(669f) Including Convection In Lattice Kinetic Monte Carlo Simulations

Authors: 
Diamond, S. L., University of Pennsylvania


Biological processes such as platelet aggregation in a blood vessel and biofilm formation are complex, multiscale phenomena that are influenced by fluid flow [1,2]. While such phenomena can be modeled entirely on the basis of continuum descriptions, the large number of discrete particles that typically must be considered suggests the application of mesoscopic simulation frameworks, such as Dissipative Particle Dynamics [3], kinetic Monte Carlo [4], and others.

In this talk, we present a lattice kinetic Monte Carlo (LKMC) model for simulating the trajectories of multiple diffusing particles that are subjected to an externally applied flow field, i.e. the flow field is not affected by the mesoscopic distribution of particles, although it can be time varying in general. The LKMC approach effectively coarse-grains out the details of single particle morphology, and is ideally suited for the study of aggregation processes because of its computational efficiency. However, it is generally applied to purely diffusive situations.

The primary input to LKMC simulations is a rate database for each possible particle move on the lattice. We first demonstrate that accounting for the local flow field around a particle with a simple bias in its rate in the direction of the flow leads to a large error in the particle trajectories, even for the case of simple one-dimensional flow. Through a detailed mathematical analysis, we show the origin of this error, and present a new algorithm that allows for the correct simulation of particle motion in systems where both diffusion and convection are present. The algorithm and analysis first are validated by comparing LKMC predictions to analytical results for Taylor-Aris dispersion in parallel plate flow. The new LKMC model is then applied to more complex situations that include two-dimensional flows. Detailed comparisons are made to continuum numerical simulations.

[1] I. V. Pivkin, P. D. Richardson, G. Karniadakis, Proceedings of the National Academy of Sciences 103, 17164 (2006)

[2] C. Picioreanu, M. C. M. van Loosdrecht, J. J. Heijnen, Biotechnology & Bioengineering 72, 205 (2001)

[3] R. D. Groot, P. B. Warren, The Journal of Chemical Physics 107, 4423 (1997)

[4] K. A. Fichthorn, W. H. Weinberg, The Journal of Chemical Physics 95, 1090 (1991)