High friction limit of the Kramers equation : the multiple time-scale approach

The purpose of the paper is to give a pedagogical introduction to the multiple time-scale technique, on the example of the high friction limit of the Kramers equation. We begin with a discussion of the standard perturbation technique as presented in van Kampen's reference book \refto{VK}, which will be shown to fail in the long-time limit. Application of the multiple time-scale technique avoids these difficulties and leads to a uniform expansion in powers of the inverse of the friction. Analogy with the Chapman-Enskog expansion is discussed.Comment: 14 pages, accepted in American Journal of Physic

Interfacial transport with mobile surface charges and consequences for ionic transport in carbon nanotubes

In this paper, we explore the effect of a finite surface charge mobility on the interfacial transport: conductance, streaming currents, electro- and diffusio-osmotic flows. We first show that the surface charge mobility modifies the hydrodynamic boundary condition for the fluid, which introduces a supplementary term depending on the applied electric field. In particular, the resulting slip length is found to decrease inversely with the surface charge. We then derive expressions for the various transport mobilities, high-lighting that the surface charge mobility merely moderates the amplification effect of interfacial slippage, to the noticeable exception of diffusio-osmosis and surface conductance. Our calculations, obtained within Poisson-Boltzmann framework, highlight the importance of non-linear electrostatic contributions to predict the small concentration/large charge limiting regimes for the transport mobilities. We discuss these predictions in the context of recent electrokinetic experiments with carbon nanotubes

Flow boundary conditions from nano- to micro-scales

The development of microfluidic devices has recently revived the interest in "old" problems associated with transport at, or across, interfaces. As the characteristic sizes are decreased, the use of pressure gradients to transport fluids becomes problematic, and new, interface driven, methods must be considered. This has lead to new investigations of flow near interfaces, and to the conception of interfaces engineered at various scales to reduce flow friction. In this review, we discuss the present theoretical understanding of flow past solid interfaces at different length scales. We also briefly discuss the corresponding phenomenon of heat transport, and the influence of surface slip on interface driven (e.g. electro-osmotic) flows.Comment: submitted to "Soft Matter

Unified non-equilibrium simulation methodology for flow through nanoporous carbon membrane

The emergence of new nanoporous materials, based e.g. on 2D materials, offers new avenues for water filtration and energy. There is accordingly a need to investigate the molecular mechanisms at the root of the advanced performances of these systems in terms of nanofluidic and ionic transport. In this work, we introduce a novel unified methodology for Non-Equilibrium classical Molecular Dynamic simulations (NEMD), allowing to apply likewise pressure, chemical potential and voltage drops across nanoporous membranes and quantifying the resulting observables characterizing confined liquid transport under such external stimuli. We apply the NEMD methodology to study a new type of synthetic Carbon NanoMembranes (CNM), which have recently shown outstanding performances for desalination, keeping high water permeability while maintaining full salt rejection. The high water permeance of CNM, as measured experimentally, is shown to originate in prominent entrance effects associated with negligible friction inside the nanopore. Beyond, our methodology allows to fully calculate the symmetric transport matrix and the cross-phenomena such as electro-osmosis, diffusio-osmosis, streaming currents, etc. In particular, we predict a large diffusio-osmotic current across the CNM pore under concentration gradient, despite the absence of surface charges. This suggests that CNMs are outstanding candidates as alternative, scalable membranes for osmotic energy harvesting.Comment: 13 pages, 16 figures, submitted to J. Chem Phy