We present here the effect of mechanical vibrations on a breath figure. By impacting a falling steel ball on a plastic plate covered on its bottom side by a breath figure, we show that in a few milliseconds, the figure can evolve even more dramatically than it would in minutes in the natural aging process. We quantify the variations of droplet number and sizes with time for various substrate accelerations and mean initial droplets radii. We show that, above an acceleration threshold, the final number of droplets decreases more and more with acceleration. We interpret this result by the contact line unpinning provoking oscillations of the droplets radii, which makes the drops contact and coalesce with neighbors. Finally, we introduce a new parameter to characterize the droplet number decrease. We have plotted it as a function of an effective Bond number built with the substrate acceleration and mean droplet radius. Interestingly, all the data fall on a single master curve.

We consider longitudinal shear flow over a $2L$-periodic array of grooves separated by solid slats of rectangular cross section. We address the case where the liquid partially invades the grooves, so a portion of the solid slat protrudes into the liquid. For flat menisci, the ratio $\lambda$ of the slip length to $L$ depends upon two geometric parameters: the ratio $\epsilon$ of the slat width to the period, and the aspect ratio $\mathrm{\Delta }$ of the protruding part of the solid slats. We analyze the singular limit $\epsilon \ll 1$ with arbitrary $\mathrm{\Delta }$ utilizing matched asymptotic expansions, with an outer region on the scale of the periodicity and an inner region on the scale of the protrusion. In the outer region, the flow is represented using a periodic array of source singularities. In the inner region, the flow is solved using a combination of Schwarz–Christoffel and Joukowsky mappings. Asymptotic matching yields $\lambda \approx (2/\pi )ln(2/\pi \epsilon A)$ wherein $A$, the scale factor in the Schwarz–Christoffel mapping, is a monotonically increasing function of $\mathrm{\Delta }$. We obtain simple approximations for $A$ for both small and large $\mathrm{\Delta }$. These lead to slip-length formulas which practically cover the entire range of relevant $\mathrm{\Delta }$ values. The agreement between the predictions of these formulas and the numerical results of Ng and Wang [Phys. Fluids 21, 013602 (2009)] is gratifying.

In this study, we present a series of simulations of gravity currents where ambient and intruding temperatures are on opposite sides of the temperature of maximum density. We use these simulations to describe how cabbeling (mixing of parcels of fluid that leads to a parcel of fluid that is denser) affects the evolution of gravity currents. We show that initially buoyant currents (called hypopycnal currents) undergo mixing in the body and tail region of the gravity current, which generates dense water from cabbeling. We investigate the maximum distance that the initial current progresses as a function of a parameter controlling the nonlinearity of the equation of state (referred to as $\mathrm{\Theta }$). We find that the maximum distance that the current progresses is a nonlinear function of $\mathrm{\Theta }$. For low $\mathrm{\Theta }$ hypopycnal currents reverse direction after they begin flowing, and cabbeling occurs over a limited spatial extent. As $\mathrm{\Theta }$ is increased, currents achieve a larger maximum distance of propagation, allowing the dense water formed by cabbeling to sink and form a secondary current along the bottom of the domain (called a hyperpycnal current). As we increase the parameter controlling the nonlinearity of the equation of state, the hyperpycnal current becomes much larger in scale. We discuss some general characteristics of the hyperpycnal current and highlight that once it forms, larger values of $\mathrm{\Theta }$ lead to a larger spatial extent of the current but narrower distributions of density and temperature.

Motivated by the ablation of vertical ice faces in salt water, we use three-dimensional direct numerical simulations to investigate the heat and salt fluxes in two-scalar vertical convection. For parameters relevant to ice-ocean interfaces in the convection-dominated regime, we observe that the salinity field drives the convection and that heat is essentially transported as a passive scalar. By varying the diffusivity ratio of heat and salt (i.e., the Lewis number Le), we identify how the different molecular diffusivities affect the scalar fluxes through the system. Away from the walls, we find that the heat transport is determined by a turbulent Prandtl number of ${\mathrm{Pr}}_t\approx 1$ and that double-diffusive effects are practically negligible. However, the difference in molecular diffusivities plays an important role close to the boundaries. In the (unrealistic) case where salt diffused faster than heat, the ratio of salt-to-heat fluxes would scale as ${\mathrm{Le}}^{1/3}$, consistent with classical nested scalar boundary layers. However, in the realistic case of faster heat diffusion (relative to salt), we observe a transition towards a ${\mathrm{Le}}^{1/2}$ scaling of the ratio of the fluxes. This coincides with the thermal boundary layer width growing beyond the thickness of the viscous boundary layer. We find that this transition is not determined by a critical Lewis number, but rather by a critical Prandtl number $\mathrm{Pr}\approx 10$, slightly below that for cold seawater where $\mathrm{Pr}=14$. We compare our results to similar studies of sheared and double-diffusive flow under ice shelves, and discuss the implications for fluxes in large-scale ice-ocean models. By coupling our results to ice-ocean interface thermodynamics, we describe how the flux ratio impacts the interfacial salinity, and hence the strength of solutal convection and the ablation rate.

