Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces

Multiphase lattice Boltzmann simulations for porous media applications

“…1 Single phase flow in a segmented, μCT image of a Dolomite sample including a a rendering of the pore volume (i.e. the complement of the rock volume) in the sample and b the steady state flow profile in the sample as computed by the LBM with bounce-back boundary conditions the mean-field theory model [87] and the stabilized diffuseinterface model [88]. In this section, we review these models with emphasis on some recent improvements and show their advantages and limitations for pore-sale simulation of multiphase flows in porous media.…”

“…C = 0 for the gas phase while C = 1 for the liquid phase). Assuming that interactions between the fluids and the solid surface are of short-range and appear in a surface integral, the total free energy of a system is taken as the following form [88], (72) where the bulk energy is taken as E 0 = βC 2 (1−C) 2 with β being a constant, κ is the gradient parameter, C s is the order parameter at a solid surface, and φ i with i = 0, 1, 2, · · · are constant coefficients. The chemical potential μ is defined as the variational derivative of the volume-integral term in Eq.…”

“…In order to prevent the negative equilibrium density on a non-wetting surface, it is necessary to retain the higher order terms in S . By choosing φ 0 = φ 1 = 0, φ 2 = 1 2 φ c , and φ 3 = 1 3 φ c , a cubic boundary condition for ∇ 2 C is established [88],…”

“…One is the order parameter distribution function, which is used to capture the interface between different phases, and the other is the pressure distribution function for solving the hydrodynamic pressure and fluid momentum. The evolution equations of the PDFs can be derived through the discrete Boltzmann equation (DBE) with the trapezoidal rule applied along characteristics over the time interval (t, t + δ t ) [88]. To ensure numerical stability in solving HDR problems, the second-order biased difference scheme is applied to discretize the gradient operators involved in forcing terms at the time t while the standard central difference scheme is applied at the time t + δ t [88,142].…”

“…The evolution equations of the PDFs can be derived through the discrete Boltzmann equation (DBE) with the trapezoidal rule applied along characteristics over the time interval (t, t + δ t ) [88]. To ensure numerical stability in solving HDR problems, the second-order biased difference scheme is applied to discretize the gradient operators involved in forcing terms at the time t while the standard central difference scheme is applied at the time t + δ t [88,142]. The resulting evolution equations are [144],…”