to the gravitational collapse in cosmology is the so-called cold collapse approximation (see, e.g., Ref.[8]), within which any force other than gravity (in particular the thermal pressure of the fluid) is neglected altogether. The view on applications to other physical situations raises the natural question of how the phenomenology of this scenario is affected by a nonvanishing thermal pressure and a large but finite range of attractions and specifically how the crossover to the spinodal decomposition scenario occurs.Colloidal particles with radii in the micrometer range, which are trapped at a fluid interface, lend themselves to study this issue. Their weight results in a force f on each particle perpendicular to the interface which deforms it and gives rise to long-ranged capillary interactions between the particles. For large colloid center-to-center ...

The evolution of an initially prepared distribution of micron-sized colloidal particles, trapped at a fluid interface and under the action of their mutual capillary attraction, is analyzed by using Brownian dynamics simulations. At a separation λ given by the capillary length of typically 1mm, the distance dependence of this attraction exhibits a crossover from a logarithmic decay, formally analogous to two-dimensional gravity, to an exponential decay. We discuss in detail the adaptation of a particle-mesh algorithm, as used in cosmological simulations to study structure formation due to gravitational collapse, to the present colloidal problem. These simulations confirm the predictions, as far as available, of a mean-field theory developed previously for this problem. The evolution is monitored by quantitative characteristics which are particularly sensitive to the formation of highly inhomogeneous structures. Upon increasing λ the dynamics shows a smooth transition from the spinodal decomposition expected for a simple fluid with short-ranged attraction to the self-gravitational collapse scenario.