We consider the steady-state deformation of an elastic filament in various unidirectional, low-Reynolds-number flows, with the filament either clamped at one end, perpendicular to the flow, or tethered at its center and deforming symmetrically about a plane parallel to the flow. We employ a slender-body model [Pozrikidis, J. Fluids Struct. 26, 393 (2010)] to describe the filament shape as a function of the background flow and a nondimensional compliance $\eta$ characterizing the ratio of viscous to elastic forces. For $\eta \ll 1$, we describe the small deformation of the filament by means of a regular perturbation expansion. For $\eta \gg 1$, the filament strongly bends such that it is nearly parallel to the flow except close to the tether point; we analyze this singular limit using boundary-layer theory, finding that the radius of curvature near the tether point, as well as the distance of the parallel segment from the tether point, scale like ${\eta }^{-1/2}$ for flow profiles that do not vanish at the tether point, and like ${\eta }^{-1/3}$ for flow profiles that vanish linearly away from the tether point. We also use a Wentzel-Kramers-Brillouin approach to derive a leading-order approximation for the exponentially small slope of the filament away from the tether point. We compare numerical solutions of the model over a wide range of $\eta$ values with closed-form predictions obtained in both asymptotic limits, focusing on particular uniform, shear and parabolic flow profiles relevant to experiments.

In this study, ensembles of experimental data are presented and utilized to compare and validate two models used in the simulation of variable-density (Atwood = 0.22), compressible turbulent mixing. Though models of this kind (Reynolds averaged Navier-Stokes and large-eddy simulations) have been validated extensively with more canonical flows in previous studies, the present approach offers novelty in the complexity of the geometry, the ensemble-based validation, and the uniformity of the computational framework on which the models are tested. Moreover, all experimental and computational tasks were completed by the authors which has led to a tightly coupled experimental configuration with its “digital twin.” The experimental divergent-shock-tube facility and its data acquisition methods are described and replicated in simulation space. A 2D Euler model which neglects the turbulent mixing at the interface is optimized to experimental data using a Gaussian process. This model then serves as the basis for both the 2D RANS and 3D LES studies that make comparisons to the mixing-layer data from the experiment. A relatively simple RANS model is shown to produce good agreement with experimental data only at late flow development times. The LES ensembles generally show good agreement with experimental data but display sensitivity to the characterization of initial conditions. Resolution-dependent behavior is also observed for certain higher-order statistics of interest. Overall, the LES model successfully captures the effects of divergent geometry, compressibility, and combined nonlinear instabilities inherent to the problem. The successful prediction of mixing width and its growth rate highlight the existence of three distinct regimes in the development of the instability, each with similarities to previously studied instabilities.

We investigate the rapid spreading dynamics of a viscoelastic drop on a solid. Upon contact, surface tension drives a fast motion of the contact line along the substrate. Here we resolve this motion for viscoelastic liquids by experiments on aqueous polymer solutions of varying concentration. It is found that while the contact line motion is only mildly affected by the polymers, the interface profile becomes much sharper owing to singular polymer stress. This behavior is reminiscent of that observed for viscoelastic drop coalescence; in this context we revisit the analogy between spreading and coalescence, which sheds light also on the spreading of Newtonian liquids.

