Progress in the Understanding of the Fluctuating Lattice Boltzmann Equation

We give a brief account of the development of methods to include thermal fluctuations into lattice Boltzmann algorithms. Emphasis is put on our recent work (Phys. Rev. E 76, 036704 (2007)) which provides a clear understanding in terms of statistical mechanics.Comment: Conference paper for CCP 2008, submitted to Computer Physics Communication

An improved dissipative coupling scheme for a system of Molecular Dynamics particles interacting with a Lattice Boltzmann fluid

We consider the dissipative coupling between a stochastic Lattice Boltzmann (LB) fluid and a particle-based Molecular Dynamics (MD) system, as it was first introduced by Ahlrichs and D\"unweg (J. Chem. Phys. 111 (1999) 8225). The fluid velocity at the position of a particle is determined by interpolation, such that a Stokes friction force gives rise to an exchange of momentum between the particle and the surrounding fluid nodes. For efficiency reasons, the LB time step is chosen as a multiple of the MD time step, such that the MD system is updated more frequently than the LB fluid. In this situation, there are different ways to implement the coupling: Either the fluid velocity at the surrounding nodes is only updated every LB time step, or it is updated every MD step. It is demonstrated that the latter choice, which enforces momentum conservation on a significantly shorter time scale, is clearly superior in terms of stability and accuracy, and nevertheless only marginally slower in terms of execution speed. The second variant is therefore the recommended implementation.Comment: 16 pages, 6 figure

Lattice Boltzmann simulations of soft matter systems

This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview over the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures, 76 page

Capillary filling with wall corrugations] Capillary filling in microchannels with wall corrugations: A comparative study of the Concus-Finn criterion by continuum, kinetic and atomistic approaches

We study the impact of wall corrugations in microchannels on the process of capillary filling by means of three broadly used methods - Computational Fluid Dynamics (CFD), Lattice-Boltzmann Equations (LBE) and Molecular Dynamics (MD). The numerical results of these approaches are compared and tested against the Concus-Finn (CF) criterion, which predicts pinning of the contact line at rectangular ridges perpendicular to flow for contact angles theta > 45. While for theta = 30, theta = 40 (no flow) and theta = 60 (flow) all methods are found to produce data consistent with the CF criterion, at theta = 50 the numerical experiments provide different results. Whilst pinning of the liquid front is observed both in the LB and CFD simulations, MD simulations show that molecular fluctuations allow front propagation even above the critical value predicted by the deterministic CF criterion, thereby introducing a sensitivity to the obstacle heigth.Comment: 25 pages, 8 figures, Langmuir in pres

Hydrodynamic Spinodal Decomposition: Growth Kinetics and Scaling Functions

We examine the effects of hydrodynamics on the late stage kinetics in spinodal decomposition. From computer simulations of a lattice Boltzmann scheme we observe, for critical quenches, that single phase domains grow asymptotically like $t^{\alpha}$, with $\alpha \approx .66$ in two dimensions and $\alpha \approx 1.0$ in three dimensions, both in excellent agreement with theoretical predictions.Comment: 12 pages, latex, Physical Review B Rapid Communication (in press