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

Direct numerical simulation of gas transfer across the air-water interface driven by buoyant convection

A series of direct numerical simulations of mass transfer across the air-water interface driven by buoyancy-induced convection has been carried out to elucidate the physical mechanisms that play a role in the transfer of heat and atmospheric gases. The buoyant instability is caused by the presence of a thin layer of cold water situated on top of a body of warm water. In time, heat and atmospheric gases diff use into the uppermost part of the thermal boundary layer and are subsequently transported down into the bulk by falling sheets and plumes of cold water. Using a specifically-designed numerical code for the discretization of scalar convection and diffusion, it was possible to accurately resolve this buoyant instability induced transport of atmospheric gases into the bulk at a realistic Prandtl number (Pr = 6) and Schmidt numbers ranging from Sc = 20 to Sc = 500. The simulations presented here provided a detailed insight into instantaneous gas transfer processes. The falling plumes with highly gas-saturated fluid in their core were found to penetrate deep inside the bulk. With an initial temperature difference between the water surface and the bulk of slightly above 2 K peaks in the instantaneous heat flux in excess of 1600 W/m² were observed, proving the potential effectiveness of buoyant convective heat and gas transfer. Furthermore, the validity of the scaling law for the ratio of gas and heat transfer velocities K_L / H_L ∼ (Pr/Sc)^0:5 for the entire range of Schmidt numbers considered was confirmed. A good time-accurate approximation of K_L was found using surface information such as velocity fluctuations and convection cell size or surface divergence. A reasonable time-accuracy for the K_L estimation was obtained using the horizontal integral length scale and the root-mean-square of the horizontal velocity fluctuations in the upper part of the bulk.The German Research Foundation (DFG grant UH242/6-1). Additional funding by the Helmholtz Water Network

Large-amplitude capillary waves in electrified fluid sheets

Large-amplitude capillary waves on fluid sheets are computed in the presence of a uniform electric field acting in a direction parallel to the undisturbed configuration. The fluid is taken to be inviscid, incompressible and non-conducting. Travelling waves of arbitrary amplitudes and wavelengths are calculated and the effect of the electric field is studied. The solutions found generalize the exact symmetric solutions of Kinnersley (1976) to include electric fields, for which no exact solutions have been found. Long-wave nonlinear waves are also constructed using asymptotic methods. The asymptotic solutions are compared with the full computations as the wavelength increases, and agreement is found to be excellent

Vorticity dynamics in transcritical liquid jet breakup

Contrary to common assumptions, a transcritical domain exists during the early times of liquid hydrocarbon fuel injection at supercritical pressure. A sharp two-phase interface is sustained before substantial heating of the liquid. Thus, two-phase dynamics has been shown to drive the early three-dimensional deformation and atomisation. A recent study of a transcritical liquid jet shows distinct deformation features caused by interface thermodynamics, low surface tension, and intraphase diffusive mixing. In the present work, the vortex identification method ${\lambda}_{\rho}$, which considers the fluid compressibility, is used to study the vortex dynamics in a cool liquid n-decane transcritical jet surrounded by a hotter oxygen gaseous stream at supercritical pressures. The relationship between vortical structures and the liquid surface evolution is detailed, along with the vorticity generation mechanisms, including variable-density effects. The roles of hairpin and roller vortices in the early deformation of lobes, the layering and tearing of liquid sheets, and the formation of fuel-rich gaseous blobs are analysed. At these high pressures, enhanced intraphase mixing and ambient gas dissolution affect the local liquid structures (i.e., lobes). Thus, liquid breakup differs from classical sub-critical atomisation. Near the interface, liquid density and viscosity drop by up to 10% and 70%, respectively, and the liquid is more easily affected by the vortical motion (e.g., liquid sheets wrap around vortices). Despite the variable density, compressible vorticity generation terms are smaller than the vortex stretching and tilting. Layering traps and aligns the vortices along the streamwise direction while mitigating the generation of new rollers.Comment: 51 pages, 27 figure

Investigation of Port Fuel Injector Spray Mass Distribution by Laser Induced Fluorescence

