The present study numerically investigates the effect of the Prandtl number ($0.1\le \mathrm{Pr}\le 100$) on the flow structures and heat transport mechanism in a two-dimensional rectangular rough cell of aspect ratio 2, for more than 2 decades of the Rayleigh number (${10}^7\le \mathrm{Ra}\le 5\times {10}^9$). Large-scale diffuse structures transform into finer ones with increase in either $\mathrm{Ra}$ or $\mathrm{Pr}$. The height of roughness elements relative to the thermal boundary layer (TBL) thickness establishes the level of perturbations introduced into the system. A stronger thermal forcing or larger $\mathrm{Pr}$ facilitates a thinner TBL, which triggers a quicker response from the elements in the emission of plumes. In comparison to the smooth case, heat transport is enhanced significantly with the introduction of roughness. The near invariance of the Nusselt number $\mathrm{Nu}$ with $\mathrm{Pr}$ in smooth cells is overcome in the rough cell, where a monotonically increasing heat flux is obtained. A greater presence of plumes in the domain is identified by an augmented volume fraction and thermal dissipation from plumes. The flow intensity measured in terms of the global Reynolds number $\mathrm{Re}$ shows significant improvement for ${10}^8\le \mathrm{Ra}\le 5\times {10}^9$ and $5\le \mathrm{Pr}\le 100$ in comparison to the smooth case.

The effects of stratification parameter (Sr) and flow compressibility on mixing and energy transfer of three-dimensional compressible Rayleigh-Taylor turbulence are studied numerically for initial isothermal stratification at $\mathrm{Sr}.$ ranging from 0.5 to 3.0 and at Atwood number $A_t=0.5$. Flow compressibility plays an important role in the generation of large-scale kinetic energy, which mainly comes from the conversion of potential energy for small Sr and conversion of internal energy through pressure-dilatation work for large Sr. The latter leads to that bubble heights increase rapidly and the bubbles are bigger at large Sr. The overall statistics of normalized subgrid-scale (SGS) flux of kinetic energy is nearly independent of Sr. The reverse SGS flux is much weaker than the direct SGS flux at middle scales, and increases significantly with increase of Sr. The net upscale cascade of kinetic energy can be identified at large scales, which is more obvious at larger Sr. The compression motions enhance direct SGS flux and the expansion motions strengthen the reverse SGS flux. The conditional average of SGS flux is nearly proportional to the normalized filtered velocity divergence at $\text{Sr}\le 1.0$ and the square of filtered velocity divergence at $\text{Sr}>2.0$ in compression regions. The spatially average values of the large-scale pressure-dilatation are similar for different Sr and different times, and they have relatively large negative values at small scales for large Sr.

We simulate gravity-driven dynamics of partially wetting droplets moving along a fiber using the lattice Boltzmann method. For the so-called clamshell morphology, we find three possible dynamic regimes upon varying the droplet Bond number and the fiber radius: compact droplet, droplet breakup, and droplet oscillation. For small Bond numbers, in the compact droplet regime, the droplet reaches a steady state and its velocity scales linearly with the driving body force. We find two scaling laws depending on whether the droplet size is smaller or larger compared to the fiber radius. In addition, we further identify a scaling law applicable for the barrel morphology. For higher Bond numbers, in the droplet breakup regime, satellite droplets are formed trailing the initial moving droplet. We find such droplet satellite formation is easier with increasing fiber curvature (smaller fiber radius). Finally, in the droplet oscillation regime, favored in the midrange of fiber radius, the droplet shape periodically extends and contracts along the fiber.

Flows in porous media in the low-Reynolds number regime are often modeled by the Brinkman equations. Analytical solutions to these equations are limited to standard geometries. Finite volume or element schemes can be used in more complicated geometries, but become cumbersome when there are moving boundaries that require frequent remeshing of the domain. In Newtonian fluids, the method of regularized Stokeslets has gained popularity due to its ease of implementation, including for moving boundaries, especially for swimming and pumping problems. While the corresponding method of regularized Brinkmanlets can be used in a domain consisting entirely of Brinkman medium, many applications would benefit from an easily implemented representation of flow in a domain with heterogeneous regions of Brinkman medium and Newtonian fluid. In this paper, we model flows in porous media by placing many static regularized Stokeslets randomly in three dimensions to emulate the forces exerted by the rigid porous structure. We perform numerical experiments to deduce the correspondence between the chosen density and blob size of regularized Stokeslets in our model, and a Brinkman medium. We demonstrate our model for two scenarios of microswimmers near porous media.

