The many-particle Langevin equation, written in local coordinates, is used to derive a Brownian dynamics simulation algorithm to study the dynamics of colloids moving on curved manifolds. The predictions of the resulting algorithm for the particular case of free particles diffusing along a circle and on a sphere are tested against analytical results, as well as with simulation data obtained by means of the standard Brownian dynamics algorithm developed by Ermak and McCammon [J. Chem. Phys. 69, 1352 (1978)] using explicitly a confining external field. The latter method allows constraining the particles to move in regions very tightly, emulating the diffusion on the manifold. Additionally, the proposed algorithm is applied to strong correlated systems, namely, paramagnetic colloids along a circle and soft colloids on a sphere, to illustrate its applicability to systems made up of interacting particles.

In the same sense as in the extended law of corresponding states [M. Noro and D. Frenkel, J. Chem. Phys. 113, 2941 (2000)], we propose the use of the second virial coefficient to map the hard-sphere potential onto a continuous potential. We show that this criterion provides accurate results when the continuous potential is used, for example, in computer simulations to reproduce the physical properties of systems with hard-core interactions. We also demonstrate that this route is straightforwardly applicable to any spatial dimension, does not depend on the particle density and, from a numerical point of view, is easy to implement.

Confinement modifies the properties of a fluid. The particle density is no longer uniform but depends on the distance from the walls; parallel to the walls, layers with different particle...

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