Cross-slot and four-roll-mill microdevices are commonly used for particle manipulation and characterization owing to the stagnation-point flow at the device center. Because of the solid boundaries, these devices may generate extensional Stokes flows where the velocity is a nonlinear function of position associated with a decreased pressure at the particle edges and an increased pressure at the particle middle. Our computational investigation shows that in this class of Stokes flows, an elastic capsule made of a strain-hardening membrane develops two distinct steady-state conformations at strong flows, i.e., an elongated weak dumbbell shape with rounded edges at low flow nonlinearity and a laterally extended dumbbell shape at high flow nonlinearity. These effects are more pronounced for the less strain-hardening capsules which develop a flat extended middle where the two sides of the membrane approach each other. The strong stability properties of the strain-hardening capsules (owing to the development of strong membrane tensions) contrast significantly with the behavior of droplets in these nonlinear flows which are unable to achieve highly deformed steady-state dumbbell shapes owing to their constant surface tension.

In this work, a systematic approach to efficient open flow mixing is introduced, using general theoretical concepts to identify optimized parameters of a deliberately introduced unsteady flow component. The method is applied in detail to two-dimensional (2D) advective mixing in flows resulting from the superposition of a transport flow through a channel and secondary localized cross-flows, here the vortical streaming due to a microbubble array. A simple description of stirring in a steady 2D vortex identifies the characteristic time beyond which vortex stirring becomes ineffective, with slow algebraic decay of the mix-variance. Duty cycling of the vortices introduces flow unsteadiness, for which optimum duty cycling protocols are identified, following analytically from a few selected Eulerian properties of the combined transport and vortex stirring flow. In comparison with experiments and simulations, it is shown that this simple formalism allows for the accurate prediction of optimal advective mixing, exponential in time, in the microbubble streaming case and, by extension, for any open-flow mixer with modulated secondary flow. Taking into account the effect of diffusion, estimated residence times required for complete mixing in such optimized devices are obtained.

The dynamics of the nearly periodic highly modulated turbulent wakes of two-dimensional rectangular cylinders normal to a uniform flow are investigated experimentally for thickness-to-chord ratios between 0.05 and 1.92 at Reynolds numbers around $6600$. Measurements were conducted using planar, time-resolved stereoscopic particle image velocimetry. A generalized phase average analysis, which invokes elements of mean-field theory to relate the temporal modal coefficients of the fundamental harmonic and slow-varying base-flow drift, provided a statistically significant representation of the coherent cycle-to-cycle variation of the shedding process. It is shown that the characteristics of the wake velocity fluctuations change as a function of the thickness-to-chord ratio and can be related to structural differences in the wake topology. Moreover, the trajectory of shed vortices plays an important role in distinguishing the dynamics observed for different fluctuation-amplitude cycles. Based on differences in amplitude modulation characteristics and the vortex formation region topology, three flow regimes can be defined: a thin-plate regime, for which the feedback between forming vortices and base pressure is important; a cylinder-like thick-plate regime for which the obstacle afterbody suppresses the feedback; and a long-plate regime for which wake periodicity is not associated with the classical Kármán shedding process. The present analysis highlights the importance of the feedback mechanism for the thin-plate regime and helps reconcile differences in the reported critical thickness values between regimes.

Thermal convection in a horizontal layer with uniform internal heating and stress-free constant-temperature boundaries is analyzed numerically. The work is motivated by the questions arising in the development of liquid metal batteries, in which convection is induced by the Joule heating of electrolyte. It is demonstrated that three-dimensional convection cells exist at subcritical Rayleigh numbers.

The process of shock interaction with a rigid cylinder is studied using a compressible immersed boundary method combined with a high-order weighted essentially nonoscillatory scheme. Movement of the cylinder is coupled to the flow field. First, the accuracy of the numerical scheme is validated. Then the influences of the incident shock Mach number and the cylinder diameter are discussed. The results are compared with those from cases with stationary cylinders. It is found that variation of either the incident shock Mach number or the cylinder diameter can cause different schlieren images. At a given dimensionless time, the trajectory of the upper triple point varies nonmonotonically with the incident shock Mach number while the primary reflected shock gets closer to the cylinder with increasing incident shock Mach number. For any moving case with a given incident shock Mach number and cylinder diameter, the trajectory of the upper triple point, the time evolution of the normalized vertical distance from the highest point of the primary reflected shock to the centerline of the cylinder, and the time evolution of the normalized shock detachment distance can all be predicted by linear correlation. As for the time evolution of the force exerted on the cylinder, the peak of the moving cylinder appears earlier than the stationary one in dimensionless time, with much lower value. Correlations to predict the occurrence of the peak drag and its value under different shock Mach numbers and cylinder diameters are proposed. The resulting cylinder movement is also briefly discussed.

