Chemically driven convective dissolution can occur upon reaction of a dissolving species in a host phase when the chemical reaction destabilizes an otherwise stable density stratification. An $\mathrm{A}+\mathrm{B}\to \mathrm{C}$ reaction is known to trigger such convection when, upon dissolution into the host solution, A reacts with B present in the solution to produce a sufficiently denser product C. We study numerically the effect of differential diffusion on such a chemically driven convective dynamics. We show that below the reaction front either double-diffusive or diffusive-layer convection can arise, modifying the local Rayleigh-Taylor instability. When B diffuses faster than C, the density profile contains a local maximum at the reaction front, followed by a local minimum below it. A double-diffusive instability can develop below the reaction front, accelerating the convective dynamics and thereby enhancing the dissolution rate of A into the host phase. Conversely, when B diffuses slower than C, the density profile exhibits a local maximum below the reaction front and diffusive-layer convection modes stabilize the dynamics compared to the equal diffusivity case. When B and C diffuse at equal rates but faster than A, the convective dynamics is accelerated with respect to the equal diffusivity case.

Superhydrophobic surfaces used in various applications to enhance flow and reduce drag typically consist of irregular nanostructures. However, many theoretical models and most laboratory microscale experiments dealing with these phenomena are limited to structures consisting of regular microarrays and cannot explain the macroscopic flow enhancement observed in applications. Here, we investigated microscopically the wetting and flow over fluorinated silicon nanofilaments as an example for an application-relevant, irregularly nanostructured, superhydrophobic surface. Using fluorescence correlation spectroscopy with an improved evaluation method, we found that velocity profiles are still nonlinear at distances below 1 $\mu \text{m}$ to the surface. Furthermore, we observed that the air layer in between and on the nanofilaments is not continuous on a micrometer length scale. First, there are regions with homogeneous wetting, where the air-water interface regularly touches all uppermost fibers. These regions possess a low slip length ($<5\mu \mathrm{m}$). Both the wetting and the slip length match with expectations from microarray or homogeneous porous surfaces. Second, there are large patches with air inclusions, which present two orders of magnitude higher slip lengths. Our results contribute to the understanding of the drag reduction observed in applications and can help in designing new, optimized surfaces.

In this work, a data-driven wall model for turbulent flows over periodic hills is developed using the feedforward neural network (FNN) and data from wall-resolved large-eddy simulation (WRLES). To develop a wall model applicable to different flow regimes, the flow data in the near-wall region at all streamwise locations are grouped together as the training data set. In the developed FNN wall models, we employ the wall-normal distance, near-wall velocities, and pressure gradients as input features and the wall shear stresses as output labels, respectively. A priori tests on the prediction accuracy and generalization capacity of the trained FNN wall model are carried out by comparing the predicted wall shear stresses with the WRLES data from the same cases for model training and the cases with different Reynolds numbers and hill geometries. For the instantaneous wall shear stress, the FNN predictions show an overall good agreement with the WRLES data with some discrepancies observed at locations near the crest of the hill. The correlation coefficients between the FNN predictions and WRLES predictions are larger than 0.7 at most streamwise locations. For the mean wall shear stress, the FNN predictions agree very well with WRLES data. A posteriori test is also carried out. A good performance is observed for the turbulent channel flow case. Discrepancies between the predictions from the wall-modeled LES and the WRLES are observed for the periodic hill case.

