Hybrid molecular-continuum simulations of water flow through carbon nanotube membranes of realistic thickness

We present new hybrid molecular-continuum simulations of water flow through filtration membranes. The membranes consist of aligned carbon nanotubes (CNTs) of high aspect ratio, where the tube diameters are ~1–2 nm and the tube lengths (i.e. the membrane thicknesses) are 2–6 orders of magnitude larger than this. The flow in the CNTs is subcontinuum, meaning standard continuum fluid equations cannot adequately model the flow; also, full molecular dynamics (MD) simulations are too computationally expensive for modelling these membrane thicknesses. However, various degrees of scale separation in both time and space in this problem can be exploited by a multiscale method: we use the serial-network internal-flow multiscale method (SeN-IMM). Our results from this hybrid method compare very well with full MD simulations of flow cases up to a membrane thickness of 150 nm, beyond which any full MD simulation is computationally intractable. We proceed to use the SeN-IMM to predict the flow in membranes of thicknesses 150 nm–2 μm, and compare these results with both a modified Hagen–Poiseuille flow equation and experimental results for the same membrane configuration. We also find good agreement between experimental and our numerical results for a 1-mm-thick membrane made of CNTs with diameters around 1.1 nm. In this case, the hybrid simulation is orders of magnitude quicker than a full MD simulation would be

Molecular dynamics pre-simulations for nanoscale computational fluid dynamics

We present a procedure for using molecular dynamics (MD) simulations to provide essential fluid and interface properties for subsequent use in computational fluid dynamics (CFD) calculations of nanoscale fluid flows. The MD pre-simulations enable us to obtain an equation of state, constitutive relations, and boundary conditions for any given fluid/solid combination, in a form that can be conveniently implemented within an otherwise conventional Navier–Stokes solver. Our results demonstrate that these enhanced CFD simulations are then capable of providing good flow field results in a range of complex geometries at the nanoscale. Comparison for validation is with full-scale MD simulations here, but the computational cost of the enhanced CFD is negligible in comparison with the MD. Importantly, accurate predictions can be obtained in geometries that are more complex than the planar MD pre-simulation geometry that provides the nanoscale fluid properties. The robustness of the enhanced CFD is tested by application to water flow along a (15,15) carbon nanotube, and it is found that useful flow information can be obtained

Multiscale simulation of nanofluidic networks of arbitrary complexity

We present a hybrid molecular-continuum method for the simulation of general nanofluidic networks of long and narrow channels. This builds on the multiscale method of Borg et al. (Microfluid Nanofluid 15(4):541–557, 2013; J Comput Phys 233:400–413, 2013) for systems with a high aspect ratio in three main ways: (a) the method has been generalised to accurately model any nanofluidic network of connected channels, regardless of size or complexity; (b) a versatile density correction procedure enables the modelling of compressible fluids; (c) the method can be utilised as a design tool by applying mass-flow-rate boundary conditions (and then inlet/outlet pressures are the output of the simulation). The method decomposes the network into smaller components that are simulated individually using, in the cases in this paper, molecular dynamics micro-elements that are linked together by simple mass conservation and pressure continuity relations. Computational savings are primarily achieved by exploiting length-scale separation, i.e. modelling long channels as hydrodynamically equivalent shorter channel sections. In addition, these small micro-elements reach steady state much quicker than a full simulation of the network does. We test our multiscale method on several steady, isothermal network flow cases and show that it converges quickly (within three iterations) to good agreement with full molecular simulations of the same cases

Wave propagation in an elastic waveguide: fluid-structure interactions in a spinal disease

Syringomyelia is a disease in which fluid-filled cavities, called syrinxes, form in the spinal cord (SC). The progressive expansion of syrinxes over many years compresses the surrounding nerve fibres and blood vessels, which is associated with neurological damage. In the present work we aim to elucidate the mechanics underlying syrinx formation and expansion by investigating the wave-propagation characteristics of the spinal system in healthy and diseased configurations. We use the standard biomechanical analogue consisting of cylindrical, axisymmetric solid and fluid layers. Specifically, the SC is represented as an elastic cylinder, which becomes an annulus containing inviscid fluid when a syrinx is included, and this is surrounded by inviscid fluid representing the cerebrospinal fluid (CSF) occupying the subarachnoid space, bound by a rigid dura. The model is formulated as a system of Helmholtz equations which describe axisymmetric harmonic motion of the cylindrical layers. These equations are discretised using Chebyshev polynomials and then solved as a generalised eigenvalue problem. This linear algebra approach gives explicit access to wave properties like traditional root-finding methods butwithout the need for a long wave assumption, and is also more computationally efficient than finite element/volume methods used in other spinal models.Our results reproduce the wave speeds of other syringomyelia models and the dispersion diagrams are qualitatively similar to other acoustic models with like topologies. This demonstrates the applicability of the numerical method to the biological problem. Additionally we are able to recover the associated displacement and stress modes from the eigenvectors.This investigation serves as a framework for studying cylindrical waveguides in biological systems