Flow enhancement in highly confined fluids: an equilibrium and non-equilibrium molecular dynamics study
B.D. Todd1, S.K. Kannam2, J.S. Hansen3, P.J. Daivis4 and S. De Luca1
1Mathematics, Faculty of Engineering and Industrial Sciences, and Centre for Molecular Simulation, Swinburne University of Technology, Hawthorn, VIC 3150, Australia
2IBM Research Collaboration for Life Sciences, Parkville, VIC 3052, Australia
3Department of Sciences, DNRF Centre “Glass and Time”, IMFUFA, Roskilde University, Roskilde, DK-4000, Denmark
4Applied Physics, School of Applied Sciences, RMIT University, Melbourne VIC 3000, Australia
Flow enhancement is a very important phenomenon for fluids confined to nano- and micro-scale dimensions. Large degrees of slip are believed to be responsible for very large flow enhancements of fluids such as water confined to carbon nanotubes, as reported in experimental and simulation literature. However, the extent of this flow enhancement is hotly debated, with experimental and simulation studies conflicting by as much as several orders of magnitude. In order to help provide solutions to such discrepancies, and hence clarity in this important application of fluid transport at the nano-scale, we present a new method to predict the slip velocity for a system of fluid molecules confined by atomistic walls. Even though flow is an inherently non-equilibrium phenomenon, our derivation is based in equilibrium statistical mechanics, and is seen to remain valid for experimentally accessible flow rates. Our formalism involves computing time correlation functions of relevant measurable fluid properties. These correlation functions are formed for fine-grained slabs of fluid immediately adjacent to the walls. By computing the various correlation functions at equilibrium we are able to extract the slab friction coefficient adjacent to the wall for a limiting slab width, and hence the slip velocity for a highly confined fluid, to extremely high accuracy. We present numerical results from non-equilibrium molecular dynamics (NEMD) simulations of water and methane confined to graphene sheets to verify our theoretical predictions and discuss the advantages and limitations of the current model. We then apply our method to cylindrically confined systems, such as carbon nanotubes (CNTs), and predict flow rate enhancements for water and methane flowing in CNTs of various diameters. Our results are compared with other simulation and experimental data and provide some of the most accurate results available. We furthermore show the limitations of NEMD simulations for high-slip systems and demonstrate that for such systems our equilibrium method is more accurate and computationally far less expensive. We then demonstrate that the molecular structure of fluids itself contributes to flow at the nano-scale, and that the rotation of molecules can significantly impede flow due to a coupling of intrinsic angular and linear momentum. Finally, we demonstrate a novel application of these insights by manipulating slip boundary conditions for highly confined fluid systems, in which we apply a rotating electric field to generate non-mechanical unidirectional pumping of a polar fluid such as water, providing a novel means of fluid actuation for miniaturised nanofluidic devices.