The partially averaged Navier-Stokes (PANS) equations model is used to predict the transitional Taylor-Green vortex (TGV) flow at Reynolds number 3000. A form of the closure is proposed in which the PANS procedure is applied to a variant of the Besnard-Harlow-Rauenzahn turbulence model. The TGV is a benchmark case for transitional flows in which the onset of turbulence is driven by vortex-stretching and -reconnection mechanisms. Since these physical phenomena are observed in numerous flows of variable density (e.g., oceanography and material mixing), this study constitutes the first step toward extending the PANS method to such a class of problems. We start by deriving the governing equations of the model and analyze the selection of the parameters controlling its physical resolution, $f_{\varepsilon }$ and $f_k$, through a priori testing. Afterward, we conduct PANS computations at different constant physical resolutions to evaluate the model's accuracy and cost predicting the TGV flow. This is performed through simple verification and validation exercises, and the physical and modeling interpretation of the numerical predictions. The results confirm that PANS can efficiently (accuracy vs cost) predict the present flow problem. Yet, this is closely dependent on the physical resolution of the model. Whereas high-physical-resolution ($f_k<0.50$) computations are in good agreement with the reference direct numerical simulation (DNS) studies, low-physical-resolution ($f_k\ge 0.50$) simulations lead to large discrepancies with the reference data. The physical and modeling interpretation of the results demonstrates that the origin of these distinct behaviors lies in the model's ability to resolve the phenomena driving the onset of turbulence not amenable to modeling by the closure. The comparison of the computations' cost indicates that high-physical-resolution PANS achieves the accuracy of DNS ($f_k=0.00$) at a fraction of the cost. We observe a cost reduction of one order of magnitude at the current Re, which is expected to grow with Re.

The accurate measurement of flows and aerodynamic characteristics around a bluff body has been a challenging task due to the existence of interference between the wake and mechanical model supports in wind-tunnel experiments. The present study focuses on a freestream-aligned circular cylinder with an extremely low fineness ratio (the ratio of the axial length to diameter) ranging from 0.30 to 0.50, which has never been investigated without interference from a mechanical model support. We employed a magnetic suspension and balance system to eliminate interference from the model support and measured the drag and velocity fields in the diameter-based Reynolds number between $2.0\times {10}^4$ and $7.7\times {10}^4$. As the fineness ratio decreases below 1.50, the size of the recirculation bubble increases and the velocity distribution on the central axis inside the bubble gradually converges to that of the circular disk. Furthermore, large-eddy simulations were performed in the Reynolds number of $4.0\times {10}^4$, whose drag coefficient agrees well with experiments. Based on those results, it was found that the drag coefficient monotonically converges to that of the circular disk without local maximum. This study revealed that in the low-fineness-ratio regime (0.10–0.50), a critical geometry, at which the drag coefficient shows a local maximum, does not exist in the circular cylinder. Subsequently, unsteady flow analyses were performed, where two characteristic frequencies, i.e., $\mathrm{St}=0.05$ and 0.155, were identified from power spectral densities of the drag coefficient and the pitching moment coefficient. The associated flow structures are then extracted by a phase-averaging procedure, where the phase-averaged flows with $\mathrm{St}=0.05$ represent the recirculation bubble pumping while the phase-averaged flows with $\mathrm{St}=0.155$ show nonaxisymmetric structures inside the recirculation bubble.

Previous studies have demonstrated that the complex motion of a droplet moving on a vibrated fluid surface can yield a long-term statistical behavior reminiscent of that of quantum particles. This is especially the case when the droplet is confined within a small corral. Here we investigate the motion of walkers in a large corral with the boundary constructed from a circular array of pillars that protrude through the fluid surface. Our measurements demonstrate that the structure of the corral walls affects the droplet position probability distribution.

A lattice Boltzmann simulation of a viscous fingering instability with miscible components is performed. The core ingredients of the instability are related to the molecular diffusion and the viscosity discrepancy, or, more specifically for the lattice Boltzmann model (LBM), intermolecular friction forces and partial viscosities. Generally, the instability occurs when a less viscous fluid displaces a more viscous fluid in a porous medium. The viscous fingering is first studied in the case of a binary mixture. At early times in the linear regime, the growth rate of the perturbation is computed for different Péclet numbers. The growth rate, as well as the most dangerous and cutoff numbers, increases with the Péclet number. A good agreement is found with a linear stability analysis in which a quasi-steady-state approximation is used. For intermediate times when strong nonlinear interactions take place, the development of the instability is described globally through the mixing length. A high Péclet number leads to more intense instability. Two regimes are visible: the diffusive regime, when fingers remain small and the growth of the mixing length is dominated by diffusion and proportional to $\sqrt{t^{★}}$, and the convective regime, when fingers become larger than the diffusive length and the growth of the mixing length is proportional to $t^{★}$. Finally, it is shown that the LBM can describe complex diffusion specific to the case of three species. For instance, viscous fingering could be induced by reverse diffusion despite having a stable initial flow configuration. At early times, each species exhibits different growth rates and then converges to the same value. Afterward, the same diffusive and convective regimes are also recovered for the three species but are delayed in time due to the complex diffusion mechanisms.

