It is well known, since the seminal work of Mysels et al. [Soap Films: Study of Their Thinning and a Bibliography (Pergamon Press, New York, 1959)], that the thinner parts of a foam film go up by gravity, whereas the thicker parts go down. Preparing a foam film in a controlled way, so that the top part of the film is much thicker than the bottom part at initial time, we show that this situation is indeed unstable under gravity. The observed instability is identified as a Rayleigh-Taylor-like instability and studied in the linear regime. The wavelength and the growth rate are measured as a function of the effective gravity, and as a function of the thick film extension. We theoretically derive the dispersion relation for the instability, taking into account finite size effects. The fastest mode is analytically determined and is in qualitative agreement with the experimental observations.

Here we show that the so-called Confined Selective Withdrawal technique [Evangelio, Campo-Cortés, and Gordillo, J. Fluid Mech. 804, 550 (2016)] can be used to produce compound drops whose radii and thicknesses can be easily decreased down to length scales of the order of $5\mu \text{m}$ and even smaller. This method is based on the generation of a highly stretched thin coaxial jet of two immiscible fluids that flow inside a third bulk coflowing fluid under creeping flow conditions. The subsequent capillary breakup of such coaxial jet produces, in a single step, compound droplets at rates that can be easily modulated to values of the order of 10 KHz. Using algebraic equations deduced using slender body theory, we report that the production frequency, the diameter, and the shell thickness follow well-defined scaling laws, enabling us to generate, from millimeter-sized injection tubes, and in a highly controlled way, uniformly sized double emulsions with the smallest diameters reported to date. We illustrate our results by producing micron-sized nematic shells with radii below $5\mu \text{m}$ and show that the radius of curvature of the surface and the shell thickness can be fixed independently.

In this work, we have studied the effects of surface roughness on accommodation coefficients using an in-house, direct simulation Monte Carlo solver. The solver has been modified in such a way that enables us to calculate the accommodation coefficients for a rough surface while using as inputs the surface roughness conditions and the accommodation coefficient values of a smooth surface. Supersonic flow over a flat plate is considered to characterize and study the effects of surface roughness on accommodation coefficients. Roughness is created on the flat plate by introducing a number of protrusions (modules) of different shapes and aspect ratios. These parameters (shape, aspect ratio, and number of modules) are varied systematically to analyze the effect of each parameter. It is shown that the effect of surface roughness on accommodation coefficient is distinct and solely geometry dependent, as compared to the flow-related effects such as Knudsen number, Mach number, etc. Changes in the values of accommodation coefficients between smooth and rough surfaces are analyzed in detail, and an effective-smooth surface model is proposed in this work, which is shown to take care of surface roughness effects quite accurately, without the need to model the surface roughness explicitly. Macroscopic properties like coefficient of drag, surface heat flux, and velocity profiles are compared between the rough surface and the effective-smooth surface to show the significance of modeling of roughness in the proposed manner. Through a systematic study, a generic empirical relationship is derived between surface roughness parameters and effective accommodation coefficients, using which, modeling of the surface roughness of a typical engineering surface is addressed.

Manufacturers of membrane filters have an interest in optimizing the internal pore structure of the membrane to achieve the most efficient filtration. As filtration occurs, the membrane becomes fouled by impurities in the feed solution, and any effective model of filter performance must account for this. In this paper, we present a simplified mathematical model, which (i) characterizes membrane internal pore structure via permeability or resistance gradients in the depth of the membrane; (ii) accounts for multiple membrane fouling mechanisms (adsorption, blocking, and cake formation); (iii) defines a measure of filter performance; and (iv) for given operating conditions, is able to predict the optimum permeability or resistance profile for the chosen performance measure.