When combustion instability occurs—in addition to periodic change in the nozzle flow rate caused by pressure oscillation—the instability of the liquid sheet is also affected by pressure oscillation, reflected mainly in oscillation of the internal parameters of the fluid. In this work, the parametric instability of a liquid sheet under a standing wave acoustic field was studied theoretically, and the influence of acoustic parameters on the instability of a liquid sheet was analyzed. It was found that sinuous and varicose modes were coupled in the subharmonic region. Atomization characteristics of slit nozzles under a standing wave acoustic field were studied experimentally; the effects of acoustic pressure and injector position were analyzed with respect to the acoustic field on atomization characteristics and the characteristics of nozzles in the critical state. It was found that under the same acoustic pressure, the effect of the acoustic field at the velocity antinode (VAN) was stronger than the effect at the acoustic intensity antinode (IAN), and there was little effect at the acoustic pressure antinode. There was also a critical value of acoustic pressure: when the pressure threshold was exceeded, Faraday waves were motivated at VAN and IAN. An interesting phenomenon is that the frequency of the surface wave is the same as the acoustic frequency, but the Faraday wave was found to be subharmonic rather than harmonic. The effect of flow rate on atomization characteristics was analyzed. The wavelength of the Faraday wave and breakup length of the liquid sheet were well in accord with the theoretical wavelength calculated in the analysis of liquid sheet instability.

We report on the experimental study of axisymmetric gravity-capillary standing waves generated by a vertically vibrating ring partially immersed into a fluid. Different regimes of standing waves are highlighted at the basin center depending on the forcing parameters: linear, nonlinear, and ejection regimes. For weak forcing, the standing waves display a resonant response, close to a natural frequency of the circular basin, predicted by the linear theory. For stronger forcing, we observed that the experimental spatial profile of standing waves breaks the up-down symmetry, and is well described by a third-order nonlinear theory. When the forcing is further increased, the maximum height of the axisymmetric wave crest at the basin center is found to increase linearly with its wavelength, due to the saturation of its steepness, a result well captured by a proposed model.

The liquid crystal (LC) is a state of matter that is intermediate between crystalline solid and amorphous liquid. They are anisotropic viscoelastic materials with broad applications in science and engineering, including as lubricants or additives to lubricants to reduce wear, improve load-carrying capacity, and decrease the coefficient of friction. In this paper, the Landau–de Gennes (LdG) equations are used to model the flow of LCs. The LdG equations are simplified using the Reynolds scaling analysis to form the simplified LdG equations, which are then applied to a Couette geometry and a slider bearing geometry. Both the simplified LdG model and the full LdG model are numerically solved in comsol Multiphysics®. The simplified LdG model is evaluated and verified by comparing the simulation results of the simplified LdG model with those from the full LdG model. Lubrication performance is analyzed for the slider bearing geometry with both the simplified LdG model and the full LdG model. The simplified LdG model significantly reduces simulation wall time compared to the full LdG model over the same domains.

The presented work introduces a cancellation technique, based on the linear superposition of stationary crossflow instabilities (CFIs) through the application of a streamwise series of optimally positioned discrete roughness element (DRE) arrays on a swept wing surface. The DRE arrays are designed and arranged with suitable amplitude and phase shift to induce velocity disturbance systems that destructively interact, ultimately damping the developing CFIs. The robustness of this technique is investigated for a smooth wing surface as well as in the presence of enhanced distributed surface roughness. The resulting flow fields are measured with infrared thermography and particle tracking velocimetry, allowing for the extraction of the laminar-to-turbulent transition front location and for the characterization of the local boundary layer development. The acquired data show that the superposition of suitably arranged DRE arrays can successfully suppress monochromatic CFIs, reducing their amplitude and growth and delaying the boundary layer transition to turbulence when applied on a smooth wing surface. However, the presence of elevated background roughness significantly reduces the effectiveness of the proposed method.

