Adsorption onto and lowering of surface tension $\sigma$ of fluid interfaces by surfactants is exploited in drop formation (e.g., inkjet printing) where a thinning liquid thread (radius $h)$ connects an about-to-form drop to the liquid that remains hanging from the nozzle when the former falls from it. Surfactants can affect thread pinch-off in two ways: first, by lowering $\sigma$, they lower capillary pressure $\left(\sigma /h\right)$, and second, as surfactant concentration along the interface can be nonuniform, they cause the interface to be subjected to a surface tension gradient or Marangoni stress. Recent studies show that the location where the thread breaks is devoid of surfactant, and others assert that the influence of Marangoni stress on pinch-off is negligible. We demonstrate by simulations and experiments that surfactants play a major role in drop formation and that Marangoni stresses acting near but not at the pinch point give rise to reduced rates of thread thinning and formation of multiple microthreads that distinguish pinch-off of surfactant-covered threads from surfactant-free ones. Thinning at finite Reynolds and Peclet numbers, Re and Pe, is shown to exhibit intermediate scaling regimes that have heretofore only been observed during pinch-off of threads undergoing creeping flow $\left(\text{Re}=0\right)$ while convection of surfactant is weak compared to its diffusion $\left(\text{Pe}<1\right)$.

We measure experimentally the frequency of the large-scale instability developing on a liquid jet incompletely atomized by a parallel fast gas stream. We demonstrate that this “flapping instability” can be triggered by different mechanisms: in a first regime it is synchronized with the shear instability developing upstream, provided the wavelength of this shear instability is larger than the liquid jet diameter $H_L$. When the shear instability exhibits wavelengths shorter than $H_L$, a second regime is observed where the flapping instability becomes independent of the gas stream velocity. This second regime is characterized by a constant Strouhal number, provided the Froude number of the jet is correctly taken into account.

Numerical simulations of positively buoyant suspension in a horizontally rotating cylinder were performed to study the formation of radial and axial patterns. The order parameter for the low-frequency segregated phase and dispersed phase is similar to that predicted for the settling suspension by Lee and Ladd [J. Fluid Mech. 577, 183 (2007)], which is the average angular velocity of the particles. The particle density profiles for axial bands in the buoyancy-dominated phase shows an amplitude equivalent to the diameter of the cylinder. Axial density profiles show sinusoidal behavior for the drag-dominant phase and oscillating sinusoidal behavior for the centrifugal-force-dominant phase. Results also indicate that the traveling bands are formed as a consequence of the inhomogeneous distribution of particles arising from a certain imbalance of drag, buoyancy, and centrifugal forces. In the centrifugal limit, particles move towards the center of the cylinder, aggregating to form a dense core of particles with its axis coinciding with that of the rotating cylinder, a behavior which is in contrast to the sedimenting particles. The particle distribution patterns obtained from the simulations are found to be in good agreement with the experiments of Kalyankar et al. [Phys. Fluids 20, 083301 (2008)].

We discuss the impact of dissipation on the development of the energy spectrum in wave turbulence of gravity surface waves with emphasis on the effect of surface contamination. We performed experiments in the Coriolis facility, which is a 13-m-diam wave tank. We took care of cleaning surface contamination as well as possible, considering that the surface of water exceeds $100{\mathrm{m}}^2$. We observe that for the cleanest condition the frequency energy spectrum shows a power-law decay extending up to the gravity capillary crossover (14 Hz) with a spectral exponent that is increasing with the forcing strength and decaying with surface contamination. Although slightly higher than reported previously in the literature, the exponent for the cleanest water remains significantly below the prediction from the weak turbulence theory. By discussing length and time scales, we show that weak turbulence cannot be expected at frequencies above 3 Hz. We observe with a stereoscopic reconstruction technique that the increase with the forcing strength of energy spectrum beyond 3 Hz is mostly due to the formation and strengthening of bound waves.

