Session E22: Nano Flows: Basic Flow Physics

A Reynolds lubrication equation for dense fluids valid beyond Navier-Stokes

Based on an approach for describing wave propagation in narrow channels, originally attributed to Lamb, we develop a method for extending the Reynolds Lubrication approximation to small scales for which the Navier-Stokes constitutive closures fail. The basic idea behind this approach is that the Reynolds equation is an averaged description of mass conservation and thus does not involve spatially resolved flow profiles in the transverse (gap) direction. In other words, the constitutive information required is significantly simpler and is limited to the {\it local} flowrate as a function of the gap height. Such a constitutive relation is significantly easier to obtain by experiments and/or off-line molecular simulations of pressure driven flow in constant height channels in which other control parameters of the flow rate are held constant. Using this constitutive equation results in a Reynolds-type equation that enables continuum modelling of lubrication problems at any lengthscale. The proposed methodology is demonstrated and validated for a nanoscale lubrication problem by comparison to Molecular Dynamics simulations.   

Harvesting liquid from unsaturated vapor – nanoflows induced by capillary condensation

A vapor, even subsaturated, can spontaneously form liquid in nanoscale spaces. This process, known as capillary condensation, plays a fundamental role in various contexts, such as the formation of clouds or the dynamics of hydrocarbons in the geological subsurface. However, large uncertainties remain on the thermodynamics and fluid mechanics of the phenomenon, due to experimental challenges as well as outstanding questions about the validity of macroscale physics at the nanometer scale. We studied experimentally the spatio-temporal dynamics of water condensation in a model nanoporous medium (pore radius $\sim 2$ nm), taking advantage of the color change of the material upon hydration. We found that at low relative humidities ($<60\%$RH), capillary condensation progressed in a diffusive fashion, while it occurred through a well-defined capillary-viscous imbibition front at $>60\%$RH, driven by a balance between the pore capillary pressure and the condensation stress given by Kelvin equation. Further analyzing the imbibition dynamics as a function of saturation allowed us to extract detailed information about the physics of nano-confined fluids. Our results suggest excellent extension of macroscale fluid dynamics and thermodynamics even in pores $\sim 10$ molecules in diameter.   

Thermophoresis around dimer of gold spheres for enhancement of trapping range of plasmonic tweezers

Trapping of nanomaterials by an optical radiation pressure can be effectively performed by combining an enhanced localized electric field on plasmonic structures due to surface plasmon resonance. Since an effective trapping area is limited in nanoscale, target transportation to the area from far would gain the trapping performance. This study investigates a potential of the nanomaterials transportation dispersed in the bulk liquid into the trapping area by thermophoresis. We performed numerical simulation of the electromagnetic field around a gold nanosphere dimer whose diameters are 20 - 300 nm and gap width is 1 - 50 nm as a plasmonic structure under irradiation of plane electromagnetic wave with the finite element method. Then the corresponding temperature field generated by photothermal hearing was obtained. 1 to 100 nm polystyrene spheres (PS) in water was considered. The trapping force, which includes optical gradient force, thermophoretic force, and drag force exerting on the PS, was calculated, and the range for the trapping was investigated. The results indicates that the overall trapping range strongly depends on the thermophoretic property, Soret coefficient. The possibility of wide-ranged nanomaterial trap by controlling the temperature field was confirmed.   

Capillary freezing of ionic liquids confined between metallic interfaces

Using a quartz tuning fork based AFM, we investigate the behavior of ionic liquids under confinement. Using nanorheological measurements, we show that nanometric confinements can lead to solidification and capillary freezing of the ionic liquid. We find that the critical confinement at which the liquid-solid transition occurs depends strongly on the bulk electronic properties of the confining substrate, with stronger effects observed for more metallic surfaces. This behavior is rationalized on the basis of a Gibbs-Thompson framework for the shift of the freezing transition, taking into account surface energies with the imperfect metal at the level of a Thomas-Fermi model. Finally, we show that capillary freezing can also be tuned by electrifying the confining interfaces.   

From the Nano- to the Macroscale -- Bridging Scales for the Moving Contact Line Problem

The moving contact line problem remains an unsolved fundamental problem in fluid mechanics. At the heart of the problem is its multiscale nature: a nanoscale region close to the solid boundary where the continuum hypothesis breaks down, must be resolved before effective macroscale parameters such as contact line friction and slip can be obtained. To capture nanoscale properties very close to the contact line and to establish a link to the macroscale behaviour, we employ classical density-functional theory (DFT) [1,2], in combination with extended Navier-Stokes-like equations. Using simple models for viscosity and slip at the wall, we compare our computations with the Molecular Kinetic Theory, by extracting the contact line friction, depending on the imposed temperature of the fluid [3]. A key fluid property captured by DFT is the fluid layering at the wall-fluid interface, which has a large effect on the shearing properties of a fluid. To capture this crucial property, we propose an anisotropic model for the viscosity, which also allows us to scrutinize the effect of fluid layering on contact line friction. [1] Math. Model. Nat. Phenom. 10 111 (2015) [2] Phys. Fluids 26 072001 (2014) [3] A. Nold, PhD Thesis, Imperial College London (2016)   

Thermophoresis of water droplets inside carbon nanotubes

Carbon Nanotubes (CNTs) offer unique possibilities as fluid conduits with applications ranging from lab on a chip devices to encapsulation media for drug delivery. CNTs feature high mechanical strength, chemical and thermal stability and biocompatibility therefore they are promising candidates for nanodevice fabrication. Thermal gradients have been proposed as mechanism to drive particles, fullerenes and droplets inside CNTs. Here, by conducting Molecular Dynamics (MD) simulations, we study thermophoresis of water droplets inside CNTs. We systematically change the size of the droplets, the axial thermal gradient and CNT chirality. We find that the droplet motion in the armchair CNTs exhibits two clearly delimited stages, a regime wherein the droplet is accelerated and subsequently, a regime wherein the droplet moves with constant velocity. Inside the zig zag CNTs, the droplet accelerates during a very short time and then it moves with constant velocity. We compute the net force during the droplet acceleration and find a correlation between the droplet acceleration and the magnitude of the thermal gradient without any dependence on the droplet size. Moreover, we conduct velocity constrained MD simulations to determine the friction and thermophoretic forces acting on the droplet.