The characteristics of a horizontal submerged square jet interacting with the free surface are investigated experimentally. A particle image velocimetry system is used to measure the mean flow and turbulent characteristics in the vertical symmetry plane of the jet at a Reynolds number of approximately 5500. It is shown that the effect of the free surface is to cancel the turbulent-nonturbulent interface and reduce the mean spanwise vorticity, Reynolds shear stress, and jet spreading rate in the upper shear layer in comparison to those measured in the lower shear layer. The results indicate that lowering of the jet offset height ratio increases the confinement effect of the free surface. Stronger confinement reduces the maximum mean streamwise velocity decay rate and mean surface velocity defect in the interaction region. The results also indicate a dramatic reduction in surface-normal turbulence intensity in the interaction region due to the damping effect of the free surface on the surface-normal velocity fluctuations. The decay of the surface-normal turbulence intensity near the free surface produces commensurate reductions in the surface-normal velocity fluctuation autocorrelation in the upper shear layer while enhancing the streamwise velocity fluctuation autocorrelation. The damping effect of the free surface on the surface-normal velocity fluctuations is found to be connected to the redistribution of the turbulent kinetic energy from the surface-normal velocity fluctuations to the streamwise velocity fluctuations.

The two- and three-dimensional spatio-temporal dynamics of a falling, electrified leaky dielectric film are studied. The method of weighted residuals is used to derive high-order models that account for both inertia as well as second-order electrostatic effects. The models are validated against both linear theory and direct numerical simulations of the Navier-Stokes equations. It is shown that a simplified model offers a rapid computational option at the cost of a minimal decrease in accuracy. This model is then used to perform a parametric study in three dimensions.

This study is concerned with the linear stability of the horizontal interface between thick layers of a viscous heat-conducting liquid and its vapor in a gravitational field subject to phase transition. We consider the case when the hydrostatic base state is consistent with a balanced heat flux at the liquid-vapor interface. The corrections to the growth rate of the most dangerous perturbations and cutoff wave number, characterizing the influence of phase transition on the Rayleigh-Taylor instability, are found to be different from the data in the literature. Most of the previous results were obtained in the framework of a quasiequilibrium approximation, which had been shown to conform to the limit of thin media layers under equality of the interface temperature to a saturation temperature. The main difference from the results obtained with the quasiequilibrium approach is new values of the proportionality coefficients that correlate our corrections with the intensity of weak heating. Moreover, at large values of the heat flux rate, when deviations from the approximate linear law are important, the effect of phase transition is limited and does not exceed the size of the vapor viscosity effect.

We report on an experimental, theoretical, and numerical study of slanted snaking of spatially localized parametrically excited waves on the surface of a water-surfactant mixture in a Hele-Shaw cell. We demonstrate experimentally the presence of a hysteretic transition to spatially extended parametrically excited surface waves when the acceleration amplitude is varied, as well as the presence of spatially localized waves exhibiting slanted snaking. The latter extend outside the hysteresis loop. We attribute this behavior to the presence of a conserved quantity, the liquid volume trapped within the meniscus, and introduce a universal model based on symmetry arguments, which couples the wave amplitude with such a conserved quantity. The model captures both the observed slanted snaking and the presence of localized waves outside the hysteresis loop, as demonstrated by numerical integration of the model equations.

We show that the immersion of a horizontally suspended thin film of liquid in a pool of the same fluid creates an interfacial bubble, that is, a bubble at the liquid-air interface. Varying the fluid properties, the film's size, and its immersion velocity, our experiments unveil two formation regimes characterized by either a visco-capillary or an inertio-capillary mechanism that controls the size of a produced bubble. To rationalize these results, we compare the pressure exerted by the air flow under a plunging film with the Laplace pressure needed to generate film dimpling, which subsequently yields air entrapment and the production of a bubble. This physical model explains the power-law variations of the bubble size with the governing dimensionless number for each regime.

Here we attempt to solve the fully coupled Poisson-Nernst-Planck-Navier-Stokes equations, to ascertain the influence of finite electric double layer (EDL) thickness on coupled charge and fluid dynamics over patterned charged surfaces. We go beyond the well-studied “weak-field” limit and obtain numerical solutions for a wide range of EDL thicknesses, applied electric field strengths, and the surface potentials. Asymptotic solutions to the coupled system are also derived using a combination of singular and regular perturbation, for thin EDLs and low surface potential, and good agreement between the two solutions is observed. Counterintuitively to common arguments, our analysis reveals that finite EDL thickness may either increase or decrease the “free-stream velocity” (equivalent to net throughput), depending on the strength of the applied electric field. We also unveil a critical EDL thickness for which the effect of finite EDL thickness on the free-stream velocity is the most prominent. Finally, we demonstrate that increasing the surface potential and the applied field tends to influence the overall flow patterns in the contrasting manners. These results may be of profound importance in developing a comprehensive theoretical basis for designing electro-osmotically actuated microfluidic mixtures.