A microscopic bubble of soluble gas always dissolves in finite time in an undersaturated fluid. This diffusive process is driven by the difference between the gas concentration near the bubble, whose value is governed by the internal pressure through Henry's law, and the concentration in the far field. The presence of neighboring bubbles can significantly slow down this process by increasing the effective background concentration and reducing the diffusing flux of dissolved gas experienced by each bubble. We develop theoretical modeling of such diffusive shielding process in the case of small microbubbles whose internal pressure is dominated by Laplace pressure. We first use an exact semianalytical solution to capture the case of two bubbles and analyze in detail the shielding effect as a function of the distance between the bubbles and their size ratio. While we also solve exactly for the Stokes flow around the bubble, we show that hydrodynamic effects are mostly negligible except in the case of almost-touching bubbles. In order to tackle the case of multiple bubbles, we then derive and validate two analytical approximate yet generic frameworks, first using the method of reflections and then by proposing a self-consistent continuum description. Using both modeling frameworks, we examine the dissolution of regular one-, two-, and three-dimensional bubble lattices. Bubbles located at the edge of the lattices dissolve first, while innermost bubbles benefit from the diffusive shielding effect, leading to the inward propagation of a dissolution front within the lattice. We show that diffusive shielding leads to severalfold increases in the dissolution time, which grows logarithmically with the number of bubbles in one-dimensional lattices and algebraically in two and three dimensions, scaling respectively as its square root and $2/3$ power. We further illustrate the sensitivity of the dissolution patterns to initial fluctuations in bubble size or arrangement in the case of large and dense lattices, as well as nonintuitive oscillatory effects.

We investigate the large-scale transport properties of quasi-neutrally-buoyant inertial particles carried by incompressible zero-mean periodic or steady ergodic flows. We show how to compute large-scale indicators such as the inertial-particle terminal velocity and eddy diffusivity from first principles in a perturbative expansion around the limit of added-mass factor close to unity. Physically, this limit corresponds to the case where the mass density of the particles is constant and close in value to the mass density of the fluid, which is also constant. Our approach differs from the usual over-damped expansion inasmuch as we do not assume a separation of time scales between thermalization and small-scale convection effects. For a general flow in the class of incompressible zero-mean periodic velocity fields, we derive closed-form cell equations for the auxiliary quantities determining the terminal velocity and effective diffusivity. In the special case of parallel flows these equations admit explicit analytic solution. We use parallel flows to show that our approach sheds light onto the behavior of terminal velocity and effective diffusivity for Stokes numbers of the order of unity.

We study penetrative convection of a fluid confined between two horizontal plates, the temperatures of which are such that a temperature of maximum density lies between them. The range of Rayleigh numbers studied is $\text{Ra}=\left[{10}^6,{10}^8\right]$ and the Prandtl numbers are $\text{Pr}=1$ and 11.6. An evolution equation for the growth of the convecting region is obtained through an integral energy balance. We identify a new nondimensional parameter, $\mathrm{\Lambda }$, which is the ratio of temperature difference between the stable and unstable regions of the flow; larger values of $\mathrm{\Lambda }$ denote increased stability of the upper stable layer. We study the effects of $\mathrm{\Lambda }$ on the flow field using well-resolved lattice Boltzmann simulations and show that the characteristics of the flow depend sensitively upon it. For the range $\mathrm{\Lambda }=\left[0.01,4\right]$, we find that for a fixed $\text{Ra}$ the Nusselt number, $\text{Nu}$, increases with decreasing $\mathrm{\Lambda }$. We also investigate the effects of $\mathrm{\Lambda }$ on the vertical variation of convective heat flux and the Brunt-Väisälä frequency. Our results clearly indicate that in the limit $\mathrm{\Lambda }\to 0$ the problem reduces to that of the classical Rayleigh-Bénard convection.

Superhydrophobic surfaces demonstrate promising potential for skin friction reduction in naval and hydrodynamic applications. Recent developments of superhydrophobic surfaces aiming for scalable applications use random distribution of roughness, such as spray coating and etched process. However, most previous analyses of the interaction between flows and superhydrophobic surfaces studied periodic geometries that are economically feasible only in laboratory-scale experiments. In order to assess the drag reduction effectiveness as well as interfacial robustness of superhydrophobic surfaces with randomly distributed textures, we conduct direct numerical simulations of turbulent flows over randomly patterned interfaces considering a range of texture widths $w^{+}\approx 4\text{–}26$, and solid fractions ${\varphi }_s=11\%-25\%$. Slip and no-slip boundary conditions are implemented in a pattern, modeling the presence of gas-liquid interfaces and solid elements. Our results indicate that slip of randomly distributed textures under turbulent flows is about $30\%$ less than those of surfaces with aligned features of the same size. In the small texture size limit $w^{+}\approx 4$, the slip length of the randomly distributed textures in turbulent flows is well described by a previously introduced Stokes flow solution of randomly distributed shear-free holes. By comparing DNS results for patterned slip and no-slip boundary against the corresponding homogenized slip length boundary conditions, we show that turbulent flows over randomly distributed posts can be represented by an isotropic slip length in streamwise and spanwise direction. The average pressure fluctuation on a gas pocket is similar to that of the aligned features with the same texture size and gas fraction, but the maximum interface deformation at the leading edge of the roughness element is about twice as large when the textures are randomly distributed. The presented analyses provide insights on implications of texture randomness on drag reduction performance and robustness of superhydrophobic surfaces.

