An approach of wall-modeled large-eddy simulation (WMLES) on non-body-conforming Cartesian grids is proposed. The proposed WMLES employs a partial-slip wall-boundary condition at the wall to reduce the numerical errors due to the insufficient grid resolution in the near-wall regions. Also, since the partial-slip wall-boundary condition reduces the velocity gradient in the near-wall regions, a modeled turbulent shear stress is introduced to maintain the balance of the total shear stress in the near-wall region. The proposed modeled stress augments only the shear-stress components and thus minimizes the adverse effects on the resolved turbulence. The proposed approach is crucial for obtaining the logarithmic law of the wall for the mean streamwise velocity correctly on non-body-conforming grids where the conservation laws are not strictly satisfied. The proposed WMLES is validated through the simulation of fully developed flat-plate turbulent boundary layers on non-body-conforming Cartesian grids. The mean streamwise velocity and Reynolds shear-stress profiles obtained by the proposed WMLES show good agreement with experimental data, while those obtained by the conventional nonslip wall-boundary conditions deviate far from the experimental data. The quantification analysis of the conservation errors indicates that the conservation errors are significantly reduced by introducing the partial-slip boundary condition and modeled turbulent shear stress. The proposed WMLES also shows robustness for various conditions, such as the cases with different plate angles relative to the grid lines and those with various Reynolds numbers.

Face covering, commonly known as a facemask, is considered to be one of the most effective pieces of personal protective equipment to reduce transmissions of pathogens through respiratory droplets—both large droplets and liquid aerosol particles. Facemasks inhibit the expulsion of such respiratory droplets from the user and protect the user from inhaling pathogen-laden potentially harmful droplets or their dried nuclei. While the efficacies of various dry face masks have been explored in the recent past, a comprehensive investigation of a wet mask is lacking. Yet users wear masks for an extended period and, consequently, due to the deposition of respiratory droplets released through multiple respiratory events, the mask matrix becomes wet. We, herein, present an experimental study on the dynamics of sequential impacts of droplets on masks to understand how wetness affects possible penetration and secondary atomization of the impacted droplet. Two different types of masks, hydrophobic and hydrophilic, were used in this study to evaluate the underlying physical mechanisms that control the penetration in each of them.

Face masks are used widely to mitigate the spread of infectious diseases. While their main purpose is to filter pathogenic droplets, masks also represent a porous barrier to exhaled and inhaled air flow. In this study, we characterize the aerodynamic effect of the presence of a mask by tracking the air exhaled by a person through a mask, using both infrared imaging and particle image velocimetry performed on illuminated fog droplets surrounding a subject. We show how a mask confines the exhaled flows within tens of centimeters in front of a person breathing or speaking. In addition, we show that the tissue of common surgical face masks has a low permeability, which efficiently transforms the jetlike flows of exhalation produced during breathing or speaking into quasivertical buoyancy-driven flows. Therefore, wearing a mask offers a strong mitigation of direct transport of infectious material in addition to providing a filtering function. By comparing results on human subjects and model experiments, we propose a model to rationalize how a mask changes the air flow, and thus we provide quantitative insights that are useful for descriptions of disease transmission.

Imbibition, the displacement of a nonwetting fluid by a wetting fluid, plays a central role in diverse energy, environmental, and industrial processes. While such flows are typically studied in homogeneous porous media with uniform permeabilities, in many cases, the media have multiple parallel strata of different permeabilities. How such stratification impacts the fluid dynamics of imbibition, as well as the fluid saturation after the wetting fluid breaks through to the end of a given medium, is poorly understood. We address this gap in knowledge by developing an analytical model of imbibition in a porous medium with two parallel strata, combined with a pore network model that explicitly describes fluid crossflow between the strata. By numerically solving these models, we examine the fluid dynamics and fluid saturation left after breakthrough. We find that the breakthrough saturation of nonwetting fluid is minimized when the imposed capillary number Ca is tuned to a value ${\text{Ca}}^{*}$ that depends on both the structure of the medium and the viscosity ratio between the two fluids. Our results thus provide quantitative guidelines for predicting and controlling flow in stratified porous media, with implications for water remediation, oil/gas recovery, and applications requiring moisture management in diverse materials.