Like in liquids, objects moving in granular materials experience a drag force. We investigate here whether and how an object's acceleration affects this drag force. The study is based on simulations of a canonical drag test, which involves vertically uplifting a plate through a granular packing with a prescribed acceleration pattern. Depending on the plate size, plate depth, and acceleration pattern, results provide evidence of a rate-independent regime and an inertial regime where the object acceleration strongly enhances the drag force. We introduce an elasto-inertial drag force model that captures the measured drag forces in these two regimes. The model is based on observed physical processes including a gradual, elasto-inertial mobilization of grains located above the plate. These results and analysis point out fundamental differences between mobility in granular materials upon steady and unsteady loadings.

When a buoyant bubble is inserted into a closed capillary that is slightly smaller than the capillary length, it appears stuck; exactly why this is so is a puzzle that has remained unanswered over the past 50 years. Recent calculations suggest that the bubble's motion is critically dependent on the hydrodynamics of the surrounding liquid film; however, quantitative measurements of these dynamics are lacking. We provide direct measurements of the dynamics of the liquid film surrounding a “stuck” bubble, recorded using interference microscopy. The film slowly relaxes to a constant thickness, and is stabilized by disjoining pressure at long times. The film's stability at this thickness is demonstrated by recovery after applied thermal perturbations; thus, we confirm that Bretherton's buoyant bubble is not pinned at a contact line, but is instead ostensibly stuck by extraordinarily slow flow in the surrounding liquid film whose thickness is set by a balance of capillary stress and disjoining pressure.

Collision between two droplets plays a critical role in a wide range of processes, including raindrop formation, nuclear reactions, atomization and spraying in combustors, and various cooling, coating, and painting techniques. It is known that when two droplets collide nearly head-on, they may coalesce temporarily and then separate when the impact energy is so large that the rebounding motions of internal flows tend to stretch out and break the merged droplets. If the impact is sufficiently off-center, however, two distinct mechanisms have been argued to cause breakup exclusively. That is, separation has been reported to occur above a threshold of increasing impact angle (as characterized by an impact parameter, B), due to either stretching or rotational dynamics, whereas only one of them is supposed to cause the transition from permanent coalescence to separation. Therefore, which one renders the sole mechanism leading to off-center separation is not clear in the literature. This has been a discrepancy in the past decades, considering the fact that both mechanisms have been used, respectively, in different studies to interpret and analyze the transition criteria. To resolve this ambiguity, here we demonstrate experimentally a new regime, named rotational separation, which is governed by the coupling of outer rotating flow and center rebounding flow in the tentatively united drops. This regime occurs at an intermediate B, in contrast to that dominated by stretching kinetics created at a slightly larger B. It thus indicates simultaneous existence of the two regimes but in different range on a phase diagram. Along with numerical simulations and physical models, we elucidate the two scenarios of off-center separations comprehensively and solve the long-standing puzzle.

Based on recent developments in physics-informed deep learning and deep hidden physics models, we put forth a framework for discovering turbulence models from scattered and potentially noisy spatiotemporal measurements of the probability density function (PDF). The models are for the conditional expected diffusion and the conditional expected dissipation of a Fickian scalar described by its transported single-point PDF equation. The discovered models are appraised against an exact solution derived by the amplitude mapping closure (AMC)–Johnson-Edgeworth translation (JET) model of binary scalar mixing in homogeneous turbulence.

Analysis of the energy transfer in scale space, in addition to the energy transport in physical space, is useful for obtaining a better understanding of inhomogeneous turbulence. In this work, the energy transfer in scale space is examined using the direct numerical simulation data of turbulent channel flow. A direct cascade of the streamwise and wall-normal components of the turbulent energy is seen, whereas an inverse cascade of the spanwise component is observed near the wall. The inverse energy cascade implies that the production term of the subgrid-scale (SGS) energy is negative in the averaged sense. The conditional average of the velocity field associated with the negative production is evaluated to extract typical flow structures contributing to the inverse cascade. As a result, a long streamwise vortex around the reference point, as well as a short one in the upstream region, is observed, which is reminiscent of a series of slightly tilted streamwise vortices with alternate signs of vorticity near the wall. The isosurface of the negative production attached to the long vortex suggests that the grid-scale velocity of the long vortex is enhanced by the SGS motion under the influence of the short upstream vortex. The enstrophy equation is further examined to confirm that the SGS effect increases the rotation of the long vortex.