Modern internal combustion engines have stringent requirements for performance and reduced toxic emissions. The fuel delivery system, and particularly the fuel injectors, have a vital role in reducing unburned hydrocarbons (HC) and carbon monoxide (CO) in exhaust emission. The main goal of this study is to map the spatial and temporal distribution of the spray from a low-pressure gasoline fuel injector. To attain this goal, three tasks were performed: (1) the experimental investigation of the spray oscillation as functions of operating pressure and injector timing, (2) the determination of the appropriate dye/fuel combinations for one particular experimental technique, and (3) the demonstration of the capabilities of a Computational Fluid Dynamics (CFD) code, Fluent, in the dispersed two-phase flow solutions. An experimental technique, planar laser induced fluorescence (PLIF), was employed to investigate the spatial and temporal distribution of the spray mass from a set of four-hole, split-stream port fuel injectors. The spatial and temporal spray evolution in a horizontal cross-section was imaged instantaneously via detection of fluorescence intensities. The lateral displacement of the spray mass is clearly displayed in time sequence via the PLIF images, and the spray instability is shown to be sensitively dependent upon small geometric differences along the internal flow paths. In the course of a study to develop a quantitative PLIF diagnostic for the mass distribution emanating from a liquid fuel injector, spectroscopic results were assembled for certain dye/fuel solutions. Experiments were performed with combinations of hydrocarbon solvents and organic dyes. Results are presented in the form of absorption and emission spectra, including extinction coefficients with error analysis, comparisons with data in the literature, and Stokes shift estimates. A Computational Fluid Dynamics (CFD) code, Fluent, was employed to demonstrate its capabilities in the solution of dispersed two-phase flows. The dispersed two-phase flow consists of discrete elements surrounded by a continuous phase. The continuous phase equations were solved in an Eulerian reference frame. The Lagrangian approach was used to track packets of discrete phase elements. Inputs of the numerical dispersed two-phase flow model were obtained from the conditions of the PLIF experiments. Two cases were solved with the same input and boundary conditions. In the first case the spray consists of droplets with 100 μm diameter. A linear droplet diameter distribution between 40 and 100 μm was specified in the second case. Results indicate the existence of a core region with higher velocity values for both cases. The core region appears at the spray center close to the injection tip. The increase in the spray temperature towards the outlet boundary is larger for the constant droplet diameter case than the linear droplet diameter distribution case. Negligible evaporation is observed in the solution domain for both cases

Universal sheet resistance and revised phase diagram of the cuprate high-temperature superconductors

Upon introducing charge carriers into the copper-oxygen sheets of the enigmatic lamellar cuprates the ground state evolves from an insulator into a superconductor, and eventually into a seemingly conventional metal (a Fermi liquid). Much has remained elusive about the nature of this evolution and about the peculiar metallic state at intermediate hole-carrier concentrations (p). The planar resistivity of this unconventional metal exhibits a linear temperature dependence (\rho $\propto$ T) that is disrupted upon cooling toward the superconducting state by the opening of a partial gap (the pseudogap) on the Fermi surface. Here we first demonstrate for the quintessential compound HgBa$_2$CuO$_{4+\delta}$ a dramatic switch from linear to purely quadratic (Fermi-liquid-like, \rho $\propto$ T$^2$) resistive behavior in the pseudogap regime. Despite the considerable variation in crystal structures and disorder among different compounds, our result together with prior work gives new insight into the p-T phase diagram and reveals the fundamental resistance per copper-oxygen sheet in both linear (\rho_S = A_{1S} T) and quadratic (\rho_S = A_{2S} T$^2$) regimes, with A_{1S} $\propto$ A_{2S} $\propto$ 1/p. Theoretical models can now be benchmarked against this remarkably simple universal behavior. Deviations from this underlying behavior can be expected to lead to new insights into the non-universal features exhibited by certain compounds

Levitated Spinning Graphene

A method is described for levitating micron-sized few layer graphene flakes in a quadrupole ion trap. Starting from a liquid suspension containing graphene, charged flakes are injected into the trap using the electrospray ionization technique and are probed optically. At micro-torr pressures, torques from circularly polarized light cause the levitated particles to rotate at frequencies >1 MHz, which can be inferred from modulation of light scattering off the rotating flake when an electric field resonant with the rotation rate is applied. Possible applications of these techniques will be presented, both to fundamental measurements of the mechanical and electronic properties of graphene and to new approaches to graphene crystal growth, modification and manipulation.Comment: 23 pages, 11 figure