At the molecular scale, fluids are inherently noisy with thermally induced fluctuations playing a key role in the dynamics. When mechanical instabilities, chemical reactions, and other phenomena at the microscopic scale are sensitive to these fluctuations, fluid behavior at larger scales can be significantly affected. The goal of this project is to develop stochastic numerical methods to simulate these types of multiscale problems arising in fluids. Accurate modeling of these types of multiscale phenomena requires the correct decomposition of the component processes for these fluctuations. The correct treatment of fluctuations is especially important for nonlinear systems, such as those undergoing phase transitions, nucleation, barrier-crossing, Brownian motors, noise-driven instabilities, and combustive ignition to name a few.
Over the last few years, we have developed fluctuating hydrodynamics formulations and numerical methods not only for gas mixtures (based on the compressible Landau-Lifshitz Navier-Stokes equations) but also for liquid mixtures (based on the low Mach number formulation). Our formulations are derived from the principles of nonequilibrium thermodynamics and deal with multi-species systems without the need to assume a solvent species. Our numerical methods are based on the staggered-grid finite-volume approach (preserving the discrete fluctuation-dissipation balance).
Our current focus is on extending the existing low-Mach multi-species framework to electrolyte solutions and incorporating an accurate mesoscopic description of reactions. We aim at developing accurate and robust stochastic numerical methods for the realistic simulation of microfluids under thermal fluctuations.
☞ For more information, contact John B. Bell JBBell@lbl.gov.
Using fluctuating hydrodynamics, solutions may be represented as continuum multispecies flows. However at very small scales this approach may not be able to capture certain features, such as the sharp gradients in charged specied that occur near boundaries in an electrolyte. In these cases the solvent may be represented as a continuous field, while the solute is represented as discrete particles. To acheive this we employ the immersed boundary approach, with individual particles represented by Peskin kernels.
Direct simulation Monte Carlo is a molecular method which can accuratly simulate dilute gases with far greater efficiency than molecular dynamics. It has also been shown to correctly reproduce thermal fluctuations. We apply DSMC both to perform analyses of systems invloving dilute gases, and to validate new applications of fluctuating hydrodynamics.