Thermal fluctuations of hydrodynamic flows in nanochannels

Flows at the nanoscale are subject to thermal fluctuations. In this work, we explore the consequences for a fluid confined within a channel of nanometric size. First, the phenomenon is illustrated on the basis of molecular dynamics simulations. The center of mass of the confined fluid is shown to perform a stochastic, non-Markovian motion, whose diffusion coefficient satisfies Einstein's relation, and which can be further characterized by the fluctuation relation. Next, we develop an analytical description of the thermally induced fluid motion. We compute the time- and space-dependent velocity correlation function, and characterize its dependence on the nanopore shape, size, and boundary slip at the surface. The experimental implications for mass and charge transports are discussed for two situations. For a particle confined within the nanopore, we show that the fluid fluctuating motion results in an enhanced diffusion. The second situation involves a charged nanopore in which fluid motion within the double layer induces a fluctuating electric current. We compute the corresponding contribution to the current power spectrum.