Memory effects are relevant for chaotic advection of inertial particles

A Coupled CFD-DEM Study on the Effect of Basset Force Aimed at the Motion of a Single Bubble

The physical meaning of Basset force is first studied via polynomial approximation and the Fourier series representation method. After compiling the Basset force into the coupling interface with Visual C, a dynamic mathematical model is set up to describe the upward motion behavior of a single bubble by adopting the CFD-DEM method. Afterwards, the coupling interface with Basset force proposed in this study is verified experimentally and shows very good agreements. The initial velocity, releasing depth, bubble size, density ratio and viscosity ratio are studied qualitatively due to their great importance to Basset force. The ratio of Basset force to the sum of Basset force and drag force and to buoyancy, F→Ba/(F→D+F→Ba) and |F→Ba/F→B|, are employed to quantify the contribution of Basset force quantitatively. In addition, some instructive outlooks and recommendations on a further development of appropriate and justifiable use of Basset force are highlighted at last.

Oxygen-Selective Diffusion-Bubbling Membranes with Core-Shell Structure: Bubble Dynamics and Unsteady Effects

Oxygen is the second-largest-volume industrial gas that is mainly produced using cryogenic air separation. However, the state-of-the-art cryogenic technology thermodynamic efficiency has approached a theoretical limit as near as is practicable. Therefore, there is stimulus to develop an alternative technology for efficient oxygen separation from air. Mixed ionic electronic-conducting (MIEC) ceramic membrane-based oxygen separation technology could become this alternative, but commercialization aspects, including cost, have revealed inadequacies in ceramic membrane materials. Currently, diffusion-bubbling molten oxide membrane-based oxygen separation technology is being developed. It is a potentially disruptive technology that would propose an improvement in oxygen purity and a reduction in capital costs. Bubbles play an important role in ensuring the oxygen mass transfer in diffusion-bubbling membranes. However, there is not sufficient understanding of the bubble dynamics. This understanding is important to be able to control transport properties of these membranes and assess their potential for technological application. The aim of this feature article is to highlight the progress made in developing this understanding and specify the directions for future research.

Unsteady motion of a perfectly slipping sphere

An integral expression for the translational velocity of a perfectly slipping spherical particle under a time-dependent applied force in unsteady Stokes flow is derived. For example, when the ratio of particle density to fluid density is small, our analysis pertains to an inviscid bubble in a viscous fluid. We determine an explicit form of the particle velocity under an impulsive force, wherefrom the velocity autocorrelation function and mean-squared displacement of a perfectly slipping sphere undergoing Brownian motion are obtained. The above results are contrasted against the time-dependent diffusion of a rigid sphere with no hydrodynamic slip. Finally, the thermal force power spectral density is analytically calculated for a diffusing sphere with arbitrary slip length. We suggest this quantity to be suitable to infer slip length from the measurement of nondiffusive Brownian motion.

Transport, diffusion, and energy studies in the Arnold-Beltrami-Childress map

We study the transport and diffusion properties of passive inertial particles described by a six-dimensional dissipative bailout embedding map. The base map chosen for the study is the three-dimensional incompressible Arnold-Beltrami-Childress (ABC) map chosen as a representation of volume preserving flows. There are two distinct cases: the two-action and the one-action cases, depending on whether two or one of the parameters (A,B,C) exceed 1. The embedded map dynamics is governed by two parameters (α,γ), which quantify the mass density ratio and dissipation, respectively. There are important differences between the aerosol (α<1) and the bubble (α>1) regimes. We have studied the diffusive behavior of the system and constructed the phase diagram in the parameter space by computing the diffusion exponents η. Three classes have been broadly classified-subdiffusive transport (η<1), normal diffusion (η≈1), and superdiffusion (η>1) with η≈2 referred to as the ballistic regime. Correlating the diffusive phase diagram with the phase diagram for dynamical regimes seen earlier, we find that the hyperchaotic bubble regime is largely correlated with normal and superdiffusive behavior. In contrast, in the aerosol regime, ballistic superdiffusion is seen in regions that largely show periodic dynamical behaviors, whereas subdiffusive behavior is seen in both periodic and chaotic regimes. The probability distributions of the diffusion exponents show power-law scaling for both aerosol and bubbles in the superdiffusive regimes. We further study the Poincáre recurrence times statistics of the system. Here, we find that recurrence time distributions show power law regimes due to the existence of partial barriers to transport in the phase space. Moreover, the plot of average particle kinetic energies versus the mass density ratio for the two-action case exhibits a devil's staircase-like structure for higher dissipation values. We explain these results and discuss their implications for realistic systems.