Liquid filaments, which are commonplace in daily life, nature, and technology, including inkjet printing and crop spraying, contract due to surface tension: they either retract into a single sphere or break up to produce a primary drop(s) and several smaller satellites. The latter are undesirable because they reduce printing quality and cause pollution due to spray drift. Surfactants and/or polymer additives can be used to control filament contraction and breakup. It has recently been demonstrated experimentally that the velocity at which the tips of contracting filaments retract can be increased in viscoelastic filaments that contain polymer additives compared to purely Newtonian filaments. Here, simulations are used to investigate the contraction of viscoelastic filaments whose rheology is described by the Oldroyd-B model. Filaments produced from nozzles are expected to be prestressed when they begin to contract. It is shown that the velocity with which the tips of prestressed filaments retract is greatly increased compared to filaments in which the polymer molecules are relaxed. This enhancement is explained by examining the value of $\mathit{\sigma }:\mathbf{D}$ ($\mathit{\sigma }$: Elastic stress; $\mathbf{D}$: Rate-of-strain tensor), which can be positive or negative. This quantity is positive when the flow does work on the polymer molecules but negative when the molecules do work on the flow, i.e., when elastic recoiling or unloading takes place. In prestressed filaments, elastic unloading takes place because $\mathit{\sigma }:\mathbf{D}<0$: The elastic stresses work by pulling the fluid in axially and pushing it out radially, thereby drastically increasing the tip velocity.

A robust control scheme is derived and tested for the Navier-Stokes equations for two-dimensional multiphase flow of a thin film underneath an inclined solid surface. Control is exerted via the use of an electrode parallel to the substrate, which induces an electric field in the gas phase, and a resultant Maxwell stress at the liquid-gas interface. The imposed potential at the second electrode is derived using a model predictive control loop, together with optimal control of a high-fidelity reduced-dimensional model. In this implementation the interfacial shape of the fluid is successfully controlled; however, the algorithm is sufficiently general to control any other quantity of interest.

Understanding the hydrodynamics of droplet collision is vitally important due to the inherent small-scale phenomena and various practical applications. The morphology, course trajectory, and final state of the droplets in such a collision are greatly affected by different physical parameters together with system geometry. Yet the collision behavior of droplet pairs at high density and viscosity ratios remains unexplored and unquantified, and therefore the critical density and viscosity ratios for the collision mode of droplets under geometric parameters were unknown. Through computational analyses, we address the interplay between the density ratio (60 to 800), the viscosity ratio (24 to 60), the initial offset, and the confinement on the coalescence of droplet pairs subjected to a confined shear flow. Simulations have been performed using a free-energy-based lattice Boltzmann method, with the aim of determining new regimes compared to the previous study. The results reveal that the coupling effect of density ratios and viscosity ratios contributes to generating inertia and viscous interaction forces that significantly impact the coalescence consequences. On the other hand, the wall confinement and the initial vertical offset of droplets are shown to play a significant role in either promoting or suppressing the collision mode of interacting droplets. Interestingly, we observe unusual trajectory motion of droplets for an intermediate range of density ratios (i.e., 245–600) near the critical initial offset of droplets. Regions of different collision modes are further presented in terms of phase diagrams, which reveal the critical dependency of droplet behavior on the coupling effect of density ratios, viscosity ratios, initial vertical offset, and confinement. The reported results are expected to provide new insights into the collision of pair droplets under confined shear flows in the effect of various parameters and help elucidate the intrinsic nature and the condition of coalescence.

We report on the thinning of supported liquid films driven by thermocapillarity. The liquids are oil films, of initial thicknesses of a few tens of microns. A local and moderate heating of the glass substrate on which they are spread induces a thermocapillary flow, which allows the formation of ultrathin films. We show that, within a given time range, the thinning dynamics of submicron-thick films is governed by the thermocapillary stress. It results in a simple dependency of the thickness profiles with time, which is evidenced by the collapse of the data onto a master curve. The master curve only depends on the liquid properties and on the thermal gradient, and allows a measurement of the latter. As the films further thin down to thicknesses within the range of molecular interactions, a deviation from the master curve appears. Although all investigated oils are supposedly fully wetting glass, the nature of the deviation differs between alkanes and silicone oils. We attribute the observed behaviors to differing signs of disjoining pressures, and this picture is confirmed by numerical resolution of the thin-film equation. We suggest thermocapillary flows can be used to finely probe molecular interactions.