A solid, withdrawn from a wetting liquid bath, entrains a thin liquid film. This simple process, first described by Landau, Levich, and Derjaguin (LLD), is commonly observed in everyday life. It also plays a central role in liquid capture by animals, and is widely used for surface-coating purposes in industry. Motivated by the emerging interest in the mechanics of very soft materials, and in particular the resulting elastocapillary coupling, we develop a dip-coating model that accounts for the additional presence of a soft solid layer atop the rigid plate. The elastic response of this soft layer is described by a Winkler's foundation. Using a combination of numerical, scaling, and asymptotic-matching methods, we find a new softness-dependent power-law regime for the thickness of entrained liquid at a small capillary number, which corresponds to a modified physics at play in the dynamic meniscus. The crossover between this regime and the classical dip-coating one occurs when the substrate's deformation is comparable to the thickness of the entrained liquid film.

Active drops emit/absorb chemical solutes, whose concentration gradients cause interfacial flows driving their own transport and the propulsion of the droplet. Such nonlinear coupling enables active drops to achieve directed self-propulsion despite their isotropy if the ratio of advective-to-diffusive solute transport, i.e., the Péclet number $\text{(Pe)}$, is larger than a finite critical threshold. In most experimental situations, active drops are non-neutrally buoyant and, thus, swim along rigid surfaces; yet theoretical descriptions of their nonlinear motion focus almost exclusively on unbounded domains to circumvent geometric complexity. To overcome this gap in understanding, we investigate the spontaneous emergence and nonlinear saturation of propulsion of an isotropic phoretic colloid along a rigid wall to which it is confined by a constant external force (e.g., gravity). This phoretic particle model is considered here as a limiting case for a viscous active drop. We show that, for moderate Pe, the particle motion and associated chemical transport reduce the chemically induced wall repulsion, thereby causing the particle to swim progressively closer to the wall as Pe increases. Far from hindering self-propulsion, this reduction in the particle-wall separation is accompanied by a wall-induced efficient rearrangement of the solute concentration gradients driving the particle, thus, augmenting its swimming speed.

Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearized Navier-Stokes system for a few low wave numbers. Resulting Galerkin systems comprise ordinary differential equations, with a number of degrees of freedom ranging from 144 to 600, which may be integrated to large times without any indication of numerical instability. The reduced-order models so obtained are also found to match statistics of direct numerical simulations at Reynolds number 500 and 1200 with reasonable accuracy, despite a truncation of orders of magnitude in the degrees of freedom of the system. The present models offer thus an interesting compromise between simplicity and accuracy in a canonical wall-bounded flow, with relatively few modes representing coherent structures in the flow and their dominant dynamics.

In this paper, we examine the rim fragmentation of a millimeter-sized methyl-ethyl-ketone droplet imposed by the impact of different millijoule nanosecond laser beams that correspond to droplet propulsion velocity values between 1.76 and 5.09 m/s. The numerical investigation is conducted within a physically consistent and computationally efficient multiscale framework, using the $\mathrm{\Sigma }\text{−}\mathrm{{\rm Y}}$ two-fluid model with dynamic local topology detection. Overall, the macroscopic droplet expansion and the obtained deforming shape show good agreement with the experimental observations. The influence of the laser beam energy on the droplet deformation and the evolution of the detached fragments from the rim is demonstrated. The physical mechanisms that determine the droplet expansion, including the expansion velocity and expansion rate, along with the effect of the surrounding air flow on the detached fragments, are addressed. Despite the visualization limitations inside the polydisperse cloud of fragments in the experimental results at higher laser energy, the evolution of fragments during the fragmentation process is quantified, and size distributions are obtained within the multiscale framework.