A tropical cyclone (TC) over ocean functions as a heat engine fueled by ocean moisture. By contrast, its decay past landfall is thought to be akin to a dry vortex spinning-down due to friction with the land, an intrinsically nonthermodynamic process. We study the evolution of TCs past landfall using computational simulations where we explicitly account for thermodynamics. Doing so allows us to uncover that past landfall the TC's dynamical heart—the warm core—does not simply wither away. Instead, thermodynamic processes modulated by the moisture stored in the TC invariably engender a cold core that grows underneath and at the expense of the warm core. Our findings underscore the key role of moist thermodynamics in the postlandfall evolution of TCs. Additionally, they have direct implications on the prevailing weather forecasting methods which invoke the birth of a cold core as a telltale signature of an extratropical transition.

The stability of a pulsatile quasi-two-dimensional duct flow was numerically investigated. Flow was driven, in concert, by a constant pressure gradient and by the synchronous oscillation of the lateral walls. This prototypical setup serves to aid understanding of unsteady magnetohydrodynamic flows in liquid metal coolant ducts subjected to transverse magnetic fields, motivated by the conditions expected in magnetic confinement fusion reactors. A wide range of wall oscillation frequencies and amplitudes, relative to the constant pressure gradient, were simulated. Focus was placed on the driving pulsation optimized for the greatest reduction in the critical Reynolds number for a range of friction parameters $H$ (proportional to magnetic field strength). An almost 70% reduction in the critical Reynolds number, relative to that for the steady base flow, was obtained toward the hydrodynamic limit ($H={10}^{-7}$), while just over a 90% reduction was obtained by $H=10$. For all oscillation amplitudes, increasing $H$ consistently led to an increasing percentage reduction in the critical Reynolds number. This is a promising result, given fusion relevant conditions of $H\ge {10}^4$. These reductions were obtained by selecting a frequency that both ensures prominent inflection points are maintained in the base flow and a growth in perturbation energy in phase with the deceleration of the base flow. Nonlinear simulations of perturbations driven at the optimized frequency and amplitude still satisfied the no net growth condition at the greatly reduced critical Reynolds numbers. However, two complications were introduced by nonlinearity. First, although the linear mode undergoes a symmetry-breaking process, turbulence was not triggered. Second, a streamwise invariant sheet of negative velocity formed, able to arrest the linear decay of the perturbation. Although the nonlinearly modulated base flow maintained a higher time-averaged energy, it also stabilized the flow, with exponential growth not observed at supercritical Reynolds numbers.

The compressibility effect in isothermal hypersonic boundary layer is studied with direct numerical simulation (DNS) using Helmholtz decomposition. The dilatational components of the diagonal Reynolds stress are enhanced by the cold wall condition in the near-wall region. The outward (Q1) and ejection (Q2) events are mainly located in the expansion region, while the inward (Q3) and sweep (Q4) events are primarily situated in the compression region near the wall. It is found that the cold wall condition can enhance the inward (Q3) event mainly in the compression region and enhance the ejection (Q2) event mainly in the expansion region near the wall. In particular, the cold wall can significantly enhance the positive streamwise solenoidal fluctuating velocity and negative wall-normal dilatational fluctuating velocity events. Moreover, the cold wall condition enhances the positive correlation of streamwise velocity fluctuation and fluctuating temperature, and suppresses the negative correlation of wall-normal velocity fluctuation and fluctuating temperature in the near-wall region, while it slightly weakens the negative correlation of streamwise velocity fluctuation and fluctuating temperature and the positive correlation of wall-normal velocity fluctuation and fluctuating temperature far from the wall. It is also found that the dilatational components of correlations are dominated in the near-wall region, while the solenoidal components govern the correlations far from the wall. Most of the interactions among mean and fluctuating fields of kinetic and internal energy are governed by the solenoidal components, except for the terms associated with the pressure, which are governed by the dilatational components.