Enhanced settling of nonheavy inertial particles in homogeneous isotropic turbulence: The role of the pressure gradient and the Basset history force

The Stokes drag force and the gravity force are usually sufficient to describe the behavior of sub-Kolmogorov-size (or pointlike) heavy particles in turbulence, in particular when the particle-to-fluid density ratio ρ_{p}/ρ_{f}≳10^{3} (with ρ_{p} and ρ_{f} the particle and fluid density, respectively). This is, in general, not the case for smaller particle-to-fluid density ratios, in particular not for ρ_{p}/ρ_{f}≲10^{2}. In that case the pressure gradient force, added mass effects, and the Basset history force also play important roles. In this study we focus on the understanding of the role of these additional forces, all of hydrodynamic origin, in the settling of particles in turbulence. In order to qualitatively elucidate the complex dynamics of such particles in homogeneous isotropic turbulence, we first focus on the case of settling of such particles in the flow field of a single vortex. After having explored this simplified case we extend our analysis to homogeneous isotropic turbulence. In general, we found that the pressure gradient force leads to a decrease in the settling velocity. This can be qualitatively understood by the fact that this force prevents the particles from sweeping out of vortices, a mechanism known as preferential sweeping which causes enhanced settling. Additionally, we found that the Basset history force can both increase and decrease the enhanced settling, depending on the particle Stokes number. Finally, the role of the nonlinear Stokes drag has been explored, confirming that it affects settling of inertial particles in turbulence, but only in a limited way for the parameter settings used in this investigation.

Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean

Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.

Slow approach to steady motion of a concave body in a free-molecular gas

A body in a free-molecular gas accelerated by a constant external force is considered on the basis of kinetic theory. The body is an infinitely long rectangular hollow column with one face removed, and thus it has a squarish U-shaped cross section. The concave part of the body points toward the direction of motion, and thus the gas molecules may be trapped in the concavity. Gas molecules undergo diffuse reflection on a base part, whereas specular reflection on two lateral parts. It is numerically shown that the velocity of the body approaches a terminal velocity, for which a drag force exerted by the gas counterbalances the external force, in such a way that their difference decreases in proportion to the inverse square of time for a large time. This rate of approach is slower than the known rate proportional to the inverse cube of time in the case of a body without concavity [Aoki et al., Phys. Rev. E 80, 016309 (2009)]. Based on the detailed investigation on the velocity distribution function of gas molecules impinging on the body, it is clarified that the concavity prevents some molecules from escaping to infinity. This trapping enhances the effect of recollision between the body and the gas molecules, which is the cause of the inverse power laws, and thus leads to the slower approach.

Chaotic motion of light particles in an unsteady three-dimensional vortex: experiments and simulation

We study the chaotic motion of a small rigid sphere, lighter than the fluid in a three-dimensional vortex of finite height. Based on the results of Eulerian and Lagrangian measurements, a sequence of models is set up. The time-independent model is a generalization of the Burgers vortex. In this case, there are two types of attractors for the particle: a fixed point on the vortex axis and a limit cycle around the vortex axis. Time dependence might combine these regular attractors into a single chaotic attractor, however its robustness is much weaker than what the experiments suggest. To construct an aperiodically time-dependent advection dynamics in a simple way, Gaussian noise is added to the particle velocity in the numerical simulation. With an appropriate choice of the noise properties, mimicking the effect of local turbulence, a reasonable agreement with the experimentally observed particle statistics is found.