Water droplet freezing is a common phenomenon in our daily life. In both natural scenarios and industrial production, different surface inclinations bring distinctive deformation and freezing dynamics to frozen droplets. We explore the freezing of pendent and sessile droplets at different Bond number regimes. The effect of gravity on the droplet freezing process is analyzed by considering droplet morphology, freezing front dynamics, and freezing time. It is found that gravity can significantly influence droplet freezing processes via shaping the initial droplet, resulting in the flattening or elongation of pendent and sessile droplets, respectively. We show that the droplet initial geometry is the most important parameter and it completely controls the droplet freezing. Despite the significant difference in the initial droplet shape several remarkable similarities have been found for pendent and sessile droplets at small and large Bond numbers. The final height of a frozen droplet is found to be linearly proportional to its initial height. The time evolution of the ice-liquid-air contact line is found to reproduce the power law $t^{0.5}$, but noticeably faster than the Stefan 1D icing front propagation. As a consequence, the time to freeze a droplet is faster than predicted by the Stefan model, and it is found to be dependent on the initial droplet height and base radius through a simple power law.

In this paper we examine the possible self-organization of strongly stratified turbulence around a local critical state by analyzing a dataset of a numerically simulated stratified turbulent wake. To facilitate the analysis, the turbulent flow field is decomposed into a “large-scale” flow of horizontal scales greater than the Ozmidov scale, ${\ell }_O$, and a “small-scale” flow of scales below ${\ell }_O$. A local gradient Richardson number, $\mathrm{Ri}$, characterizing the large-scale flow is calculated and then utilized to produce conditional sampling of various turbulence statistics relevant to the local dynamics. While the bulk turbulence is observed to decay by approximately one order of magnitude in terms of the dissipation rate, the median $\mathrm{Ri}$ has remained nearly constant due to the self-organization of flow structures under strong stratification; the subsampled $\mathrm{Ri}$ distribution peaks around $1/4$ for regions in the upper quartile of local dissipation. Regions of small $\mathrm{Ri}$ are found to be associated with large dissipation and large net transfer of energy to the small scales. Regions of “back-scatter” of kinetic energy to large scales, where the local eddy viscosity, ${\nu }_e$, takes a negative value, are also observed. Occurrence of a large magnitude of both positive and negative ${\nu }_e$ appears to be most frequent around the critical value of $\mathrm{Ri}\sim 1/4$, indicating an intense two-way exchange of kinetic energy between the large and small scales around the local critical state. The threshold behavior of $\mathrm{Ri}$ underscores the dynamical significance of the critical $\mathrm{Ri}$ of $1/4$ for locally self-sustained turbulence in a strongly stratified configuration and bears some resemblance to the celebrated self-organized criticality dynamics [Bak et al., Phys. Rev. Lett. 59, 381 (1987)].

Recent observations indicate that the evolution of homogenous turbulence near its initial conditions is characterized by nonclassical, out-of-equilibrium scaling laws for the energy spectrum and dissipation rate. Based on these two observations, this work derives expressions for the evolution of the kinetic energy, interscale energy flux, and integral length scale, for homogenous decaying turbulence cascades near initial conditions. As expected, the predictions differ from those of the equilibrium Kolmogorov theory. Validation is provided using data from direct numerical simulations.

In this paper, we use a combination of high-speed imaging and total internal reflection microscopy to study postcontact spreading dynamics and bubble entrapment of droplets impacting on surfaces lubricated with an immiscible fluid, following dimple and film modes of contact. The postcontact droplet spreading entraps two types of bubbles: (i) surface and (ii) bulk, where the former occurs when the bubbles remain at the droplet-surface interface and the latter takes place within the droplet because of the impact-induced air-cavity closure. The dimple mode of droplet-surface contact shows an absence of central surface bubble due to the contact point at the drop center and the subsequent axisymmetric spreading. The surface radial bubbles can be suppressed by tuning the impact velocity, liquid surface tension, and viscosity. Early-stage postcontact spreading dynamics are then studied for the dimple mode, where a viscocapillary scaling for the spreading radius $r_{\mathrm{wet}}$ versus time $t$ of $r_{\mathrm{wet}}\sim t$ is observed. Finally, the critical capillary number for wetting failure scaling is used to predict the presence of surface radial bubble entrapment with good accuracy.