We study the effect of magnetic field on the rheology of magnetic micro-swimmers suspensions. We use a model of a dilute suspension under simple shear and subjected to a constant magnetic field. Particle shear stress is obtained for both pusher and puller types of micro-swimmers. In the limit of low shear rate, the rheology exhibits a constant shear stress, called actuated stress, which only depends on the swimming activity of the particles. This stress is induced by the magnetic field and can be positive (brake state) or negative (motor state). In the limit of low magnetic fields, a scaling relation of the motor-brake effect is derived as a function of the dimensionless parameters of the model. In this case, the shear stress is an affine function of the shear rate. The possibilities offered by such an active system to control the rheological response of a fluid are finally discussed.

Superhydrophobic surfaces have been shown to produce significant drag reduction in both laminar and turbulent flows by introducing an apparent slip velocity along an air-water interface trapped within the surface roughness. In the experiments presented within this study, we demonstrate the existence of a surface tension gradient associated with the resultant Marangoni flow along an air-water interface that causes the slip velocity and slip length to be significantly reduced. In this study, the slip velocity along a millimeter-sized air-water interface was investigated experimentally. This large-scale air-water interface facilitated a detailed investigation of the interfacial velocity profiles as the flow rate, interfacial curvature, and interface geometry were varied. For the air-water interfaces supported above continuous grooves (concentric rings within a torsional shear flow) where no surface tension gradient exists, a slip velocity as high as 30% of the bulk velocity was observed. However, for the air-water interfaces supported above discontinuous grooves (rectangular channels in a Poiseuille flow), the presence of a surface tension gradient reduced the slip velocity and in some cases resulted in an interfacial velocity that was opposite to the main flow direction. The curvature of the air-water interface in the spanwise direction was found to dictate the details of the interfacial flow profile with reverse flow in the center of the interface for concave surfaces and along the outside of the interface for convex surfaces. The deflection of the air-water interface was also found to greatly affect the magnitude of the slip. Numerical simulations imposed with a relatively small surface tension gradient along the air-water interface were able to predict both the reduced slip velocity and back flow along the air-water interface.

At transcritical conditions, the transition of a fluid from a liquidlike state to a gaslike state occurs continuously, which is associated with significant changes in fluid properties. Therefore, boiling in its conventional sense does not exist and the phase transition at transcritical conditions is known as “pseudoboiling.” In this work, direct numerical simulations (DNS) of a channel flow at transcritical conditions are conducted in which the bottom and top walls are kept at temperatures below and above the pseudoboiling temperature, respectively. Over this temperature range, the density changes by a factor of 18 between both walls. Using the DNS data, the usefulness of the semilocal scaling and the Townsend attached-eddy hypothesis are examined in the context of flows at transcritical conditions—both models have received much empirical support from previous studies. It is found that while the semilocal scaling works reasonably well near the bottom cooled wall, where the fluid density changes only moderately, the same scaling has only limited success near the top wall. In addition, it is shown that the streamwise velocity structure function follows a logarithmic scaling and the streamwise energy spectrum exhibits an inverse wave-number scaling, thus providing support to the attached-eddy model at transcritical conditions.

Miscible displacement flows within the gap of a nonuniform Hele-Shaw cell are considered, theoretically and experimentally. The cell is vertical and it can be diverging or converging. A light fluid displaces a heavy fluid downwards. The displacement imposed velocity is sufficiently large so that diffusive effects are negligible within our time scale of interest. For certain flow parameters, the displacement flow is characterized by a symmetric, two-dimensional penetration of the light fluid into the heavy one, for which a lubrication approximation approach is developed to simplify the governing equations and find a semianalytical solution for the flux functions. The solutions reveal how the cell nonuniformity may affect the propagation of the interface between the two fluids, versus the other flow parameters, i.e., the viscosity ratio $\left(m\right)$ and a buoyancy number $\left(\chi \right)$, for which a detailed flow regime classification is presented. Our results demonstrate that the presence of nonuniformity adds a unique spatiotemporal nature to these displacements which is not the case for uniform cell flows. The combination of the model and experiments reveals the existence of self-spreading, spike, and unstable (viscous fingering) flow regimes, which may occur at various spatial positions within the cell. A converging cell may allow a transition from spike to self-spreading or unstable regime, whereas a diverging cell may offer a transition from self-spreading or unstable to spike regime. Our work demonstrates that the novel spatiotemporal nature of nonuniform cell flows must be considered through the numerical solution of the interface propagation equation, to yield accurate predictions about the flow behaviors at various spatial positions.

