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The COVID-19 pandemic imposes a severe challenge to the health care providers and patients in dental clinics as the dental procedures produce abundant airborne materials. Although dental practices use a multi-layered protective procedure to reduce the potential danger from dental aerosols, it is still beneficial to suppress the aerosol generation from the origin as much as possible. Reducing the aerosol generation (especially the droplets of smaller diameters) from the very beginning will ease the burden on all subsequent layers of protection. In this work, we first provide a relatively complete picture of the structure of the spray produced by the air turbine handpiece. We found that the spray consists of two domains: one is the canopy shaped centrifugal zone and the other is a dense ballistic spray core. The droplets from the centrifugal zone are much smaller than those of the spray core and, hence, are more prone to stay in the air. The location of the centrifugal zone also makes it more challenging to be contained by the mouth or rubber dam. To suppress the atomization of the centrifugal zone, we used the food-additive carboxymethylcellulose sodium (CMC-Na) water solutions of different concentrations. The data show that the viscoelastic property of the 0.5 wt. % CMC-Na water solution can effectively suppress the aerosol generation of the centrifugal zone.

In this paper, we present an immersed boundary-lattice Boltzmann flux solver (IB-LBFS) to simulate the interactions of viscous flow with deformable elastic structures, namely, two-dimensional (2D) and three-dimensional (3D) capsules formed by elastic membranes. The IB-LBFS is based on a finite-volume formulation and makes use of hydrodynamic conservation equations with fluxes computed by a kinetic approach; thus, it is more flexible and efficient than the standard immersed boundary-lattice Boltzmann methods. The membrane of the 2D capsule is represented by a set of discrete Lagrangian points, with in-plane and bending forces acting on the membrane obtained by a finite difference method. In contrast, the membrane of a 3D capsule is discretized into flat triangular elements with membrane forces calculated by an energy-based finite-element method. The IB-LBFS is first validated by studying the deformation of a circular capsule in a linear Newtonian and a power-law shear flow. Next, the deformation dynamics of a spherical, an oblate spheroidal, and a biconcave capsule in a simple shear flow are simulated. For an initially spherical capsule, the tank-treading motion of its membrane is reproduced at the steady state; while for oblate spheroidal and biconcave capsules, the swinging and tumbling motions are observed. Furthermore, under certain parameter settings, the transient mode from tumbling to swinging motions is also found, showing a rich and complex dynamic behavior of non-spherical capsules. These results indicate that the IB-LBFS can be employed in future studies concerning the dynamics of a capsule suspension in more realistic flows.

In this paper, we develop an efficient Boltzmann-equation-based mesoscopic approach to simulate three-dimensional (3D) compressible turbulence, using reduced Gauss–Hermite quadrature (GHQ) orders by redefining the second distribution in terms of the total energy in the double distribution function approach. This allows the use of two sets of 3D off-lattice discrete particle velocity models, namely, a 27 discrete velocity model of the seventh-order GHQ accuracy (D3V27A7) combined with a 13 discrete velocity model of the fifth-order GHQ accuracy (D3V13A5), to achieve full consistency with the Navier–Stokes–Fourier system. The source terms in the Boltzmann–Bhatnagar–Gross–Krook system are designed to adjust both the Prandtl number and bulk-to-shear viscosity ratio. Compressible decaying homogeneous isotropic turbulence (DHIT) is simulated at low and moderate turbulent Mach numbers to validate our code. It is observed that the simulation results are in good agreement with those in the existing literatures. Furthermore, the terms in the transport equation of turbulent kinetic energy are analyzed in detail, to illustrate four different transient stages from the initial random flow field to the developed DHIT. It is shown that the transient pressure-dilatation transfer happens rapidly, while the small-scale vortical structures take a longer time to establish physically. Compared to the existing literatures, our approach represents the most efficient mesoscopic scheme for compressible turbulence under the double distribution function formulation.

