ABSTRACT
We propose a method to generate statistically similar reconstructions of two-phase media. As with previous work, we initially characterize the microstructure of the material using two-point correlation functions (a subset of spatial correlation functions) and then generate numerical reconstructions using a simulated annealing method that preserves the geometric relationships of the material's phase of interest. However, in contrast to earlier contributions that consider reconstructions composed of discrete arrays of pixels or voxels alone, we generate reconstructions based on assemblies of continuous, three-dimensional, interpenetrating objects. The result is a continuum description of the material microstructure (as opposed to a discretized or pixelated description), capable of efficiently representing large disparities in scale. Different reconstruction methods are considered based on distinct combinations of two-point correlation functions of varying degrees of complexity. The quality of the reconstruction methods are evaluated by comparing the total pore fraction, specific surface area of the percolating cluster, pore fraction of the percolating cluster, tortuosity, and permeability of the reconstructions to those of a set of reference assemblies. Elsewhere it has been proposed that two-phase media could be statistically reproduced with only two spatial correlation functions: the two-point probability function (the probability that two points lie within the same phase) and the lineal path function (the probability that a line between two points lies entirely within the same phase). We find that methods employing the two-point probability function and lineal path function are improved if the percolating cluster volume is also considered in the reconstruction. However, to reproduce more complicated geometric assemblies, we find it necessary to employ the two-point probability, two-point cluster, and lineal path function in addition to the percolating cluster volume to produce a generally accurate statistical reconstruction.
ABSTRACT
This paper describes a method for implementing surface reaction kinetics in lattice Boltzmann simulations. The interpolated boundary conditions are capable of simulating surface reactions and dissolution at both stationary and moving solid-fluid and fluid-fluid interfaces. Results obtained with the boundary conditions are compared to analytical solutions for first-order and constant-flux kinetic surface reactions in a one-dimensional half space, as well as to the analytical solution for evaporation from the surface of a cylinder. Excellent agreement between analytical and simulated results is obtained for a wide range of diffusivities, lattice velocities, and surface reaction rates. The boundary model's ability to represent dissolution in binary fluid mixtures is demonstrated by modeling diffusion from a rising bubble and dissolution of a droplet near a flat plate.