The leading-edge slat of a multielement wing is a significant contributor to the acoustic signature of an aircraft during the approach phase of the flight path. An experimental study of the two-dimensional 30P30N geometry is undertaken to further understand the flow physics and specific noise source mechanisms. The mean statistics from particle image velocimetry (PIV) shows the differences in the flow field with angle of attack, including the interaction between the cove and trailing-edge flow. Phase-locked PIV successfully links narrow-band peaks found in the surface pressure spectrum to shear layer instabilities and also reveals that a bulk cove oscillation at a Strouhal number based on a slat chord of 0.15 exists, indicative of shear layer flapping. Unsteady surface pressure measurements are documented and used to estimate spanwise coherence length scales. A narrow-band frequency prediction scheme is also tested and found to agree well with the data. Furthermore, higher-order spectral analysis suggests that nonlinear effects cause additional peaks to arise in the power spectrum, particularly at low angles of attack.

The Derviche Tourneur sodium experiment, a spherical Couette magnetohydrodynamics experiment with liquid sodium as the medium and a dipole magnetic field imposed from the inner sphere, recently underwent upgrades to its diagnostics to better characterize the flow and induced magnetic fields with global rotation. In tandem with the upgrades, a set of direct numerical simulations were run to give a more complete view of the fluid and magnetic dynamics at various rotation rates of the inner and outer spheres. These simulations reveal several dynamic regimes, determined by the Rossby number. At positive differential rotation there is a regime of quasigeostrophic flow, with low levels of fluctuations near the outer sphere. Negative differential rotation shows a regime of what appear to be saturated hydrodynamic instabilities at low negative differential rotation, followed by a regime where filamentary structures develop at low latitudes and persist over five to ten differential rotation periods as they drift poleward. We emphasize that all these coherent structures emerge from turbulent flows. At least some of them seem to be related to linear instabilities of the mean flow. The simulated flows can produce the same measurements as those that the physical experiment can take, with signatures akin to those found in the experiment. This paper discusses the relation between the internal velocity structures of the flow and their magnetic signatures at the surface.

We present a weakly nonlinear theory for the development of fingering instabilities that arise at the interface between two immiscible viscous fluids flowing radially outward in a uniform three-dimensional (3D) porous medium. By employing a perturbative second-order mode-coupling scheme, we investigate the linear stability of the system as well as the emergence of intrinsically nonlinear finger branching events in this 3D environment. At the linear stage, we find several differences between the 3D radial fingering and its 2D counterpart (usual Saffman-Taylor flow in radial Hele-Shaw cells). These include the algebraic growth of disturbances and the existence of regions of absolute stability for finite values of viscosity contrast and capillary number in the 3D system. On the nonlinear level, our main focus is to get analytical insight into the physical mechanism resulting in the occurrence of finger tip-splitting phenomena. In this context, we show that the underlying mechanism leading to 3D tip splitting relies on the coupling between the fundamental interface modes and their first harmonics. However, we find that in three dimensions, in contrast to the usual 2D fingering structures normally encountered in radial Hele-Shaw flows, tip splitting into three branches can also be observed.

Advances in solution-based printing and surface patterning techniques for additive manufacturing demand a clear understanding of particle dynamics in drying colloidal droplets and its relationship with deposit structure. Although the evaporation-driven deposition has been studied thoroughly for the particles dispersed in the bulk of the droplet, few investigations have focused on the particles strongly adsorbed to the droplet surface. We modeled the assembly and deposition of the surface-active particles in a drying sessile droplet with a pinned contact line by the multiphase lattice Boltzmann-Brownian dynamics method. The particle trajectory and its area density profile characterize the assembly dynamics and deposition pattern development during evaporation. While the bulk-dispersed particles continuously move to the contact line, forming the typical “coffee-ring” deposit, the interface-bound particles migrate first toward the apex and then to the contact line as the droplet dries out. To understand this unexpected behavior, we resolve the droplet velocity field both in the bulk and within the interfacial region. The simulation results agree well with the analytical solution for the Stokes flow inside an evaporating droplet. At different stages of evaporation, our study reveals that the competition between the tangential surface flow and the downward motion of the evaporating liquid-vapor interface governs the dynamics of the interface-bound particles. In particular, the interface displacement contributes to the particle motion toward the droplet apex in a short phase, while the outward advective flow prevails at the late stage of drying and carries the particles to the contact line. The final deposit of the surface-adsorbed particles exhibits a density enhancement at the center, in addition to a coffee ring. Despite its small influence on the final deposit in the present study, the distinct dynamics of surface-active particles due to the interfacial confinement could offer a new route to deposition control when combined with Marangoni effects.

