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A compound droplet subject to three-dimensional oscillatory shear flow is studied using a three-phase lattice Boltzmann model. Firstly, focusing on low values of capillary number (Ca) where the compound droplet eventually reaches steady-state oscillatory condition, we study the effect of oscillatory period, viscosities of inner and outer fluids of the compound droplet, wall confinement and Ca on the droplet behavior. As the oscillatory period increases, the maximum deformation parameters gradually approach the steady-state values in the corresponding simple shear flow for both inner and outer droplets, and the compound droplet is more synchronous with applied shear. We demonstrate for the first time that due to high pressure near two tips inside the outer droplet the inner droplet may rotate counterintuitively in a direction opposite to the outer one. The compound droplet undergoes larger deformation when either droplet is less viscous, which also decreases the synchronization between inner and outer droplets. Increasing confinement ratio not only promotes the deformations of both constituent droplets, but also makes them more synchronous with applied shear. It is also found that the maximum deformation parameters of both droplets increase linearly with Ca up to Ca=0.35 but deviate from the linearity at higher Ca, where multipeaked oscillations are observed for the deformation of the inner droplet, which can be due to the extensional flow resulting from the rapid contraction of the outer droplet. We then analyze the breakup behavior of compound droplet in the oscillatory shear flow for varying confinement ratios, and compare the findings with those in simple shear flow. The critical capillary number for droplet breakup exhibits a non-monotonic behavior with the confinement ratio in both shear flows, but its value is always higher in oscillatory shear flow than in simple shear flow. As the confinement ratio increases, in the case of oscillatory shear flow, the drople

Although the thermal conductivity of molecular gases can be measured straightforwardly and accurately, it is difficult to experimentally determine its separate contributions from the translational and internal motions of gas molecules. Yet, this information is critical in rarefied gas dynamics as the rarefaction effects corresponding to these motions are different. In this paper, we propose a novel methodology to extract the translational thermal conductivity (or equivalently, the translational Eucken factor) of molecular gases from the Rayleigh–Brillouin scattering (RBS) experimental data. From the numerical simulation of the Wu et al. (J. Fluid Mech., vol. 763, 2015, pp. 24–50) model we find that, in the kinetic regime, in addition to bulk viscosity, the RBS spectrum is sensitive to the translational Eucken factor, even when the total thermal conductivity is fixed. Thus it is not only possible to extract the bulk viscosity, but also the translational Eucken factor of molecular gases from RBS light scattering spectra measurements. Such experiments bear the additional advantage that gas–surface interactions do not affect the measurements. By using the Wu et al. model, bulk viscosities (due to the rotational relaxation of gas molecules only) and translational Eucken factors of N2 , CO2 and SF6 are simultaneously extracted from RBS experiments.

The Couette flow is one of the fundamental problems of rarefied gas dynamics, which has been investigated extensively based on the linearized Boltzmann equation (LBE) of hard-sphere molecules and simplified kinetic model equations. However, how the different intermolecular potentials affect the viscous slip coefficient and the structure of Knudsen layer remains unclear. Here, a novel synthetic iteration scheme (SIS) is developed for the LBE to find solutions of Couette flow accurately and efficiently: the velocity distribution function is first solved by the conventional iterative scheme, then it is modified such that in each iteration i) the flow velocity is guided by an ordinary differential equation that is asymptotic-preserving at the Navier–Stokes limit and ii) the shear stress is equal to the average shear stress. Based on the Bhatnagar–Gross–Krook model, the SIS is assessed to be efficient and accurate. Then we investigate the Knudsen layer function for gases interacting through the inverse power-law, shielded Coulomb, and Lennard-Jones potentials, subject to diffuse-specular and Cercignani–Lampis gas-surface boundary conditions. When the tangential momentum accommodation coefficient (TMAC) is not larger than one, the Knudsen layer function is strongly affected by the potential, where its value and width increase with the effective viscosity index of gas molecules. Moreover, the Knudsen layer function exhibits similarities among different values of TMAC when the intermolecular potential is fixed. For Cercignani–Lampis boundary condition with TMAC larger than one, both the viscous slip coefficient and Knudsen layer function are affected by the intermolecular potential, especially when the “backward” scattering limit is approached. With the asymptotic theory by Jiang and Luo (2016) [14] for the singular behavior of the velocity gradient in the vicinity of solid surfaces, we find that the whole Knudsen layer function can be well fitted by the power series ∑n=0 2

For ultra-thin gas lubrication, the surface-to-volume ratio increases dramatically when the flow geometry is scaled down to the micro/nano-meter scale, where surface roughness, albeit small, may play an important role in gas slider bearings. However, the effect of surface roughness on the pressure and load capacity (force) in gas slider bearings has been overlooked. In this paper, on the basis of the generalized Reynolds equation, we investigate the behavior of a gas slider bearing, where the roughness of the slider surface is characterized by the Weierstrass-Mandelbrot fractal function, and the mass flow rates of Couette and Poiseuille flows are obtained by deterministic solutions to the linearized Bhatnager-Gross-Krook equation. Our results show that the surface roughness reduces the local mass flow rate as compared to the smooth channel, but the amount of reduction varies for Couette and Poiseuille flows of different Knudsen numbers. As a consequence, the pressure rise and load capacity in the rough bearing become larger than the ones in the smooth bearing in the slip and early transition flow regimes, e.g., a 6% roughness could lead to an increase of 20% more bearing load capacity. However, this situation is reversed in the free-molecular flow regime, as the ratio of the mass flow rates between Couette and Poiseuille flows is smaller than that in the smooth channel. Interestingly, between the two extremes, we have found a novel "rarefaction cloaking" effect, where the load capacity of a rough bearing equals to that of a smooth bearing at a certain range of Knudsen numbers, as if the roughness does not exist. © 2017 Author(s).

Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries. © 2017 American Physical Society.

Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article, we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues., Schlumberger-Doll Research Center, Netherlands Organization for Scientific Research (NWO/STW (Vidi grant 10787), Foundation for Fundamental Research on Matter (Netherlands) (FOM/Shell IPP (09iPOG14 - “Detection and guidance of nanoparticles for enhanced oil recovery”)), Los Alamos National Laboratory (LDRD Program and Institutional Computing Program), Japan. Ministry of Education, Culture, Sports, Science and Technology (International Institute for Carbon Neutral Energy Research (WPI-I2CNER)), National Science Fund for Distinguished Young Scholars (China) (Thousand Youth Talents Program)