A detailed experimental study was performed in a supersonic isolator with incoming Mach numbers of 1.85 and 2.70 to investigate the potential of a micro-ramp as a form of shock train control. Two types of upstream wedges were arranged to produce flow fields with and without background waves (BWs). Wall pressure measurements of the primary and corner regions and schlieren visualization with multiple knife edges were performed to investigate the shock train flow field. The micro-ramp controlled flow fields of the shock train at the two incoming Mach numbers are found to show common characteristics. The micro-ramp suppresses the upstream propagation of the shock train and improves the ability of its downstream flow field to resist adverse pressure gradients. The control effect of the micro-ramp is enhanced in the shock train flow field with BWs. An incoming Mach number of 1.85 leads to shortening or even elimination of the Mach stem in the shock train leading edge under micro-ramp control, weakening the intensity of the shock, inhibiting the thickening of the boundary layer caused by the impingement of the shock, and slowing down the contraction of the supersonic core flow. The micro-ramp has little influence on the morphological structure of the shock train under an incoming Mach number of 2.70. The main control effect of the micro-ramp is to suppress the sudden jump of the shock train and prevent the large upstream movement of the shock train and large-area boundary layer separation that result from the sudden movement of the shock train under an incoming Mach number of 2.70.

We perform a point-particle Lagrange simulation to investigate the effect of the wall-normal external force and the particle inertia on the clustering and deposition of particles in wall-bounded turbulence. It is found that the mean slip velocity of particles in the outer layer equals the production of the Stokes number (St) and a dimensionless force parameter ($\psi$). The first-time collision velocity of particles when they impact the wall is recorded and the mean deposition velocity $\langle v_d\rangle$ is compared with the mean slip velocity in the outer layer. An anomalous enhancement of $\langle v_d\rangle$ is reported and the relative velocity increment, $\langle v_d\rangle /\left(\mathrm{St}\psi \right)-1$, shows an increasing-decreasing trend as the Stokes number increases. The largest enhancement of the deposition velocity is observed for particles with moderate inertia due to (1) the preferential distribution of particles in the near-wall high-velocity regions and (2) the insufficient deceleration of inertial particles in the viscous sublayer. Given a strong wall-normal force, the clustering of particles is inhibited, leading to a decline in the relative velocity increment. Finally, we show that the deposition velocity resembles the terminal velocity in a stationary fluid when the particle relaxation length is considerably smaller than the thickness of the viscous sublayer.

When a drop laden with solid particles and suspended in a liquid passes through a narrow pore, its interface experiences strong shear and elongation, and the raft of particles may accumulate toward the back of the drop. Using well-controlled formulations of Pickering drops driven at set pressure, we determine the two conditions for which solid particles are expelled from the oil-water interface after a Pickering drop passes a converging-diverging pore: (i) particles accumulation at the rear of the drop is such that surface pressure builds up at the interface and (ii) surface pressure relaxation by buckling is impaired by geometrical constraints. These two conditions are rationalized using three nondimensional numbers: the capillary number, the particle to pore size ratio, and the drop to particle size ratio, which allow us to account for the viscous shear at the interface, the stability of the lubricating film between the pore wall and the drop, the drag on the raft of particles adsorbed at the interface, and its mechanical behavior.

Direct numerical simulations (DNS) of forced (statistically stationary) isotropic turbulence are used to assess the characteristics of the intense vorticity structures (IVS) or “worms” at higher Reynolds numbers than previously available. The simulations cover a range of Taylor-based Reynolds numbers in the range $90\le {\mathrm{Re}}_{\lambda }\le 399$, for a resolution of $k_{\max }\eta \approx 2.0$, where $k_{\max }$ is the maximum resolved wave number and $\eta$ is the Kolmogorov microscale. Most of the IVS characteristics are confirmed at the higher Reynolds numbers analyzed in this work; e.g., the results confirm that the mean radius of the IVS $\langle R_{ivs}\rangle$ is approximately equal to $\langle R_{ivs}\rangle /\eta \approx 4–5$ and that the mean radius is equal to the radius of the stationary Burgers vortex $\langle R_{ivs}/R_B\rangle \approx 1.0$, with $R_B=2{(\nu /\alpha )}^{1/2}$, where $\nu$ is the kinematic viscosity and $\alpha$ is the (locally) imposed rate of strain. Moreover, the tangential velocity of the IVS scales with the root-mean-square velocity of the flow $U_{ivs}\sim u^{\prime }$. These IVS characteristics seem to be robust and relatively independent of the Reynolds number; however, there are other quantities for which the classical results do not hold. A notable example is the mean length of the IVS ($L_{ivs}$), which previous works, carried out at smaller Reynolds numbers, claimed to scale with either the Taylor microscale $\lambda$ or the integral scale of turbulence $L$. It turns out that the correct scaling for this quantity can be observed only at ${\mathrm{Re}}_{\lambda }\gtrsim 200$, and the results consistently show that $L_{ivs}$ scales with the Kolmogorov microscale $L_{ivs}\sim \eta$, with a mean value equal to $\langle L_{ivs}\rangle \approx 60\eta$. The present findings provide further evidence that ${\mathrm{Re}}_{\lambda }\gtrsim 200$ is required for the small scales to be fully developed.

