Water, water, everywhere, Nor any drop to drink?

With the world’s population set to exceed nine billion by the end of the century, the demand for fresh water will become ever more acute. Applying nanotechnology to filter seawater in coastal areas could provide part of the answer, as Jason Reese explain

Some consequences of non-local-equilibrium in hypersonic aerodynamic flows

In simulating high-speed, high-altitude aerodynamics it is important to be able to capture physical phenomena that are due to the non-local-equilibrium nature of the rarefied gas flow (this is in addition to any effects due to dissociation, ionisation and energy partition in diatomic molecules). The physical effects of the gas rarefaction can be particularly important close to any solid surface, where they have implications for the heat transfer and mechanical stresses experienced by the surface, and hence on the design of the leading edges and control surfaces of aerodynamic vehicles

Dissipative mass flux and sound wave propagations in monatomic gases

Predicting sound wave dispersion in monatomic gases is a fundamental gas flow problem in rarefied gas dynamics. The Navier-Stokes-Fourier model is known to fail where local thermodynamic equilibrium breaks down. Generally, conventional gas flow models involve equations for mass-density without a dissipative mass contribution. In this paper we observe that using a dissipative mass flux contribution as a non-local-equilibrium correction can improve agreement between the continuum equation prediction of sound wave dispersion and experimental data. Two mass dissipation models are investigated: a preliminary model that simply incorporates a diffusive density term in the set of three conservation equations, and another model derived from considering microscopic fluctuations in molecular spatial distributions

Rarefied hypersonic flow simulations using the Navier-Stokes equations with non-equilibrium boundary conditions

This paper investigates the use of Navier-Stokes-Fourier equations with non-equilibrium boundary conditions (BCs) for simulation of rarefied hypersonic flows. It revisits a largely forgotten derivation of velocity slip and temperature jump by Patterson, based on Grad’s moment method. Mach 10 flow around a cylinder and Mach 12.7 flow over a flat plate are simulated using both computational fluid dynamics using the temperature jump BCs of Patterson and Smoluchowski and the direct simulation Monte-Carlo (DMSC) method. These flow exhibit such strongly non-equilibrium behaviour that, following Patterson’s analysis, they are strictly beyond the range of applicability of the BCs. Nevertheless, the results using Patterson’s temperature jump BC compare quite well with the DSMC and are consistently better than those using the standard Smoluchowski temperature jump BC. One explanation for this better performance is that an assumption made by Patterson, based on the flow being only slightly non-equilibrium, introduces an additional constraint to the resulting BC model in the case of highly non-equilibrium flows

Perspectives on the simulation of micro gas and nano liquid flows

Micro- and nano-scale fluid systems can behave very differently from their macro-scale counterparts. Remarkably, there is no sufficiently accurate, computationally efficient, and — most importantly — generally agreed fluid dynamic model that encapsulates all of this important behaviour. The only thing that researchers can agree on is that the conventional Navier-Stokes fluid equations are unable to capture the unique complexity of these often locally non-thermodynamic-equilibrium flows. Here, we outline recent work on developing and exploring new models for these flows, highlighting, in particular, slip flow as a quintessential non-equilibrium (or sub-continuum) phenomenon. We describe the successes and failures of various hydrodynamic and molecular models in capturing the non-equilibrium flow physics in current test applications in micro and nano engineering, including the aerodynamic drag of a sphere in a rarefied gas, and the flow of water along carbon nanotubes

Simulating fluid flows in micro and nano devices : the challenge of non-equilibrium behaviour

We review some recent developments in the modelling of non-equilibrium (rarefied) gas flows at the micro- and nano-scale, concentrating on two different but promising approaches: extended hydrodynamic models, and lattice Boltzmann methods. Following a brief exposition of the challenges that non-equilibrium poses in micro- and nano-scale gas flows, we turn first to extended hydrodynamics, outlining the effective abandonment of Burnett-type models in favour of high-order regularised moment equations. We show that the latter models, with properly-constituted boundary conditions, can capture critical non-equilibrium flow phenomena quite well. We then review the boundary conditions required if the conventional Navier-Stokes-Fourier (NSF) fluid dynamic model is applied at the micro scale, describing how 2nd-order Maxwell-type conditions can be used to compensate for some of the non-equilibrium flow behaviour near solid surfaces. While extended hydrodynamics is not yet widely-used for real flow problems because of its inherent complexity, we finish this section with an outline of recent 'phenomenological extended hydrodynamics' (PEH) techniques-essentially the NSF equations scaled to incorporate non-equilibrium behaviour close to solid surfaces-which offer promise as engineering models. Understanding non-equilibrium within lattice Boltzmann (LB) framework is not as advanced as in the hydrodynamic framework, although LB can borrow some of the techniques which are being developed in the latter-in particular, the near-wall scaling of certain fluid properties that has proven effective in PEH. We describe how, with this modification, the standard 2nd-order LB method is showing promise in predicting some rarefaction phenomena, indicating that instead of developing higher-order off-lattice LB methods with a large number of discrete velocities, a simplified high-order LB method with near-wall scaling may prove to be just as effective as a simulation tool

Molecular free path distribution in rarefied gases

We present the results of investigations into the distribution of molecular free paths in rarefied gases using molecular dynamics simulations. Our tests on a range of different gas densities and confinements (unbounded, single bounding wall and parallel bounding walls) indicate that the molecules perform Lévy-type flights, irrespective of the presence of a bounding wall. The free paths most closely follow a power-law distribution. Simulations of gases confined by planar surfaces indicate that the local molecular mean free path varies sharply close to a solid surface. These results may yield new insight into diffusive transport in rarefied gases, in particular, the constitutive behaviour of gas flows in micro- and nanoscale devices

Modeling of Knudsen layer effects in micro/nanoscale gas flows

We propose a power-law based effective mean free path (MFP) model so that the Navier-Stokes-Fourier equations can be employed for the transition-regime flows typical of gas micro/nanodevices. The effective MFP model is derived for a system with planar wall confinement by taking into account the boundary limiting effects on the molecular free paths. Our model is validated against molecular dynamics simulation data and compared with other theoretical models. As gas transport properties can be related to the mean free path through kinetic theory, the Navier-Stokes-Fourier constitutive relations are then modified in order to better capture the flow behavior in the Knudsen layers close to surfaces. Our model is applied to fully developed isothermal pressure-driven (Poiseuille) and thermal creep gas flows in microchannels. The results show that our approach greatly improves the near-wall accuracy of the Navier-Stokes-Fourier equations, well beyond the slip-flow regime

Behaviour of microscale gas flows based on a power-law free path distribution function

We investigate a power-law form for the probability distribution function of free paths of dilute gas molecules in a confined region. A geometry-dependent effective molecular mean free path (MFP) model is then derived for a planar wall confinement, by taking into account the boundary limiting effects on the molecular paths. The power-law based effective MFP is validated against molecular dynamics simulation data and compared with exponential effective MFP models. The Navier-Stokes constitutive relations are then modified according to the kinetic theory of gases i.e. transport properties can be described in terms of the free paths which the molecules describe between collisions. Results for isothermal pressure-driven Poiseuille gas flows in micro-channels are reported, and we compare results with conventional hydrodynamic models, solutions of the Boltzmann equation and experimental data