This paper uses numerical approaches to investigate the effect of droplet deformation and internal circulation on droplet dynamics. Although droplet drag is a classical area of study, there are still theoretical gaps in understanding the motion of large droplets. In applications such as spray combustion, droplets of various sizes are generated and move with the flow. Large droplets tend to deform in the flow, and they have complex interactions with the flow because of this deformation. To better model spray, the physical understanding of droplets needs to be improved. Under spray conditions, droplets are subjected to a high-temperature-and-pressure environment, and the coupling between liquid and gas is enhanced. Therefore the deformation and internal circulation will affect the droplet drag coefficient more significantly than they would under atmospheric conditions. To study the mechanism of how droplet shape and internal circulation influence droplet dynamics, we have used direct numerical simulation (DNS) to simulate a droplet falling at its terminal velocity in high-pressure air. An in-house code developed for interface-capturing DNS of multiphase flows is employed for the simulation. The drag coefficient is calculated, and the results are consistent with the existing literature for slightly deformed droplets. The results show that the drag coefficient is directly related to the droplet deformation and droplet internal circulation. This paper also develops an analytical theory to account for the effect of the Weber number and fluid properties on droplet deformation.

This study focuses on frequency dependence effects on glottal jet dynamics with a focus on the physiological condition in which the vocal folds do not fully close. Incomplete closure occurs naturally in children and adult females. But there are also pathological conditions that can be problematic. Experiments were conducted using a 10× scaled-up model in a free surface water tunnel. Two-dimensional vocal fold models with semicircular medial surfaces were stepper motor driven inside a square duct with constant opening and closing speeds. Cases with complete vocal fold closure and incomplete closure to only 15% of the maximum gap were examined. Time-resolved digital particle image velocimetry and pressure measurements along the duct centerline were made at $\mathrm{Re}=7200$ over equivalent life frequencies from 52.5 to 97.5 Hz. Phase-averaged and cycle-to-cycle analysis of key contributors to sound production were conducted. As would be expected, acoustically relevant parameters, e.g., fluctuations in volume flow rate and transglottal pressure, are attenuated when vocal folds do not close completely. The key findings of this study, however, lie in statistical and dimensional scaling analysis of frequency dependencies of terms in the streamwise integral momentum equation. Specifically, the unsteady inertial term appears to become increasingly significant with increasing frequency and may be a key differentiator between lower frequency phonation, i.e., male voices, and the higher frequencies of children and adult females. These frequency effects, however, do not appear to be relevant to pathological conditions characterized by incomplete vocal fold closure.

Coating processes are limited by the onset of dynamic wetting failure beyond a critical substrate speed. In this work, we study the influence of thermal Marangoni flow on dynamic wetting with the objective of delaying wetting failure to higher substrate speeds. A two-dimensional hydrodynamic model is developed to examine steady-state dynamic wetting of a Newtonian liquid in a parallel-plate geometry where a temperature gradient between the plates generates thermal Marangoni flow. The dynamics of the air displaced by the liquid are accounted for, and the Galerkin finite-element method is used to calculate steady-state solutions and find the critical substrate (bottom plate) speed at which wetting failure occurs. It is found that thermal Marangoni flow directed toward the dynamic contact line at the substrate delays wetting failure to a higher speed, whereas flow away from the contact line causes wetting failure at a lower speed. Flow toward the contact line reduces the bending of the air-liquid interface and increases the thickness of the air film near the contact line. This lowers the magnitude of pressure gradients in the air phase and facilitates removal of air from the contact line, delaying the entrainment of air and consequently wetting failure to higher speeds. In contrast, flow away from the contact line increases interface bending at a given speed, leading to thinning of the air film near the contact line and causing wetting failure at lower speeds. The findings presented in this study suggest a novel strategy for designing faster coating processes through the application of thermal Marangoni flow.

Scale decomposition is ubiquitous in the analysis of complex fluid flows. Often with an eye towards reduced order modeling, considerable effort has been invested in the development of novel sets of basis functions for such decompositions. The most successful sets of basis functions have been developed in the Eulerian perspective, where traditional tools of calculus and newer methods from data science can be most easily leveraged. Here, we take advantage of recent interest in graph-based approaches to Lagrangian coherence as well as new methods for the scale analysis of complex networks to introduce a new scale decomposition that is instead fully Lagrangian and based on transport. To do so, we adapt a technique from network science know as the graph Fourier transform and develop a novel graph correlation function that allows us to quantitatively describe our Lagrangian decomposition as a function of scale. This method allows better interpretability of the dynamic consequences of kinematic coherence as well as the ability to perform traditional Eulerian tasks (such as decomposition, filtering, and compression) on Lagrangian quantities. We illustrate our techniques on examples drawn from coherent-structure analysis, ocean mixing, and cloud physics.