On the modelling of isothermal gas flows at the microscale

This paper makes two new propositions regarding the modelling of rarefied (non-equilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking high-order, or extended, hydrodynamic models for these flows. This standing time-varying shear-wave problem does not require boundary conditions to be specified at a solid surface, so is useful for assessing whether fluid models can capture rarefaction effects in the bulk flow. We assess a number of different proposed extended hydrodynamic models, and we find the R13 equations perform the best in this case. Our second proposition is a simple technique for introducing non-equilibrium effects caused by the presence of solid surfaces into the computational fluid dynamics framework. By combining a new model for slip boundary conditions with a near-wall scaling of the Navier--Stokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional second-order slip model. We show that this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strain-rate inversion that is evident from molecular simulations. The model's generality to non-planar geometries is demonstrated by examining low-speed flow around a micro-sphere. It shows a marked improvement over conventional predictions of the drag on the sphere, although there are some questions regarding its stability at the highest Knudsen numbers

Dynamics of liquid nano-threads : fluctuation-driven instability and rupture

The instability and rupture of nanoscale liquid threads is shown to strongly depend on thermal fluctuations. These fluctuations are naturally occurring within molecular dynamics (MD) simulations and can be incorporated via fluctuating hydrodynamics into a stochastic lubrication equation (SLE). A simple and robust numerical scheme is developed for the SLE that is validated against MD for both the initial (linear) instability and the nonlinear rupture process. Particular attention is paid to the rupture process and its statistics, where the `double-cone’ profile reported by Moseler & Landmann [Science, 2000, 289(5482): 1165-1169] is observed, as well as other distinct profile forms depending on the flow conditions. Comparison to the Eggers’ similarity solution [Physical Review Letters, 2002, 89(8): 084502], a power law of the minimum thread radius against time to rupture, shows agreement only at low surface tension; indicating that surface tension cannot generally be neglected when considering rupture dynamics

Coupled continuum hydrodynamics and molecular dynamics method for multiscale simulation

We present a new hybrid methodology for carrying out multiscale simulations of flow problems lying between continuum hydrodynamics and molecular dynamics, where macro/micro lengthscale separation exists only in one direction. Our multiscale method consists of an iterative technique that couples mass and momentum flux between macro and micro domains, and is tested on a converging/diverging nanochannel case containing flow of a simple Lennard-Jones liquid. Comparisons agree well with a full MD simulation of the same test case

Capturing the Knudsen layer in continuum-fluid models of non-equilibrium gas flows

In hypersonic aerodynamics and microflow device design, the momentum and energy fluxes to solid surfaces are often of critical importance. However, these depend on the characteristics of the Knudsen layer - the region of local non-equilibrium existing up to one or two molecular mean free paths from the wall in any gas flow near a surface. While the Knudsen layer has been investigated extensively using kinetic theory, the ability to capture it within a continuum-fluid formulation (in conjunction with slip boundary conditions) suitable for current computational fluid dynamics toolboxes would offer distinct and practical computational advantages

A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations

For gas flows in microfluidic configurations, the Knudsen layer close to the wall can comprise a substantial part of the entire flow field and has a major effect on quantities such as the mass flow rate through micro devices. The Knudsen layer itself is characterized by a highly nonlinear relationship between the viscous stress and the strain rate of the gas, so even if the Navier-Stokes equations can be used to describe the core gas flow they are certainly inappropriate for the Knudsen layer itself. In this paper we propose a "wall-function" model for the stress/strain rate relations in the Knudsen layer. The constitutive structure of the Knudsen layer has been derived from results from kinetic theory for isothermal shear flow over a planar surface. We investigate the ability of this simplified model to predict Knudsen-layer effects in a variety of configurations. We further propose a semi-empirical Knudsen-number correction to this wall function, based on high-accuracy DSMC results, to extend the predictive capabilities of the model to greater degrees of rarefaction

Development of LaRC 160/NR150B2 polyimide graphite hybrid composites

A method for co-curing NR150B2 and LaRC 160 prepregs into hybrid composites was developed. The processing characteristics and the properties of the hybrid composites were compared with those of laminates fabricated from the individual component prepregs. Resin forms were selected and optimized and a new NR150 formulation was investigated. The new formulation greatly facilitated the processing and the performance of this system. Quality control techniques were evaluated and developed, high quality laminates were fabricated from both individual resin systems, and hybrid laminates were successfully co-cured. Optimum hybrid forms were investigated and several novel approaches were explored. An optimum hybrid system was developed that utilizes a LaRC curing schedule but shows no degradation of mechanical properties after aging 500 hr in air at 260 C

Water transport through (7,7) carbon nanotubes of different lengths using molecular dynamics

Non-equilibrium molecular dynamics simulations are used to investigate water transport through (7,7) CNTs, examining how changing the CNT length affects the internal flow dynamics. Pressure-driven water flow through CNT lengths ranging from 2.5 to 50 nm is simulated. We show that under the same applied pressure difference an increase in CNT length has a negligible effect on the resulting mass flow rate and fluid flow velocity. Flow enhancements over hydrodynamic expectations are directly proportional to the CNT length. Axial profiles of fluid properties demonstrate that entrance and exit effects are significant in the transport of water along CNTs. Large viscous losses in these entrance/exit regions lead into central “developed” regions in longer CNTs where the flow is effectively frictionless

The usefulness of higher-order constitutive relations for describing the Knudsen layer

The Knudsen layer is an important rarefaction phenomenon in gas flows in and around microdevices. Its accurate and efficient modeling is of critical importance in the design of such systems and in predicting their performance. In this paper we investigate the potential that higher-order continuum equations may have to model the Knudsen layer, and compare their predictions to high-accuracy DSMC (direct simulation Monte Carlo) data, as well as a standard result from kinetic theory. We find that, for a benchmark case, the most common higher-order continuum equation sets (Grad's 13 moment, Burnett, and super-Burnett equations) cannot capture the Knudsen layer. Variants of these equation families have, however, been proposed and some of them can qualitatively describe the Knudsen layer structure. To make quantitative comparisons, we obtain additional boundary conditions (needed for unique solutions to the higher-order equations) from kinetic theory. However, we find the quantitative agreement with kinetic theory and DSMC data is only slight

Advances in Hybrid Molecular/Continuum Methods for Micro and Nano Flows

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Next generation uid ow systems are likely to depend on micro or nano scale dynamics that make the system behaviour multiscale in both space and time. There may be strong or weak separation between the length scales and between the time scales in di erent parts of the ow, and these scale-separations may also vary in space and time. In this paper we discuss a practical approach to improving the e ciency of hybrid particle/continuum models of such multiscale ows. Our focus is on adapting the solution method to the local scale-separation conditions, in order to balance compu- tational e ciency with accuracy. We compare results from our new hybridisation in space and time with full molecular simulations of benchmark nanoscale ows