We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary differential equations parametrized by neural networks that retain clear physical structure information, such as free energy, diffusion, conservative motion, and external forces. For high-dimensional problems with a low-dimensional slow manifold, an autoencoder with metric-preserving regularization is introduced to find the low-dimensional generalized coordinates on which we learn the generalized Onsager dynamics. Our method exhibits clear advantages over existing methods on benchmark problems for learning ordinary differential equations. We further apply this method to study Rayleigh-Bénard convection and learn Lorenz-like low-dimensional autonomous reduced-order models that capture both qualitative and quantitative properties of the underlying dynamics. This forms a general approach to building reduced-order models for forced-dissipative systems.

We derive a metric to assess the reliability of linear constitutive relations that describe nonequilibrium hydrodynamic transport. The derivation of the metric utilizes the first-order perturbation to equilibrium Maxwellian velocity density function in the Chapman-Enskog expansion. The metric is defined as the contribution to macroscopic quantities from those regions of phase-space volume wherein the first-order perturbation becomes unphysical. The volume of these subregions of phase-space and, therefore, the corresponding contribution to macroscopic quantities increases with the strength of nonequilibrium (equivalently, the gradients of physical observables). Physical interpretation and performance of the metric are examined for a nonreactive sonic boundary layer flow. The metric provides the first apriori estimate of uncertainties on physical observables computed from the Navier-Stokes equations. The assigned uncertainties can be propagated in the flow field to assess the applicability of the Navier-Stokes equations for flows with strong nonequilibrium and/or rarefied gas physics.

We observe a novel type of shear banding in the rheology of thixotropic yield-stress fluids that is due to the coupling of both nonlocality and thixotropy. The latter is known to lead to shear banding even in homogeneous stress fields. Yet, in the presence of nonlocal effects such bands appear smoothed by the continuous shear rate variation across the shear band. Here, we introduce a simple nonlocal model for the shear banding (NL-SB), and we implement it for the analysis of sub-mm rheo-MRI velocimetry measurements of a milk microgel suspension in a cone-and-plate geometry. The proposed NL-SB model enables quantifying the cooperativity length, yielding values in the order of the aggregate size in the microgel.

This study numerically investigates the bifurcation aspect of the wide-gap spherical Couette flow (SCF), with an emphasis on the competition among polygonal coherence with different wave numbers observed over transitional Reynolds numbers. Focusing on a representative case, the half-radius ratio $\eta =1/2$, we confirm that the axisymmetric state becomes unstable over the first transitional Reynolds number at which the fourfold spiral state bifurcates, using the continuation method based on the Newton–Raphson algorithm. The Galerkin-spectral method was employed to numerically solve the governing equations. It is found that the threefold spiral state bifurcates from the axisymmetric state at a slightly higher Reynolds number than the first transitional Reynolds number. The attraction of the threefold spiral state expands rapidly with an increase in the Reynolds number, which is determined by verifying the distance of the unstable periodiclike state to both spiral states in the state space. This aspect of the state space explains the experimentally bistable realization of different equilibrium states over the first transitional Reynolds number. This study also found that the periodiclike state is composed of the three- and fourfold spiral states, similar to a beat with two different frequencies.

We study the free-surface deformation dynamics of an immersed glassy thin polymer film supported on a substrate, induced by an air nanobubble at the free surface. We combine analytical and numerical treatments of the glassy thin film equation, resulting from the lubrication approximation applied to the surface mobile layer of the glassy film, under the driving of an axisymmetric step function in the pressure term accounting for the nanobubble's Laplace pressure. Using the method of Green's functions, we derive a general solution for the film profile. We show that the lateral extent of the surface perturbation follows an asymptotic viscocapillary power-law behavior in time, and that the film's central height decays logarithmically in time in this regime. This process eventually leads to film rupture and dewetting at finite time, for which we provide an analytical prediction exhibiting explicitly the dependencies in surface mobility, film thickness, and bubble size, among others. Finally, using finite-element numerical integration, we discuss how nonlinear effects induced by the curvature and film profile can affect the evolution.

The relaxation dynamics of a bent rod immersed in a fluid is studied experimentally for various rod materials and sizes and fluid viscosities. One extremity of the rod is clamped while its free end is displaced from its equilibrium position by a controlled distance. For large bending stiffness or low viscosity, the dynamics is underdamped and the rod oscillates around its equilibrium position with a well-defined frequency and a damped amplitude. In contrast, for low bending stiffness or large viscosity, the dynamics is overdamped and the rod relaxes to its equilibrium position without oscillating. We show the existence of two overdamped regimes where the relaxation dynamics is characterized by two different polynomial decays showing that the viscous force is not proportional to the rod velocity. The system is modeled using the dynamical beam equation supplemented by the viscous force experienced by a rigid cylinder moving at a constant speed in a fluid. In spite of this approximation, the model describes the dynamics in good approximation and provides a simple explanation for the existence of two overdamped regimes which originate from a change of the viscous force behavior as the Reynolds number varies. The model is then used to characterize the overdamped relaxation dynamics of the papillae of the bee tongues observed during nectar feeding. We show that the papillae relaxation is not complete when the sugar concentration exceeds 30% which impacts the amount of nectar collected per lap and yields an optimal concentration around 55% for the energy intake rate.

