A hybrid fluctuating hydrodynamics and kinetic Monte Carlo method for modeling chemically-powered nanoscale motion

We present a stochastic multiscale method for modeling heterogeneous catalysis at the nanoscale. The system is decomposed into the fluid domain and the catalyst-fluid interface. We implemented the fluctuating hydrodynamics framework to model the diffusion of the chemical species in the fluid domain, and the chemical master equation to describe the catalytic activity at the interface. The coupling between the domains occurs simultaneously. Using a simple one-dimensional (1D) linear model, we showed that the predictions of our scheme are in excellent agreement with deterministic simulations. The method was specifically developed to model the spatially asymmetric catalysis on the surface of self-propelled nanoswimmers. Numerical simulations showed that our approach can estimate the uncertainty in the swimming velocity resulting from inherent stochastic nature of the chemical reactions at the catalytic interface. Although the method has been applied to simple 1D and 2D models, it can be generalized to handle different geometries and more sophisticated chemical reactions. Therefore, it can serve as a practical mathematical tool to study how the efficiency of chemically powered nanomachines is affected by the interplay between structural complexity, nonlinear reactivity, and nonequilibrium fluctuations.