Decomposing thermal fluctuations in fluids with hydrodynamic modes*

Presenter:
Xiaohui Deng
Authors
Xiaohui Deng (Hong Kong University of Sci&Tech)
Xiaoyu Wei (Hong Kong University of Sci&Tech)
Xiaoping Wang (Hong Kong University of Sci&Tech)
Ping Sheng (Hong Kong University of Sci&Tech)

Abstract
Thermal fluctuations are usually manifest as tiny displacement velocity variations or as molecular self diffusion. We report the analytic solution of the complete set of 2D hydrodynamic modes in a channel geometry, under the Navier slip boundary condition. By using this complete set, thermal fluctuations and their consequences can be expressed in terms of the hydrodynamic modes. In particular, the fluctuation dissipation theorem can be written in terms of the eigenvalues of the hydrodynamic modes as an expression for the diffusion constant D. Our work offers a new perspective on fluid system’s inherent thermal fluctuations and its reliance on the boundary condition. In particular, it offers a way to spatially tune the thermal fluctuations by modulating the hydrodynamic boundary condition