Jean-Christophe Desplat

LUDWIG: A parallel Lattice-Boltzmann code for complex fluids

This paper describes Ludwig, a versatile code for the simulation of Lattice-Boltzmann (LB) models in 3D on cubic lattices. In fact, Ludwig is not a single code, but a set of codes that share certain common routines, such as I/O and communications. If Ludwig is used as intended, a variety of complex fluid models with different equilibrium free energies are simple to code, so that the user may concentrate on the physics of the problem, rather than on parallel computing issues. Thus far, Ludwigs main application has been to symmetric binary fluid mixtures. We first explain the philosophy and structure of Ludwig which is argued to be a very effective way of developing large codes for academic consortia. Next we elaborate on some parallel implementation issues such as parallel I/O, and the use of MPI to achieve full portability and good efficiency on both MPP and SMP systems. Finally, we describe how to implement generic solid boundaries, and look in detail at the particular case of a symmetric binary fluid mixture near a solid wall. We present a novel scheme for the thermodynamically consistent simulation of wetting phenomena, in the presence of static and moving solid boundaries, and check its performance.

3D spinodal decomposition in the inertial regime

We simulate late-stage coarsening of a 3D symmetric binary fluid using a lattice Boltzmann method. With reduced lengths and times l and t respectively (scales set by viscosity, density and surface tension) our data sets cover 1 100 we find clear evidence of Furukawas inertial scaling (l ~ t^{2/3}), although the crossover from the viscous regime (l ~ t) is very broad. Though it cannot be ruled out, we find no indication that Re is self-limiting (l ~ t^{1/2}) as proposed by M. Grant and K. R. Elder [Phys. Rev. Lett. 82, 14 (1999)].

Simulating colloid hydrodynamics with lattice Boltzmann methods

We present a progress report on our work on lattice Boltzmann methods for colloidal suspensions. We focus on the treatment of colloidal particles in binary solvents and on the inclusion of thermal noise. For a benchmark problem of colloids sedimenting and becoming trapped by capillary forces at a horizontal interface between two fluids, we discuss the criteria for parameter selection, and address the inevitable compromise between computational resources and simulation accuracy.

Lattice Boltzmann for Binary Fluids with Suspended Colloids

A new description of the binary fluid problem via the lattice Boltzmann method is presented which highlights the use of the moments in constructing two equilibrium distribution functions. This offers a number of benefits, including better isotropy, and a more natural route to the inclusion of multiple relaxation times for the binary fluid problem. In addition, the implementation of solid colloidal particles suspended in the binary mixture is addressed, which extends the solid–fluid boundary conditions for mass and momentum to include a single conserved compositional order parameter. A number of simple benchmark problems involving a single particle at or near a fluid–fluid interface are undertaken and show good agreement with available theoretical or numerical results

Nonequilibrium steady states in sheared binary fluids

We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture undergoing phase separation with full hydrodynamics in two dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite domain lengths L(x,y) in the directions (x,y) of velocity and velocity gradient. Apparent scaling exponents are estimated as Lx approximately gamma (-2/3) and Ly approximately gamma(-3/4). We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.

Binary fluids under steady shear in three dimensions

We simulate by the lattice Boltzmann method the steady shearing of a binary fluid mixture with full hydrodynamics in three dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite correlation lengths in all three spatial directions. Using large simulations, we obtain at moderately high Reynolds numbers apparent scaling exponents comparable to those found by us previously in two dimensions (2D). However, in 3D there may be a crossover to different behavior at low Reynolds number: accessing this regime requires even larger computational resources than used here.

Interfacial dynamics in 3D binary fluid demixing: animation studies

The late-stage phase ordering, in three dimensions, of fully symmetric binary fluid mixtures is studied via a lattice Boltzmann method. We present time-resolved maps of the fluid velocity fields and also animated visualizations of the interfacial motion. These show distinct features corresponding to regimes where viscous, crossover and inertial hydrodynamic scaling have previously been identified. Specifically, while the interface is overdamped in the viscous regime, it exhibits recoil after topological reconnection at intermediate and higher inertia; and in our most inertial runs the interface shows extensive underdamped capillary disturbances not attributable to topological reconnection events. The advantages and practicality of presenting such dynamical data in fully animated form are demonstrated and briefly discussed. This papers animations are available from the Multimedia Enhancements page as individual files and also packed into archives (two formats).

LB Simulation of 3D Spinodal Decomposition in the Inertial Regime

Abstract We present simulation results of late-stage coarsening of a 3D symmetric binary fluid using a lattice Boltzmann method on a 2563 grid. With reduced lengths and times L, T (scales set by viscosity, density and surface tension) our datasets taken together cover 1 < L < 105, 10 < T < 108, equivalent to Reynolds numbers 0.1 < Re < 350.At Re < 100 we find clear evidence of Furukawas inertial scaling (L proportional to T 2/3), after a very broad crossover from the viscous regime (L proportional to T).