Bounce-back schemes represent the most popular boundary treatments in the lattice Boltzmann method (LBM) when reproducing the no-slip condition at a solid boundary. While the lattice Boltzmann equation used in LBM for interior nodes is known to reproduce the Navier–Stokes (N–S) equations under the Chapman–Enskog (CE) approximation, the unknown distribution functions reconstructed from a bounce-back scheme at boundary nodes may not be consistent with the CE approximation. This problem could lead to undesirable effects such as nonphysical slip velocity, grid-scale velocity, pressure noises, the local inconsistency with the N–S equations, and sometimes even a reduction of the overall numerical-accuracy order of LBM. Here, we provide a systematic study of these undesirable effects. We first derive the explicit structure of the mesoscopic distribution function for interior nodes. Then, the bounce-back distribution function is examined to identify the hidden errors. It is shown that the relaxation parameters in the collision models play a key role in determining the magnitude of the hidden error terms, and there exists an optimal setting, which can suppress or eliminate most of these undesirable effects. While the existence of this optimal setting is derived previously for unidirectional flows, here, we show that this optimal setting can be extended to non-uniform flows under certain conditions. Finally, a systematic numerical benchmark study is carried out, including non-uniform and unsteady flows. It is shown that, in all these flows, our theoretical analyses of the hidden errors can guide us to significantly improve the quality of the simulation results.

In order to treat immiscible two-phase flows at large density ratios and high Reynolds numbers, a three-dimensional code based on the discrete unified gas kinetic scheme (DUGKS) is developed, incorporating two major improvements. First, the particle distribution functions at cell interfaces are reconstructed using a weighted essentially non-oscillatory scheme. Second, the conservative lower-order Allen–Cahn equation is chosen instead of the higher-order Cahn–Hilliard equation to evolve the free-energy-based phase field governing the dynamics of two-phase interfaces. Five benchmark problems are simulated to demonstrate the capability of the approach in treating two-phase flows at large density ratios and high Reynolds numbers, including three two-dimensional problems (a stationary droplet, Rayleigh–Taylor instability, and a droplet splashing on a thin liquid film) and two three-dimensional problems (binary droplets collision and Rayleigh–Taylor instability). All results agree well with the previous numerical and experimental results. In these simulations, the density ratio and the Reynolds number can reach a large value of [Formula: see text]. Our improved approach sets the stage for the DUGKS scheme to handle realistic two-phase flow problems.

The principle of an optical flow method is formulated for neutron radiography (NR) flow diagnostics to determine high-resolution velocity fields of two-phase flows. This method is based on solving an optical flow equation derived from the continuous equation for NR image analysis as an inverse problem using a variational method. The mathematical definition and physical meaning of the optical flow in NR images of a two-phase flow are clarified. As an example, the optical flow method is used to extract complex velocity fields from a time sequence of dynamic NR images acquired in an air–water two-phase flow in a flat bubbler.

Recently, the COVID-19 virus pandemic has led to many studies on the airborne transmission of expiratory droplets. While limited experiments and on-site measurements offer qualitative indication of potential virus spread rates and the level of transmission risk, the quantitative understanding and mechanistic insights also indispensably come from careful theoretical modeling and numerical simulation efforts around which a surge of research papers has emerged. However, due to the highly interdisciplinary nature of the topic, numerical simulations of the airborne spread of expiratory droplets face serious challenges. It is essential to examine the assumptions and simplifications made in the existing modeling and simulations, which will be reviewed carefully here to better advance the fidelity of numerical results when compared to the reality. So far, existing review papers have focused on discussing the simulation results without questioning or comparing the model assumptions. This review paper focuses instead on the details of the model simplifications used in the numerical methods and how to properly incorporate important processes associated with respiratory droplet transmission. Specifically, the critical issues reviewed here include modeling of the respiratory droplet evaporation, droplet size distribution, and time-dependent velocity profile of air exhaled from coughing and sneezing. According to the literature review, another problem in numerical simulations is that the virus decay rate and suspended viable viral dose are often not incorporated; therefore here, empirical relationships for the bioactivity of coronavirus are presented. It is hoped that this paper can assist researchers to significantly improve their model fidelity when simulating respiratory droplet transmission.