Ionic transport in one- and two-dimensional (2D) electrolytic cells operating at high voltage with a nonsymmetric electrolyte consisting of three species is simulated numerically. The numerical simulations are aimed at elucidating the differences in the onset of the electroconvective instability in the nonsymmetric electrolyte in a 2D electrolytic cell compared with that for a symmetric binary electrolyte. An extensive parametric study is performed to determine the mechanisms governing the onset of the instability. In addition, the main characteristics of the spatiotemporal evolution of the electroconvective instability are investigated. By focusing on the characteristics typical of the onset of the electroconvective instability in a nonsymmetric electrolyte, we are able to offer a physical interpretation and a detailed discussion of the origin and development of this instability.

The main concern of this paper is to investigate the effects on the stability behavior of wall suction or injection for external boundary-layer flow over a heated, porous plate for a fluid with temperature-dependent viscosity. The wall suction or injection are applied to the flow by a simple modification for the no-penetration condition and the current boundary conditions on the flat plate. Liquid-type viscosities are found to entrain both the velocity and temperature profiles closer to the plate with increasing both temperature sensitivity and suction intensity, whereas gas-type viscosities are found to exhibit the reverse effect with increasing flow injection and decreasing temperature dependence. We present then the linear stability analysis and find that increasing both the temperature dependence (from gas- to liquid-type behavior) and suction intensity of the fluid leads to increasing critical Reynolds number to a point of maximum stability. We note also that increasing both the Prandtl number (Pr) and flow suction in the liquid-type behavior results in an increased critical Reynolds number. The magnitudes of the perturbation eigenfunctions are considered before utilising them to obtain solutions to an energy balance integral. We find that the eigenfunction profiles are imitative of the narrowing of their mean flow counterparts when increasing either the temperature dependence or the flow suction. Our results are then confirmed by the energy analysis, where we find a significant reduction in the energy produced by the disturbance with increasing suction intensity and ultimately leads to a more stable flow. Overall, there is a strong destabilizing effect with increasing injection and the temperature-dependent viscosity over a heated plate. In summary, the findings indicate that increasing the wall suction and temperature dependence results in significantly more stable flows. It is worth noting that application and extension of this study are considered in the context of chemical vapor deposition reactors.

Ionic liquids have remarkable properties and are commonly harnessed for green chemistry, lubrication and energy applications. In this paper, we study a thermoresponsive ionic liquid (IL) solution which has the property of phase separating above a critical temperature, an interesting feature for the recovery of the IL-rich phase. For this purpose, we generate a temperature gradient in a microfluidic cavity where the confinement strengthens wetting effects and enhances the demixing. In this experimental configuration, we report the separation patterns along the phase diagram of the binary mixture composition. Three separation dynamics regime are identified that may display complex three-dimensional flows. In spite of this complexity, we rationalize all the observed regimes. Only two regimes lead to a complete spatial separation of the two phases. Interestingly, one is reminiscent of a Marangoni instability in radial geometry, even at confinement below $100\mu \mathrm{m}$. We believe this work will find applications in the recycling of ILs.

Novel numerical simulations investigating the Richtmyer-Meshkov instability (RMI) with surface tension are presented. We solve the two-phase compressible Euler equation with surface tension and interface reconstruction by a volume-of-fluid method. We validate and bridge existing theoretical models of effects of surface tension on the RMI in the linear, transitional, and nonlinear postshock growth regimes. After deriving a consistent nondimensional formulation from an existing linear incompressible theory predicting perturbation development under large surface tension, we find good agreement with theoretical prediction in the small-amplitude (linear) oscillatory regime for positive Atwood numbers, and we show that negative Atwood numbers can be accommodated by an appropriate modification to the theory. Next, we show good agreement with nonlinear theory for asymptotic interface growth in the limit of small surface tension. Finally, we use the nondimensional formulation to define a heuristic criterion which identifies the transition from the linear regime to the nonlinear regime at intermediate surface tension. These results highlight the utility of this numerical method for compressible problems featuring surface tension, and they pave the way for a broader investigation into mixed compressible/incompressible problems.