Direct numerical simulations are presented for pressure-driven and simple shear channel flow of cell suspensions. The presence, motion, and deformation of cells are accounted for on the basis of the immersed interface method. Deformable microparticles are also included to model blood contained or pharmaceutical particles. The study focuses on the effects of channel height on the hydrodynamic diffusion characteristics of the contained particles. Although such effects are rather expected to be significant, they have not been systematically considered in the literature. The proximity with the bounding walls affects the mobility of the particles, even more so due to the low-Reynolds-number prevailing conditions. For pressure-driven flow the diffusivities increase with distance from the wall due to the increasing mobility and reach a channel-size-dependent maximum due to the diminishing local shear rate. Near the channel center, where the mean shear rates vanish, diffusivities remain finite owing to convection from cross-flow sweeps generated from the interaction of eddies formed in the opposing walls. It is suggested that the hydrodynamic mobility and its dependence on distance from the walls should be added to factors affecting the diffusivities, such as the local shear rate and the cell volume fraction and elasticity.

The surface-normal impingement of a liquid jet emanating from a nozzle is of use in numerous technological applications (e.g., surface cleaning, waterjet cutting, and needle-free injection). Upon impact, the (Rayleigh) jet is characterized as either a steady-state (time-invariant) jet, a wavy jet, or a droplet train. The present study experimentally investigates the force imparted by these three distinctly different processes for identical nozzle flow conditions (i.e., velocity and jet diameter). Force models are developed based on Rayleigh jet theory, and they are shown to compare well with the measurements. The force induced by the wavy jet is sinusoidal, oscillating about the steady-state force, while the droplet train force is discrete with periods of zero induced force. Due to conservation of momentum, the peak force experienced by the droplet train is significantly higher than that of the steady stream. This identifies the droplet train as the dominant process to obtain higher peak forces than the continuous stream counterparts during impact with a surface. This can then be used as a means to increase the performance of applications such as waterjet cutting and surface cleaning.

Direct numerical simulation of swirling pipe flows is performed to investigate the effects of swirl on turbulence statistics as well as the inertial regime. The swirling motion is imposed via a constant azimuthal body force coupled with a body force in the axial direction that drives the flow. The friction Reynolds number is ${\text{Re}}_{\tau }\approx 170$ with a pipe length of $8\pi \delta$ (where $\delta$ is the pipe radius). The simulations are performed at various swirl numbers. The swirling motion introduces additional drag into the flow and reduces the bulk flow rate for the swirl strengths investigated in this study. We also show from our data as well as via the mean equations that similar to the total axial stress, the total azimuthal stress when normalized by the azimuthal friction velocity follows a linear decrease from wall to the pipe centerline independent of swirl strength. In the inertial regime, with negligible viscous effects, the linear relationship holds for the turbulent shear stresses. We derive the modified axial mean momentum equation, which when studied alongside the azimuthal momentum equation shows that increasing the swirl strength increases the inertial region in the pipe by pushing the beginning of the inertial region closer to the wall. This effect is governed by the axial viscous forces rather than the azimuthal ones.

In order to better understand deviations from equilibrium in turbulent flows, it is meaningful to characterize the dynamics rather than the statistics of turbulence. To this end, the Lyapunov theory provides a useful description of turbulence through the study of the perturbation dynamics. In this work, the Lyapunov spectrum of forced homogeneous isotropic turbulent flows is computed. Using the Lyapunov exponents of a flow at different Reynolds numbers, the scaling of the dimension of the chaotic attractor for a three-dimensional homogeneous isotropic flow is obtained through direct computation. The obtained Gram-Schmidt vectors (GSVs) are analyzed. For the range of conditions studied, it is found that the chaotic response of the flow coincides with regions of large velocity gradients at lower Reynolds numbers and enstrophy at higher Reynolds numbers, but does not coincide with regions of large kinetic energy. Further, the response of the flow to perturbations is more and more localized as the Reynolds number increases. Finally, the energy spectrum of the GSVs is computed and is shown to be almost insensitive to the Lyapunov index.