Face masks play a critical role in reducing the transmission risk of COVID-19 and other respiratory diseases. Masks made with nanofibers have drawn increasingly more attention because of their higher filtration efficiency, better comfort, and lower pressure drop. However, the interactions and consequences of the nanofibers and microwater droplets remain unclear. In this work, the evolution of fibers made of polymers with different contact angles, diameters, and mesh sizes under water aerosol exposure is systematically visualized. The images show that capillarity is very strong compared with the elasticity of the nanofiber. The nanofibers coalesce irreversibly during the droplet capture stage as well as the subsequent liquid evaporation stage. The fiber coalescence significantly reduces the effective fiber length for capturing aerosols. The nanofiber mesh that undergoes multiple droplet capture/evaporation cycles exhibits a fiber coalescing fraction of 40%–58%. The hydrophobic and orthogonally woven fibers can reduce the capillary forces and decrease the fiber coalescing fraction. This finding is expected to assist the proper design, fabrication, and use of face masks with nanofibers. It also provides direct visual evidence on the necessity to replace face masks frequently, especially in cold environments.

Rarefied pressure-driven gaseous flow with heat transfer in a microchannel with a backward facing micro-step is investigated in this paper using the lattice Boltzmann method (LBM) in slip and transition flow regimes. In a novel approach, a two-relaxation-time LB equation is used to solve the flow velocity and the single-relaxation-time to handle the heat transfer. The asymmetric relaxation time is determined by equating the analytical second-order slip velocity boundary condition and the slip velocity obtained from applying the implemented bounce back specular boundary condition in the LBM. A second-order implicit temperature jump boundary condition is also implemented to capture the rarefaction effect on the fluid temperature at walls. Velocity slip, temperature jump, centerline temperature, and Nusselt number variations are evaluated for channels with and without the micro-step for a wide range of the Knudsen number. Effects of the micro-step on the rarefied gaseous flow and convective heat transfer are evaluated and discussed. The numerical model is verified by comparing with direct simulation Mont Carlo results.

Interface-resolved direct numerical simulations of the particle-laden turbulent flows in a square duct are performed with a direct-forcing fictitious domain method. The effects of the finite-size particles on the mean and root-mean-square (RMS) velocities are investigated at the friction Reynolds number of 150 (based on the friction velocity and half duct width) and the particle volume fractions ranging from 0.78% to 7.07%. Our results show that the mean secondary flow is enhanced and its circulation center shifts closer to the center of the duct cross section when the particles are added. The reason for the particle effect on the mean secondary flow is analyzed by examining the terms in the mean streamwise vorticity equation. It is observed that the particles enhance the gradients of the secondary Reynolds normal stress difference and shear stress in the near-wall region near the corners, which we think is mainly responsible for the enhancement in the mean secondary flow. Under a prescribed driving press...

A fundamental tenet of statistical mechanics is that the rate of collision of two objects is related to the expectation value of their relative velocities. In pioneering work by Saffman and Turner [J. Fluid Mech. 1, 16 (1956)], two different formulations of this tenet are used to calculate the collision kernel Γ between two arbitrary particle size groups in a turbulent flow. The first or spherical formulation is based on the radial component wr of the relative velocity w between two particles: Γsph=2πR2〈|wr|〉, where wr=w⋅R/R, R is the separation vector, and R=|R|. The second or cylindrical formulation is based on the vector velocity itself: Γcyl=2πR2〈|w|〉, which is supported by molecular collision statistical mechanics. Saffman and Turner obtained different results from the two formulations and attributed the difference to the form of the probability function of w used in their work. A more careful examination reveals that there is a fundamental difference between the two formulations. An underlying assum...