A theoretical model is constructed to understand and predict the aeroacoustic feedback coupling of dual impinging jet (DIJ) configurations of the type encountered in supersonic vertical takeoff and landing aircraft. The proposed model extends the single impinging jet (SIJ) framework of Powell, which derives impinging tone frequencies from the speeds of downstream convecting features and upstream propagating acoustic waves generated by periodic ground impingement. The SIJ feedback mechanism dominates each jet, but fails to predict anomalous changes in acoustic characteristics due to the proximal second jet. The new DIJ model eliminates this shortcoming by introducing a third, acoustically coupled DIJ global feedback loop that augments the two individual SIJ loops. It is shown that the two principal length parameters, nozzle to ground ($H$) and internozzle separation ($S$) distances, can foster a synchronized coresonance condition in which the coupled global feedback loop interacts with preferred individual SIJ feedback modes. The occurrence of this coupled dynamic state is quantified by a coresonance factor $R_{\text{DIJ}}$, a metric from 0 to 1 that relates all three feedback loops in the DIJ system. We focus on a configuration where the coupling is primarily acoustic in nature, specifically, two identical underexpanded Mach 1.27 jets. Experimental and numerical simulations are used to calibrate the model inputs at select points in the parameter space, and predictions from the model are then shown to be generally applicable by comparisons with acoustic measurements at other conditions. In particular, the model successfully predicts the damping or amplification of SIJ impinging tones due to the influence of the second jet, as well as overall sound pressure level trends as a function of impingement height.

We use lubrication theory to study the bow wave ahead of a squeegee as it moves steadily over a horizontal layer of fluid. If the squeegee is infinitely long with a small gap at its base then the motion is two dimensional and we obtain an analytic prediction for the flow thickness. For a relatively long straight squeegee on a layer of viscous fluid with no gap, we deploy a two-dimensional approximation, which enables the flow thickness in the bow wave to be determined relative to the thickness at the squeegee. The analysis is completed by balancing the flux into the bow wave with the transverse flux perpendicular to the squeegee associated with hydrostatic pressure gradients. The simple method is adapted to squeegees that are angled to the direction of translation. For a layer of viscoplastic fluid that has a relatively high yield stress, the bow wave is quasiplugged and this observation enables a different flux balance to be used to determine the flow thickness. The predictions are compared favorably to numerical results.

Acoustic handling of dense suspension of microparticles has relevance in lab-on-a-chip, food, and pharmaceutical technologies. So far the studies on acoustic focusing of dense suspensions treat the particles to be of the same size, i.e., monodisperse. Here, the flow of dense bidisperse suspensions of microparticles in a microfluidic channel flow exposed to a standing acoustic wave field is studied. Experiments show selective enrichment of the larger particles along the channel center where the smaller particles are depleted. A continuum-based model reveals that the particle migration is governed by the combined influence of shear-induced migration and acoustic radiation forces. The migration behavior of the suspended particles along the channel length is quantified in terms of the degree of focusing, relating to the particle migration toward the center of the channel, and the degree of segregation, relating to the separation of larger and smaller particles. It is observed that both the degree of focusing and segregation varies directly with the intensity of the acoustic field and the ratio of particle sizes and inversely with the suspension volume fraction.