Understanding and modulating the cross-stream motion of a surfactant-coated droplet in pressure driven flow has great implications in many practical applications. A combination of interfacial viscosity and Marangoni stress acting over a surfactant-coated droplet in pressure driven flow offers greater flexibility to modulate the cross-stream motion of it. Despite the intense theoretical and numerical research towards manipulating the surfactant-laden Newtonian droplets in Poiseuille flow, the experimental investigations are relatively scarce. Herein, we report our study on understanding the influence of interfacial viscosity on the cross-stream motion of a surfactant-coated Newtonian droplet in both isothermal and nonisothermal Poiseuille flow from a theoretical as well as an experimental perspective. A theoretical model has been developed to understand the effect of interfacial viscosity on the lateral migration of a droplet under the assumptions of negligible shape deformation, fluid inertia, and thermal convection. Theoretical analysis is performed under two limiting conditions: (i) when the transport of surfactants is dominated by surface diffusion and (ii) the transportation of surfactants is dominated by surface convection. Our theoretical analysis shows that both the dilatational as well as the shear surface viscosities suppress the lateral migration velocity of the droplet. Experiments have been performed to validate the theoretically predicted droplet trajectories and to understand the influence of channel confinement on the lateral migration of the droplet. Experiments show that the droplet travels faster towards the centerline of the flow in a highly confined domain. The results presented in this study could provide new vistas in designing and analyzing various droplet-based microfluidic, biomedical, and bio-microfluidic devices.

We studied the segregation of single large intruder particles in monodisperse granular materials. Experiments were carried out in a two-dimensional shear cell using different intruder and media diameters, whose quotient defined a size ratio $R$ that ranged from 1.2 to 3.333. When sheared, the intruders segregated and rotated at different rates, which depended on their $R$ values and depth. The vertical intruder trajectories as a function of time were curved due to nonconstant depth-dependent segregation rates. An analysis that considered the lithostatic pressure distribution and a size ratio dependence was done to capture the trajectories and the general segregation rate behavior. As a result of a strain rate analysis, we observed a greater expansion rate around the intruders when $R$ values were larger, which in turn promoted faster segregation. Experiments with large $R$ values showed that intruder rotation was weak and local shear rates were low. In contrast, experiments with $R$ closer to unity resulted in strong intruder rotation, high local shear rates, and contraction below the intruder. Therefore, an intruder with a diameter close to that of the medium was likely to segregate due to a rotation mechanism. We propose that large particle segregation depends on size ratio, local expansion rate, and, to a lesser extent, the local shear rate. Based on our observations we redefine large particle segregation as two well-defined processes dependent on $R$ and the local strain rate.

The ambient conditions surrounding liquid droplets determine their growth or shrinkage. However, the precise fate of a liquid droplet expelled from a respiratory puff as dictated by its surroundings and the puff itself has not yet been fully quantified. From the view of airborne disease transmission, such as SARS-CoV-2, knowledge of such dependencies is critical. Here, we employ direct numerical simulations (DNS) of a turbulent respiratory vapor puff and account for the mass and temperature exchange with respiratory droplets and aerosols. In particular, we investigate how droplets respond to different ambient temperatures and relative humidity ($\mathrm{RH}$) by tracking their Lagrangian statistics. We reveal and quantify that in cold and humid environments, as there the respiratory puff is supersaturated, expelled droplets can first experience significant growth, and only later followed by shrinkage, in contrast to the monotonic shrinkage of droplets as expected from the classical view by Wells in 1934. Indeed, cold and humid environments diminish the ability of air to hold water vapor, thus causing the respiratory vapor puff to supersaturate. Consequently, the supersaturated vapor field drives the growth of droplets that are caught and transported within the humid puff. To analytically predict the likelihood for droplet growth, we propose a model for the axial RH based on the assumption of a quasistationary jet. Our model correctly predicts supersaturated RH conditions and is in good quantitative agreement with our DNS. Our results culminate in a temperature-RH map that can be employed as an indicator for droplet growth or shrinkage.