The effect of nonuniform seeding on the dispersion of fluid elements and heavy particles has been investigated in two-dimensional, incompressible mixing layers. The cross-stream dispersion of fluid elements can be enhanced using nonuniform seeding with most particles near the saddle point because of the greater lateral extent of streamlines in this region, though the increase in dispersion compared to a uniform seeding occurs only after a few vortex turnover times. Compared to fluid elements, additional mechanisms—ejection from vortex cores, separatrix crossing, and the effect of the initial particle velocity—must be considered in the analysis of nonuniform seeding on heavy particle dispersion. The influences of these additional mechanisms are first investigated in a Stuart vortex. With increasing response time, vortex ejection and separatrix crossing shift the streamwise position maximizing lateral transport towards the vortex core. While changes in the initial particle velocity increase/decrease displacement, lateral dispersion may still be enhanced by appropriate nonuniform seeding of particles near the saddle point. Numerical simulations of the incompressible Navier–Stokes equations are then used to study cross-stream dispersion in a temporally evolving two-dimensional mixing layer. Stokes numbers St in the calculations were 0.05, 1, 10, and 100 where St is defined as the ratio of the particle response time to the time scale formed using the vorticity thickness of the initial mean flow. Particles were initially distributed nonuniformly at the interface between the two streams or along a line parallel to the interface. Simulation results show that the seeding location maximizing lateral dispersion is both time and Stokes number dependent, with larger increases in dispersion for the interface seeding. For Stokes numbers of order unity cross-stream dispersion exhibits a weak dependence on initial position since particles are efficiently ejected from the vortex core with subsequent motion confined to the nearby region outside the separatrix in one of the freestreams. Simulation results also show that substantial increases in particle dispersion can be obtained using nonuniform seedings relative to that obtained from an initially uniform distribution.

Numerical experiments have been performed to study the geometric collision rate of finite-size particles with zero inertia (i.e., fluid elements) in isotropic turbulence. The turbulent flow was generated by the pseudospectral method. We argue that the formulation of Saffman and Turner [J. Fluid Mech. 1, 16 (1956)] for the average collision kernel is correct only under the assumptions that the particles are kept in the system after collision and allowed to overlap in space. This was confirmed, for the first time, by numerical experiments to within a numerical uncertainty as small as 1%. Finite corrections to the Saffman and Turner result must be made if one applies the theory to actual coagulation process where particles are not allowed to overlap before collision and particles are removed from a given size group after collision. This is due to the fact that Saffman and Turner assumed a uniform, time-independent concentration field in their formulation of the average collision kernel, while in the actual modeling of population evolution the particle number concentration changes in time and may be locally nonuniform as a result of a biased removal process due to spatially nonuniform coagulation rates. However, the quantitative level of the deviations from the Saffman and Turner result remain to be explained. Numerical experiments in simple shear flow were also conducted to elaborate our findings.

Dynamic equations for the scalar autocorrelation and scalar‐velocity cross correlation spectra have been derived for a passive scalar with a uniform mean gradient using the Eddy Damped Quasi Normal Markovian (EDQNM) theory. The presence of a mean gradient in the scalar field makes all correlations involving the scalar axisymmetric with respect to the axis pointing in the direction of the mean gradient. Equivalently, all scalar spectra will be functions of the wave number k and the cosine of the azimuthal angle designated as μ. In spite of this complication, it is shown that the cross correlation vector can be completely characterized by a single scalar function Q(k). The scalar autocorrelation spectrum, in contrast, has an unknown dependence on μ. However, this dependency can be expressed as an infinite sum of Legendre polynomials of μ, as first suggested by Herring [Phys. Fluids 17, 859 (1974)]. Furthermore, since the scalar field is initially zero, terms beyond the second order of the Legendre expansion are shown to be exactly zero. The energy, scalar autocorrelation, and scalar‐velocity cross correlation were solved numerically from the EDQNM equations and compared to results from direct numerical simulations. The results show that the EDQNM theory is effective in describing single‐point and spectral statistics of a passive scalar in the presence of a mean gradient.

