Boundary conditions for surface reactions in lattice Boltzmann simulations

A surface reaction boundary condition in multicomponent lattice Boltzmann simulations is developed. The method is applied to a test case with nonlinear reaction rates and nonlinear density profiles. The results are compared to the corresponding analytical solution, which shows that the error of the method scales with the square of the lattice spacing.

Figure 1

The analytical solution to the mass flux, as predicted by Eq. (C5) for $c_B/c_A=1$ (top), $c_B/c_A=10$ (middle), and $c_B/c_A={10}^2$ (bottom).

Figure 2

The analytical solution to the density profiles of component $A$ (solid line) and component $B$ (dashed line) for $c_B/c_A=3$ and $\kappa L=2log(c_B/c_A)\approx 2.2$, where $\kappa$ is defined in Eq. (C3d).

Figure 3

The relative difference between the mass flux predicted by the LB simulation and by Eq. (C5). (top) Effect of density curvature. Parameters: $L/\Delta x=4$, $c_B\Delta t/\Delta x=1/\sqrt{3}$, $n=1$, $\left[m_A+m_B\right]/\overline{\rho }\Delta t\Omega \sqrt{c_A^2+c_B^2}=${0.2, 0.53, 1.4, 3.8, 10}, $k\Delta t/\Delta x=${0.010, 0.032, 0.1, 0.32, 1.0}, and $c_B/c_A=2$ ($\square$), 3 ($▿$), 4 ($▵$), 5 ($◊$). The dashed line represents $y\sim x$. (bottom) Effect of reaction curvature. Parameters: $L/\Delta x=4$, $c_B\Delta t/\Delta x=1/\sqrt{3}$, $c_A/c_B=1$, $\left[m_A+m_B\right]/\overline{\rho }\Delta t\Omega \sqrt{c_A^2+c_B^2}=${0.2, 0.53, 1.4, 3.8, 10}, $k\Delta t/\Delta x=${0.010, 0.032, 0.1, 0.32, 1.0}, and $n=4$ ($\square$), 9 ($▿$), 16 ($▵$), 25 ($◊$). The dashed line represents $y\sim x$.