We develop an analytical model to describe recent experimental observations of levitation of evaporating microscale droplets over heated solid surfaces at temperatures far below the Leidenfrost point. Viscous flow patterns around the droplet are determined from the solution of the equation for the Stokes stream function in bipolar coordinates. The results are compared to the predictions of models representing microscale droplets as point sources in the Stokes flow equations. Formulas for the force acting on the droplet as a result of moist air flow around it are derived and used to obtain predictions of levitation height as a function of droplet size which are in very good agreement with the experimental data. In addition to gravity, three physical mechanisms are identified which contribute to the force acting on the droplet: repulsive interaction of the droplet with the solid, spatially nonuniform evaporation along the liquid surface, and thermocapillary effect. The first two act against gravity and allow droplets to levitate despite competing thermocapillary stresses which push the moist air out of the region between the droplet and the solid. Relative importance of the three mechanisms is evaluated based on an analytical model of heat transfer both inside and outside of the droplet.

The adiabatic behavior of two-dimensional (2D) fluid vortices subject to slowly varying, time-dependent external strain flows is studied theoretically, and experimentally using magnetized non-neutral electron plasmas. Here the $\mathbf{E}\times \mathbf{B}$ drift dynamics of the electrons perpendicular to the magnetic field are analogous to the motion of fluid vorticity under the 2D Euler equations describing ideal fluids. A low-dimensional elliptical vortex patch model is used along with a WKB approximation to derive a formula for the breaking of an adiabatic invariant due to the changing external flow. The invariant is interpreted as the amplitude of a perturbative oscillation about a stable fixed point corresponding to a steady elliptical vortex. Smooth, hyperbolic tangent and piecewise linear ramp functions are considered for the external strain time dependence. Standard exponential breaking is observed in the former case, whereas the latter exhibits a power-law breaking curve with periodic modulation. It is found that a driving term in the equations of motion contributes the majority of the breaking whereas the frequency variation plays a weaker, but significant role. The experimental data agree closely with the theoretical model. The most significant deviation is due to inviscid damping behavior associated with the smooth edges of the experimental vortices, which tends to reduce the amplitude of the oscillation. The results are compared and contrasted with other related experimental, numerical, and theoretical work.

Segregation, or demixing, of flowing mixtures of size-disperse noncohesive spherical particles is well understood. However, most particle systems in industry and geophysics involve nonspherical particles. Here, the segregation of bidisperse mixtures of millimeter-sized particles having various shapes is characterized using discrete element method simulations of gravity-driven free-surface granular heap flow. As a proxy for nonspherical particles, we study mixtures of cylindrical particles that vary widely in both their length and diameter ratios, including both disks and rods, as well as mixtures of cylindrical and spherical particles. The propensity to segregate is measured with a segregation length scale that characterizes the segregation velocity of the two species for these types of mixtures, identical to the approach for mixtures of spherical particles. Surprisingly, segregation can be predicted based solely on the volume ratio of the two species, regardless of particle shape. The segregation length scale increases linearly with the log of the volume ratio for volume ratios varying from 0.1 to 10 in the same way as it does for bidisperse mixtures of spherical particles. Thus, segregation properties based on spherical particles can be directly applied to nonspherical particles.

A previous formulation of plume merger [Rooney, J. Fluid Mech. 796, 712 (2016)] is generalized to model both Boussinesq and non-Boussinesq plume rise in a corner of arbitrary angle $2\pi /n$ where $n\ge 1$. The Boussinesq plume theory predicts the correct near- and far-field similarity solutions when $n$ is noninteger. Moreover, an alternate entrainment assumption is proposed whereby the rate of entrainment per unit height correlates directly to the plume perimeter. Model predictions made using this alternative entrainment assumption agree well with a previous prediction for the plume volume flux when $n=2$. For non-Boussinesq plumes, the theory also approaches the correct near- and far-field similarity limits. When the source area is compact, and regardless of the corner angle, the non-Boussinesq height, i.e., height over which non-Boussinesq effects are important, is small compared to the contact height between the plume and the corner. When the source area is relatively large, the non-Boussinesq height can be comparable to the contact height; enhanced non-Boussinesq effects are observed for smaller corner angles. Our Boussinesq theory is adapted to the natural ventilation model developed by Linden et al. [J. Fluid Mech. 212, 309 (1990)] and agrees well with previous experimental and theoretical predictions for the steady-state depth of the layer of discharged plume fluid that accumulates along the ceiling of the (ventilated) interior space. For non-Boussinesq plumes, the counterpart theory compares satisfactorily with previously measured results of fire plume mass flux.

