Pattern formation in binary fluids confined between rough, chemically heterogeneous surfaces.

Using a mesoscale model for hydrodynamics, we simulate driven flow of AB binary fluids past surfaces that contain well-defined roughness or asperities. The geometry and wetting properties of the asperities are found to have a dramatic effect on the flow patterns. We isolate conditions where the A fluid forms vertical bands that bridge the asperities and an imposed shear (or pressure gradient) drives the system to form monodisperse droplets of A within the B fluid. The size of the droplets can be tailored by varying the morphology of the asperities. The surfaces needed to create this rich dynamical behavior are used as the stamps in microcontact printing; thus, the parameter space can readily be accessed experimentally, and the predictions suggest an efficient method for forming emulsions with well-controlled morphologies.

Simulation of chemical erosion in rough fractures.

We report on numerical simulations of acid erosion in a fractured specimen of Carrara marble. The simulations combine two recent advances in lattice-Boltzmann methodology to accurately and efficiently calculate the velocity field in the pore space. A tracer diffusion algorithm was then used to calculate the distribution of reactants in the fracture, and the local erosion rate was obtained from the flux of tracer particles across the surfaces. Our results show that at large length scales, erosion leads to increased heterogeneity via channel formation, whereas at small length scales it tends to smooth out the roughness in the local aperture.

Accuracy and stability of a lattice-Boltzmann model with subgrid scale boundary conditions.

A lattice-Boltzmann method has recently been developed to incorporate solid-fluid boundary conditions on length scales less than the grid spacing. By introducing a real numbered parameter, specified at each node and representing the fluid volume associated with that node, we were able to accurately simulate arbitrary geometries without the need to specify surface normals. In this paper a detailed description of the rules is presented and the accuracy and stability of the method is discussed, based on numerical results for flow in systems with planar surfaces and for flow through periodic arrays of disks and spheres.

Lattice-boltzmann model with sub-grid-scale boundary conditions

A lattice-Boltzmann method has been developed to incorporate solid-fluid boundary conditions on length scales less than the grid spacing. By introducing a continuous parameter, specified at each node and representing the fluid volume fraction associated with that node, we obtain second-order accuracy for boundaries at arbitrary positions and orientations with respect to the grid. The method does not require surface normals, and can therefore be applied to irregular geometries such as porous media. The new rules conserve mass and momentum, and reduce to the link bounce-back rule at aligned interfaces.

Simulation of low-Reynolds-number flow via a time-independent lattice-Boltzmann method.

We present a numerical method to solve the equations for low-Reynolds-number (Stokes) flow in porous media. The method is based on the lattice-Boltzmann approach, but utilizes a direct solution of time-independent equations, rather than the usual temporal evolution to steady state. Its computational efficiency is 1-2 orders of magnitude greater than the conventional lattice-Boltzmann method. The convergence of the permeability of random arrays of spheres has been analyzed as a function of mesh resolution at several different porosities. For sufficiently large spheres, we have found that the convergence is quadratic in the mesh resolution.