An analysis of the Lagrangian motion for small particles denser than surrounding fluid in a two‐dimensional steady cellular flow is presented. The Stokes drag, fluid acceleration, and added mass effect are included in the particle equation of motion. Although the fluid motion is regular, the particle motion can be either chaotic or regular depending on the Stokes number and density ratio. The implications of chaotic motion to particle mixing and dispersion are discussed. Chaotic orbits lead to the dispersion of particle clouds which has many of the features of turbulent dispersion. The mixing process of particles is greatly enhanced since the chaotic advection has the property of ergodicity. However, a high dispersion rate was found to be correlated with low fractal dimension and low mixing efficiency. A similar correlation between dispersion and mixing was found for particles convected by a plane shear mixing layer.

A six‐dimensional nonlinear dynamic system describing the Lagrangian motion of a heavy particle in the Arnold–Beltrami–Childress (ABC) flow was numerically studied. Lyapunov exponents and fractal dimension were used to quantify the chaotic motion. A single set of ABC flow parameters and a limited set of initial conditions were used. Given these restrictions, the following were found. (1) Attractor fractal dimension varies significantly with Stokes number, and, depending on inertia, periodic, quasiperiodic, and chaotic attractors may exist. (2) Particle drift reduces the fractal dimension when the drift is small. It can also cause irregular jumps when the drift parameter is close to one. (3) Quasiperiodic orbits on smooth two‐dimensional manifolds were shown to be the most common ultimate solutions of the system when either the inertia or the drift is relatively large. (4) Different initial conditions can lead to different attracting sets; however, most of them have the same dimension. (5) A direct measure of dispersion based on mean square displacement was defined, but no relation between this dispersion measure and fractal dimension was found.

The chaotic dynamics of Lagrangian motion of particles in a steady Arnold–Beltrami–Childress (ABC) flow and a pseudoturbulence are investigated and the Lyapunov exponents and fractal dimensions of particle trajectories for different particle inertia and particle drift velocity are computed. The dispersion process of particles could be characterized by the fractal dimension and dispersion coefficients. The interesting behavior of fractal dimension of particle motion in ABC flow suggested the similarity of particle motion in ABC flow and in a mixing layer. The relationship between particle dispersion coefficient and fractal dimension was nearly linear for the pseudoturbulence.

Within the context of heavy particles suspended in a turbulent airflow, we study the eff ects of gravity on acceleration statistics and radial relative velocity (RRV) of inertial particles. The turbulent flow is simulated by direct numerical simulation (DNS) on a 256 3 grid and the dynamics of O(10 6 ) inertial particles by the point-particle approach. For particles/droplets with radius from 10 to 60 µm, we found that the gravity plays an important role in particle acceleration statistics: (a) a peak value of particle acceleration variance appears in both the horizontal and vertical directions at a particle Stokes number of about 1.2, at which the particle horizontal acceleration clearly exceeds the fluid-element acceleration; (b) gravity constantly disrupts quasi-equilibrium of a droplet’s response to local turbulent motion and amplifies extreme acceleration events both in the vertical and horizontal directions and thus eff ectively reduces the inertial filtering mechanism. By decomposing the RRV of the particles into three parts: (1) diff erential sedimentation, (2) local flow shear, and (3) particle diff erential acceleration, we evaluate and compare their separate contributions. For monodisperse particles, we show that the presence of gravity does not have a significant e ff ect on the shear term. On the other hand, gravity suppresses the probability distribution function (pdf) tails of the diff erential acceleration term due to a lower particle-eddy interaction time in presence of gravity. For bidisperse cases, we find that gravity can decrease the shear term slightly by dispersing particles into vortices where fluid shear is relatively low. The di ff erential acceleration term is found to be positively correlated with the gravity term, and this correlation is stronger when the diff erence in colliding particle radii becomes smaller. Finally, a theory is developed to explain the eff ects of gravity and turbulence on the horizontal and vertical acceleration variances of inertial particles at small Stokes numbers, showing analytically that gravity aff ects particle acceleration variance both in horizontal and vertical directions, resulting in an increase in particle acceleration variance in both directions. Furthermore, the eff ect of gravity on the horizontal acceleration variance is predicted to be stronger than that in the vertical direction, in agreement with our DNS results. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4915121]