We experimentally investigate the interaction between individual bubble deformations and collective distortions of segmented flows in nonlinear microfluidic geometries. Using highly viscous carrier fluids, we study the evolution of monodisperse trains of gas bubbles from a square to a smoothly corrugated microchannel characterized with a series of extensions and constrictions along the flow path. The hysteresis in the bubble shape between accelerating and decelerating flow fields is shown to increase with the capillary number. Measurements of instantaneous bubble velocities reveal the presence of a capillary pull that produces a nonmonotonic behavior for the front velocity in accelerating flow regions. Functional relationships are developed for predicting the morphology and dynamics of viscous multiphase flow patterns at the pore scale.

In this paper, we report on the structure and dynamics of double helix vortex breakdown in a turbulent annular swirling jet. Double helix breakdown has been reported previously for the laminar flow regime, but this structure has rarely been observed in turbulent flow. The flow field is investigated experimentally by means of time-resolved tomographic particle image velocimetry. Notwithstanding the axisymmetric nature of the time-averaged flow, analysis of the instantaneous three-dimensional (3D) vortical structures shows the existence of a vortex core along the central axis which breaks up into a double helix downstream. The winding sense of this double helix is opposite to the swirl direction $\left(m=-2\right)$ and it is wrapped around a central vortex breakdown bubble. This structure is quite different from double helix breakdown found in laminar flows where the helix is formed in the wake of the bubble and not upstream. The double helix precesses around the central axis of the jet with a precessing frequency corresponding to a Strouhal number of 0.27.

The interaction of trailing vortices of an upstream wing with rigid and flexible downstream wings has been investigated experimentally in a wind tunnel, using particle image velocimetry, hot-wire, force, and deformation measurements. Counter-rotating upstream vortices exhibit increased meandering when they are close to the tip of the downstream wing. The upstream vortex forms a pair with the vortex shed from the downstream wing and then exhibits large displacements around the wing tip. This coupled motion of the pair has been found to cause large lift fluctuations on the downstream wing. The meandering of the vortex pair occurs at the natural meandering frequency of the isolated vortex, with a low Strouhal number, and is not affected by the frequency of the large-amplitude wing oscillations if the downstream wing is flexible. The displacement of the leading vortex is larger than that of the trailing vortex; however, it causes highly correlated variations of the core radius, core vorticity, and circulation of the trailing vortex with the coupled meandering motion. In contrast, co-rotating vortices do not exhibit any increased meandering.

We investigate the nonlinear dynamics and stability of an evaporating liquid layer subject to vapor recoil, capillarity, thermocapillarity, ambient cooling, viscosity, and negative or positive gravity combined with buoyancy effects in the lubrication approximation. Using linear theory, we identify the mechanisms of finite-time rupture, independent of thermocapillarity and direction of gravity, and predict the effective growth rate of an interfacial perturbation which reveals competition among the mechanisms. A stability diagram is predicted for the onset of long-wave (LW) evaporative convection. In the two-dimensional simulation, we observe well-defined capillary ridges on both sides of the valley under positive gravity and main and secondary droplets under negative gravity, while a ridge can be trapped in a large-scale drained region in both cases. Neglecting the other non-Boussinesq effects, buoyancy does not have a significant influence on interfacial evolution and rupture time but makes contributions to the evaporation-driven convection and heat transfer. The average Nusselt number is found to increase with a stronger buoyancy effect. The flow field and interface profile jointly manifest the LW Marangoni-Rayleigh-Bénard convection under positive gravity and the LW Marangoni convection under negative gravity. In the three-dimensional simulation of moderate evaporation with a random perturbation, the rupture patterns are characterized by irregular ridge networks with distinct height scales for positive and negative gravity. A variety of interfacial and internal dynamics are displayed, depending on evaporation conditions, gravity, Marangoni effect, and ambient cooling. Reasonable agreement is found between the present results and the reported experiments and simulations. The concept of dissipative compacton also sheds light on the properties of interfacial fractalization.