Flow past a rotating cylinder of various surface characteristics is investigated experimentally in a flowing soap film of a soap film tunnel. Experiments are carried out at Reynolds numbers $\sim 200$ and 250 with cylinders of different levels of hydrophobicity and normalized rotation rates (ratio of surface speed of cylinder to free-stream velocity) varying from 0 to 4.36. The diagnostic is done with flow visualization using interference technique, and quantitative measurements are obtained with particle image velocimetry. Global wake structure of a rotating hydrophobic/nonhydrophobic cylinder at various rotation rates is presented in this work. Reynolds number and hydrophobicity are found to have a substantial effect on the onset of the transition regime. Interestingly, the transition of von Kármán vortex shedding to single-signed vortex shedding occurred at a transition zone with no evidence of region of suppression in soap film tunnel experiments. The shed single-signed vortices at a rotation rate above the transition regime are of an opposite sense to the cylinder rotation direction. The experimental evidence of this new vortex shedding mode in a soap film tunnel is presented using flow visualization and particle image velocimetry. In addition, inequality in the shedding frequency of counterclockwise and clockwise vortices is observed whose value reaches maximum before the transition zone and then decreases. A higher rotation rate of 4.36 made the counterclockwise vorticity completely wrap around the cylinder at Reynolds number $\sim 250$. Consequently, the stagnation point got lifted off from the surface at $\sim {135}^{\circ }$. The relative circulation of shed clockwise vortices to counterclockwise vortices is observed to be increasing with rotation rate and reaches maximum at the transition zone. The variation of the Strouhal number with rotation rate for shed clockwise vortices is observed to be increasing until the transition regime, and subsequently it decreases. The Strouhal number for hydrophobic cylinders was found to be less compared to nonhydrophobic cylinder and was also observed to decrease with increase in hydrophobicity. The study of the far-wake structure shows the evidence of distortion in the wake structure due to the elongation of vortex pairs for both hydrophobic and nonhydrophobic cylinders.

We study the motion of low viscous nonwetting droplet in a Hele-Shaw cell, while it is pushed by an external phase of imposed flow rate, at low capillary numbers. In this regime, the droplet's mobility, defined as the ratio between the droplet velocity and the external phase mean velocity, evolves nonlinearly with the capillary number, a signature of the different dissipation mechanisms at play. Experiments are performed with surfactant free air bubbles in fluorinated oil, and with surfactant laden fluorinated oil droplets in water. We propose a model based on a power balance which takes into account the dissipation in the thin wetting film trapped between the bubble (or the drop) and the channel wall. The full topography of this thin film is obtained theoretically for the bubble case. By contrast, the presence of surfactants in the drop case induces uncontrolled boundary conditions at the interface, thus imposing to use the experimental topography measured in the previous paper [Reichert et al., J. Fluid Mech. 850, 708 (2018)]. Remarkably, the model reproduces the experimental velocities and shows that the velocity can be strongly affected by a stagnant cap effect at the rear of the drop, even if localized in less than a few percents of the total film area.

In wall-bounded parallel flows, sustained turbulence can occur even while laminar flow is still stable. Channel flow is one of such flows and displays spatiotemporal fluctuating patterns of localized turbulence along its way from and to featureless turbulence. By direct numerical simulation, we study the observed inconsistency between turbulence decay according to a two-dimensional directed-percolation $\left(2D\text{−}\mathrm{DP}\right)$ scenario and the presence of sustained oblique localized turbulent bands (LTBs) below the DP critical point. Above Reynolds number ${\mathrm{Re}}_{\mathrm{g}}\approx 700$, sustained LTBs are observed; most LTBs have the same orientation so that the spanwise symmetry of the LTB pattern is broken below ${\mathrm{Re}}_2\approx 1000$. The frequency of transversal splitting, by which an LTB generates another one with opposite obliqueness, so that turbulence spreading becomes intrinsically two dimensional, increases in the range ${\mathrm{Re}}_{\mathrm{g}}<\mathrm{Re}<{\mathrm{Re}}_2$. It reaches a critical rate at ${\mathrm{Re}}_2$, beyond which symmetry is restored. The $2D\text{−}\mathrm{DP}$ behavior is retrieved only above ${\mathrm{Re}}_2$. A mean-field model is proposed which qualitatively accounts for the above symmetry-restoring bifurcation by considering interactions between space-averaged densities of LTBs propagating in either direction.

