(746a) A Lattice Kinetic Monte Carlo Method for Advective Systems

The lattice kinetic Monte Carlo (LKMC) method is a particularly appealing mesoscopic technique for simulating spatially-resolved particulate systems because of its inherent simplicity, computational efficiency, and versatility. However, the vast majority of LKMC simulations have been applied towards problems in which diffusion is the sole transport mechanism, i.e., in which external flow is absent. Example applications are extremely diverse, ranging from defect diffusion in metals and semiconductors [1], to crystal growth [2], to thrombosis in blood flow [3]. Recently, Flamm et al. [4,5] introduced an LKMC algorithm for including advective particle transport in a prescribed fluid flow field. In this technique, the advective force exerted on each particle due to fluid flow was used to augment particle hopping rates in the direction of the fluid flow. The algorithm was shown to predict accurately the temporal evolution of a collection of particles under strongly non-equilibrium conditions, including two-dimensional Taylor dispersion in a straight channel and in an expansion flow. However, the method was not evaluated under equilibrium, or weakly non-equilibrium, conditions where adherence to detailed balance becomes relevant.

Here, we develop and analyze new rate expressions for advective LKMC for particulate flow situations. Using equilibrium and non-equilibrium test problems, we show that the new algorithm is able to correctly predict particle dynamics under general flow conditions, while also satisfying detailed balance. In the equilibrium case, the method is analyzed in the context of biased particle diffusion in a non-linear potential field, and the results compared to those from Metropolis Monte Carlo simulations. Using this comparison, we show that the new technique exactly satisfies detailed balance. Next, Taylor dispersion simulations are used to probe the performance of the method in a non-equilibrium setting. Using Brownian dynamics (BD) simulations as a reference, we demonstrate a relationship between the LKMC lattice spacing and the BD timestep. This relationship is used to derive formal error estimates for LKMC simulation of advection-diffusion problems. We conclude by discussing the relative computational advantages of BD and LKMC.

[1] J. Dai, J. M. Kanter, S. S. Kapur, W. D. Seider, and T. Sinno, Phys. Rev. B 72, 134102 (2005).

[2] A. C. Levi and M. Kotrla, J. Phys.: Condens. Matter 9, 299 (1997).

[3] M. H. Flamm et al., Blood 120, 190 (2012).

[4] M. H. Flamm, S. L. Diamond, and T. Sinno, J. Chem. Phys. 130, 094904 (2009).

[5] M. H. Flamm, T. Sinno, and S. L. Diamond, J. Chem. Phys. 134, 034905 (2011).