The absolute permeability of porous media is an important parameter for various technological applications ranging from ground water hydrology to hydrocarbon recovery to microfluidics. There are scaling relationships between the geometric structure of a porous domain and its absolute permeability within a given class of structure. However, there exists no universal relationship between permeability and structure. We use network models of porous domains and apply the max-flow min-cut theorem to extract insights into the structures that most influence absolute permeability. The max-flow min-cut theorem states that the maximum flow through any network is exactly the sum of the edge weights that define the minimum cut. We hypothesize that the min-cut can be related to network permeability. We demonstrate that flow in porous media can be modeled as described by the max-flow min-cut theorem, which provides an approach to measure the absolute permeability of three-dimensional digital images of porous media. The max-flow of a network is found to correspond to its absolute permeability for over four orders of magnitude and identifies structural regions that result in significant energy dissipation. The findings are beneficial for the design of porous materials, as a subroutine for digital rock studies, the simplification of large network models, and further fundamental studies on the structure and flow properties of porous media.

We conduct a series of three-dimensional computations to investigate the convective flow generated by the interaction between the vertical solute gradient and the horizontal thermal gradient. The first set of computations is carried out under a wide range of boundary values considered by previous experimental studies, which mostly have a strongly stratified solute gradient. Results show that the convection invariably develops into the so-called fully developed flow composed of the largest number of horizontal convection layers under all the conditions considered. Within each layer, there prevails an array of salt-finger vortices. The multilayered structure changes with boundary values systematically, while the convection layer bears a layer thickness so that the positive thermal buoyancy can balance with the negative solute buoyancy. In the second set of computations, we consider the boundary conditions so that the thermal buoyancy is much larger than the solute buoyancy. In such a weakly stratified solute gradient and a thermal-diffusion-dominated environment, the computational domain is filled with a sizeable convective circulation while no salt finger occurs.

We report an experimental study of Lagrangian velocity and acceleration in turbulent Rayleigh-Bénard convection using particle tracking velocimetry, with the Rayleigh number Ra spanning from $5.4\times {10}^8$ to $1.3\times {10}^{10}$. The measurements were made in two representative regions of a cylindrical convection cell with aspect ratio unity, where an abundant amount of thermal plumes are passing through constantly. The results are compared with those obtained in the cell's central region, where plumes are passing through much less frequently. It is found that the probability density functions (pdf's) of the three velocity components almost collapse with each other and follow Gaussian distribution for all the regions in the high Ra range, but they behave differently and deviate from the Gaussian function for lower Ra numbers. For the acceleration, the pdf's in all the regions exhibit a stretched exponential form, but for lower Ra cases the amount of stretching is much more pronounced in the plume-abundant regions as compared to that in the cell center. This difference is more evident in terms of acceleration variance: for $\mathrm{Ra}\lesssim 4.3\times {10}^9$, the acceleration variances in the plume-abundant regions are larger than those in the central region and show a different Ra-dependent power law. As Ra number increases, the acceleration variances obtained in different regions gradually merge into a single master curve that follows the Heisenberg-Yaglom prediction for homogeneous and isotropic turbulence. A consistent transitional behavior is also observed in the kinetic energy dissipation rate. Through a detailed examination of the possible balance relations between acceleration and other small-scale properties, our results show that the acceleration in the plume-abundant regions is balanced with a combination of thermal and kinetic energy dissipation rates, which suggests that the turbulent flow in these regions is governed by a mixed dynamics with contributions from both thermal plumes and turbulent background fluctuations. This picture is supported by a modified Heisenberg-Yaglom relation and also by the scaling behaviors of the Eulerian structure functions in the inertial range. The observed transitional behaviors can be understood as a result of the evolution in the circulation path of the large-scale flow, which changes from an ellipse to a more squarish shape with increasing Ra.