Decapod crustaceans have appendages with an array of rigid hairs covered in chemoreceptors, used to sense and track food. Crustaceans directly influence the flow behavior by changing the speed of flow past the hairy surface, thereby manipulating the Reynolds number ($\text{Re}$). Hairs act either as a rake, diverting flow around the hair array, or as a sieve, filtering flow through the hairs. In our experiments, we uncover a third transitional phase: deflection, where the flow partially penetrates the hair array and is deflected laterally. We develop a reduced-order model that predicts the flow phase based on the depth of the boundary layer on a single hair. This model with no fitting parameters agrees very well with our experimental data. Additionally, our model agrees well with measurements of both chemosensing and suspension-feeding crustaceans and can be generalized for many different geometries.

The net movement of Lagrangian particles under water waves comprises a Stokes drift in the direction of wave propagation and an Eulerian return flow in the opposing direction. Accurate prediction of the Eulerian return flow in the ocean is of importance in modeling the transport of plastic pollution, oil, wreckage, and sediment. Herein, we derive a multiple-scales solution for the Eulerian mean flow under wave packets that is valid for all water depths, relative to both the length of the wave and the length of the wave packet. To validate this solution, we carry out particle tracking velocimetry experiments in a long flume to extract the mean motion from Lagrangian seeding particles under wave packets, finding good agreement. The extraction technique is able to deal with small background motion and subharmonic error waves associated with wave generation by the paddle, the latter being relatively large in finite-depth flume experiments. In finite depth, the return flow is forced by both the divergence of the Stokes transport on the wave-packet scale and the formation of a non-negligible mean set-down underneath the packet, which acts like a bounding streamtube in the form of a convergent-divergent duct. The magnitude of the horizontal return flow is thus enhanced, with particular relevance to transport in the finite-depth coastal environment.

We consider self-propelled droplets that are driven by internal flow. Tracer particles, which are advected by the flow, in general follow chaotic trajectories, even though the motion of the autonomous swimmer is completely regular. The flow is mixing, and for Péclet and Batchelor numbers, which are realized, e.g., in eukaryotic cells, advective mixing can substantially accelerate and even dominate transport by diffusion.

We apply a data-based, linear dynamic estimator to reconstruct the velocity field from measurements at a single sensor point in the wake of an aerofoil. In particular, we consider a NACA0012 aerofoil at $\text{Re}=600$ and ${16}^{\circ }$ angle of attack. Under these conditions, the flow exhibits a vortex shedding limit cycle. A reduced-order model of the flow field is extracted using proper orthogonal decomposition (POD). Subsequently, a subspace system identification algorithm (N4SID) is applied to extract directly the estimator matrices from the reduced output of the system (the POD coefficients). We explore systematically the effect of the number of states of the estimator, the sensor location, the type of sensor measurements (one or both velocity components), and the number of POD modes to be recovered. When the signal of a single velocity component (in the stream wise or cross stream directions) is measured, the reconstruction of the first two dominant POD modes strongly depends on the sensor location. We explore this behavior and provide a physical explanation based on the nonlinear mode interaction and the spatial distribution of the modes. When, however, both components are measured, the performance is very robust and is almost independent of the sensor location when the optimal number of estimator states is used. Reconstruction of the less energetic modes is more difficult, but still possible. Finally, we assess the robustness of the estimator at off-design conditions, at $\text{Re}=550$ and 650.