In this paper, we study systematically the effects of forcing time scale in the large-scale stochastic forcing scheme of Eswaran and Pope [“An examination of forcing in direct numerical simulations of turbulence,” Comput. Fluids 16, 257 (1988)] on the simulated flow structures and statistics of forced turbulence. Using direct numerical simulations, we find that the forcing time scale affects the flow dissipation rate and flow Reynolds number. Other flow statistics can be predicted using the altered flow dissipation rate and flow Reynolds number, except when the forcing time scale is made unrealistically large to yield a Taylor microscale flow Reynolds number of 30 and less. We then study the effects of forcing time scale on the kinematic collision statistics of inertial particles. We show that the radial distribution function and the radial relative velocity may depend on the forcing time scale when it becomes comparable to the eddy turnover time. This dependence, however, can be largely explained in term...

The dispersion of fluid elements distributed nonuniformly at the interface of a two‐dimensional, temporally evolving mixing layer was studied. The average transverse dispersion of fluid elements was found to be either enhanced or reduced markedly by simply varying the initial number density distribution along the interface. The increase in dispersion is due to the nonuniform stretching of the interface during the growth of the vortical structure. This naturally leads to a conclusion that the dispersion rate of particles in a spatially evolving mixing layer can be controlled by injecting particles nonuniformly in time.

The effect of randomly generated shocklets on velocity gradients in a three-dimensional compressible isotropic turbulence was systematically studied. The forced flows obtained from high-resolution simulations had a turbulent Mach number of 1.0 and a Taylor microscale Reynolds number around 180. The shock detection algorithm developed by Samtaney et al. [“Direct numerical simulation of decaying compressible turbulence and shocklet statistics,” Phys. Fluids 13, 1415 (2001)] was applied to extract the shocklets. Using reference frames moving with the detected shocks, we obtained statistical properties of velocity and its gradients both upstream and downstream of the shocks. It was shown that the shocks induced flow modulation at a wide range of length scales, including the inertial subrange scales. The shocks intensified enstrophy in the shock regions and this enhanced enstrophy production was partially redistributed over various scales and dissipated by straining and viscous effects outside the shock region...

The small-scale motions relevant to the collision of heavy particles represent a general challenge to the conventional large-eddy simulation (LES) of turbulent particle-laden flows. As a first step toward addressing this challenge, we examine the capability of the LES method with an eddy viscosity subgrid scale (SGS) model to predict the collision-related statistics such as the particle radial distribution function at contact, the radial relative velocity at contact, and the collision rate for a wide range of particle Stokes numbers. Data from direct numerical simulation (DNS) are used as a benchmark to evaluate the LES using both a priori and a posteriori tests. It is shown that, without the SGS motions, LES cannot accurately predict the particle-pair statistics for heavy particles with small and intermediate Stokes numbers, and a large relative error in collision rate (up to 60%) may arise when the particle Stokes number is near StK=0.5. The errors from the filtering operation and the SGS model are eval...

Kinematic descriptions of the rate of collision between two groups of particles are central to a variety of problems in cloud microphysics, engineering applications, and statistical mechanics. When particles are uniformly distributed, the collision kernel Γ depends on the statistics of relative velocities among colliding particles. In the pioneering work by Saffman and Turner [“On the collision of drops in turbulent clouds,” J. Fluid Mech. 1, 16 (1956)], two different formulations were used to calculate Γ between two arbitrary particle size groups in a turbulent flow. The first or spherical formulation is based on the radial or longitudinal component wr of the relative velocity w between two particles at contact: Γsph=2πR2⟨∣wr∣⟩, where R is the geometric collision radius. The second or cylindrical formulation is based on the vector velocity itself: Γcyl=πR2⟨∣w∣⟩. It was shown previously by Wang et al. [“Statical mechanical descriptions of turbulent coagulation,” Phys. Fluids 10, 2647 (1998)] that the sphe...