Using direct numerical simulation, the dynamics of ellipsoidal particles in a turbulent channel flow is examined at three values of the friction Reynolds number, ${\text{Re}}_{\tau }=180$, 400, and 550. Once the flow has reached a statistically steady state, the Lagrangian tracking of $300000$ prolate ellipsoids, modeled as point particles, is conducted. A global parameter based on entropy is used to follow the evolution of the particle concentration and reveals that, when expressed in wall units, the duration of the transient period increases with the Reynolds number. Once the particle distribution has reached a statistically stationary state, the distribution is closer to the uniform distribution for high values of ${\text{Re}}_{\tau }$, with a small influence of the aspect ratio, but a noticeable effect of particle inertia. In the viscous sublayer, where the mean velocity gradient causes Jeffery-like orbiting of the ellipsoids, preferential orientation is affected by ${\text{Re}}_{\tau }$. The stronger fluctuations of the fluid vorticity occurring at higher ${\text{Re}}_{\tau }$ are responsible for a destabilization of the weakly stable rotation orbits of the spheroids. Spinning particles are more likely to align with the fluid seen vorticity and spend less time aligned with the mean flow, while tumbling particles are more likely to be found out of the mean velocity-gradient plane.

We introduce an original chemical reaction between two transparent reactant solutions (fluorescin and potassium ferricyanide), producing a fluorescent product in water (fluorescein). The reaction has a tunable kinetics, allowing the quantitative investigation of the interplay between molecular diffusion and reaction kinetics in various reactant field topologies. We document the chemical reaction kinetics and its sensitivity to ambient pH, temperature, reactants concentrations, etc., and we implement it in two simple reactant-contacting geometries in a Hele-Shaw cell. The resulting reaction-diffusion zones and product formation rates exhibit either the reaction-controlled or diffusion-controlled regimes, as well as a new “diffusio-chemical” regime which we show to be inherent to the early time transient dynamics of any bimolecular reaction between initially segregated reactants. The potential interest of this reaction, opening prospects for the study of reactive mixing, is underlined.

In this experimental study we consider the geometric focusing of internal waves by the horizontal oscillation of a torus in a stratified or rotating stratified fluid. In order to minimize viscous dissipation the experiments have been conducted at the $13\text{−}\mathrm{m}$-large Coriolis platform and a large torus was used so that a Stokes number of approximately 6000 was reached. For such large Stokes numbers the waves are bimodal, i.e., they are emitted at the critical locations where the rays are tangential to the torus boundary such that each section of the torus generates for each direction of propagation two wave rays. In contrast to the unimodal case for which these waves diffuse into a single wave beam and there is a single focusing region, there are now four focal regions where the waves emitted from the inner and outer sides of the sections meet. The focusing of the waves on the axis gives rise to strongly nonlinear processes. A linear theory for internal waves emitted by an oscillating torus is presented. For small oscillation amplitudes, we obtain a reasonable agreement of the bimodal wave structure with this linear theory. Resonant wave triads are observed in the stratified (nonrotating) case, similar to the triads of unimodal waves previously observed at moderate Stokes numbers. In the presence of background rotation, no triad is present since the oscillation frequency falls outside the range for which triads can exist. For higher oscillation amplitudes, the waves become highly nonlinear. This results in a spreading of the fundamental wave beams which have relatively less energy than for small oscillation amplitudes, while higher harmonics in the focal region and in the boundary layer of the torus have slightly more energy. A similar tendency is observed for inertia-gravity waves. A large spectrum of waves in resonant interactions is thus observed. This behavior strongly differs from its moderate-Stokes-number counterpart for which higher oscillation amplitudes result in an increase of the energy of the fundamental wave beams. In contrast to observations for small Stokes numbers that showed a decrease in Richardson number with the oscillation amplitude, the Richardson number near the torus and in the focusing region remains constant and close to 1, and overturning wave motions are absent. The results are discussed in the context of the ocean.

We show how the overall concentration distribution of the product in a randomly stirred reactive mixture is modified by the chemical reaction. We decipher the intermingled effects of stretching enhanced diffusion and chemical production on the evolution of each concentration level, and show why chemical kinetics contributes to a “rectification” mechanism when low concentration levels grow faster than higher ones. The rectification amounts to a compression of the product concentration distribution, which is found to be narrower around its mean than for a pure, nonreactive scalar. This phenomenon is illustrated through a series of quantitative experiments in which scalar mixing and the effects of the reaction are measured concomitantly, but independently.

This paper is associated with a video winner of a 2020 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2020.GFM.V0019.