Computer simulations of giant fluctuations in mixing fluids

New York University, New York NY

Investigators

Abstract

Thermal fluctuations in non-equilibrium systems exhibit remarkable behavior compared to equilibrium systems. Giant fluctuations in binary mixtures of miscible fluids have been observed, including in recent experiments in microgravity. Novel mathematical and computational challenges need to be addressed in order to include thermal fluctuations in traditional computational fluid dynamics in a way that is consistent with statistical mechanics. This proposal is concerned with the design, mathematical analysis, and computer implementation of finite-volume methods for fluctuating hydrodynamics of fluid mixtures, as well as applications to diffusively mixing fluids in gravity. The following research directions are proposed: (1) Multi-resolution numerical schemes for solving the compressible stochastic continuum equations; (2) Algorithms for incompressible, and (3) low Mach fluctuating hydrodynamics of miscible mixtures on staggered and collocated grids; (4) Simulations of giant fluctuations and comparisons to experiments; (5) Study of the contribution of advection by velocity fluctuations to transport in finite non-equilibrium systems. Flows at micro and nano scales typical of new devices and biological systems are affected by thermal fluctuations. These effects are often assumed small and are not included in traditional computational fluid dynamics. However, giant fluctuations in the concentration of a polymer solution have been observed in recent experiments conducted in microgravity on a research space shuttle. Computer simulations are ideally suited for studying the details of this phenomenon and comparing the predictions of existing theory to the experimental findings. However, our community still lacks the appropriate computational tools, including both algorithms and large-scale parallel codes, to attack this problem. The investigator and his colleagues will develop such tools and use them to answer important scientific questions concerning fluctuations in fluids, in close collaboration with experimentalists. The developed algorithms will be implemented in a public domain code whose development is funded through a Software Infrastructure for Sustained Innovation NSF grant.