Magnetic levitation was used to measure the growth rate $\mathrm{\Sigma }$ vs wave vector $k$ of a Rayleigh-Taylor instability in a three-layer fluid system, a crucial step in the elucidation of interface coupling in finite-layer instabilities. For a three-layer (low-high-low density) system, the unstable mode growth rate decreases as both the height $h$ of the middle layer and $k$ are reduced, consistent with an interface coupling $\propto e^{-kh}$. The ratios of the three-layer to the established two-layer growth rates are in good agreement with those of classic linear stability theory, which has long resisted verification in that configuration.

The dynamics of an elastic sheet lubricated by a thin liquid film on a wetting solid substrate is examined using both numerical simulations of a long-wave lubrication equation and a quasistatic model. Interactions between the liquid and the wetting substrate are modeled by a disjoining pressure that gives rise to an ultrathin (precursor) film. For a fluid interface without elastic bending stiffness, a flat precursor film may be linearly unstable and evolve towards an equilibrium of a single “drop” connected to a flat ultrathin film. Similar behavior is found when the thin film is covered by an elastic sheet: The sheet deforms, rearranging the thin liquid film, and contributes regulating surface forces such as a bending resistance and/or a tensile force, which may arise from interactions between the sheet and liquid or inextensibility of the sheet. Glasner's quasistatic model [Phys. Fluids 15, 1837 (2003)], developed for a liquid film, is adopted to investigate the combined effects of elastic and tensile forces in the sheet on the thin film dynamics. The equilibrium height of the drop is found to vary inversely with the bending rigidity. When the elastic sheet is inextensible (such as a lipid bilayer membrane), a compressive tensile force may occur and the equilibrium film height is dependent less on the bending rigidity and more on the excess area of the membrane. Analyses of the lubrication equation also show that the precursor film transitions monotonically to the core film for tension-dominated dynamics. In contrast, for elasticity-dominated dynamics, a spatial oscillation of film height in the contact line region is found. In addition, elasticity in the sheet causes a sliding motion of the thin film: the contact angle is rendered zero by elasticity, and the contact line moves at a finite speed.

Synchronous multipoint measurements were performed in the atmospheric surface layer at the Qingtu Lake Observation Array site to obtain high-Reynolds-number $[{\mathrm{Re}}_{\tau }\sim O\left({10}^6\right)]$ data. Based on the selected high-quality data in the near-neutral surface layer, the spatial length scales of the large-scale dominant structures in the outer region of the turbulent boundary layer are investigated. The characteristic length scales are extracted from the two-point streamwise velocity correlations. Results show that the spatial length scales are invariant over a three order of magnitude change in Reynolds number $[{\mathrm{Re}}_{\tau }\sim O\left({10}^3\right)-O\left({10}^6\right)]$. However, they increase significantly with the wall-normal distance, showing reasonable collapses on outer-scaled axes. The variation of the spanwise width scale in the logarithmic region follows a linear increase, with the rate of increase much larger than that in the wake region. Moreover, the variation of the wall-normal length scale is also revealed, which displays a qualitative behavior similar to that of the spanwise width scale. The universal laws revealed in the present work contribute to a better understanding of the dominant structures in the outer region of the turbulent boundary layer at high Reynolds numbers.

This paper presents a linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cone. The base flow is considered parallel to the axis of the cone at the inlet. The angle of attack is zero and hence the base flow is axisymmetric. A favorable pressure gradient develops in the streamwise direction due to cone angle. The Reynolds number is calculated based on the cone radius $a$ at the inlet and freestream velocity $U_{\infty }$. The base flow velocity profile is fully nonparallel and nonsimilar. Linearized Navier-Stokes equations (LNSEs) are derived for the disturbance flow quantities in the spherical coordinates. The LNSEs are discretized using the Chebyshev spectral collocation method. The discretized LNSEs along with the homogeneous boundary conditions form a general eigenvalues problem. Arnoldi's iterative algorithm is used for the numerical solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds number from 174 to 1046, semicone angles $2^{\circ },4^{\circ }$, and $6^{\circ }$, and azimuthal wave numbers from 0 to 5. It is found that the global modes are more stable at higher semicone angle $\alpha$, due to the development of favorable pressure gradient. The effect of transverse curvature is reduced at higher $\alpha$. The spatial structure of the eigenmodes shows that the flow is convectively unstable. The spatial growth rate $A_x$ increases with an increase in $\alpha$ from $2^{\circ }$ to $6^{\circ }$. Thus, the effect of an increase in $\alpha$ is to reduce the temporal growth rate ${\omega }_i$ and increase the $A_x$ of the global modes at a given Reynolds number.

In a recent article, Canton et al. [J. Canton et al., Phys. Rev. Fluids 1, 081501(R) (2016)] reported significant drag reduction in turbulent channel flow by using large-scale, near-wall streamwise swirls following the control strategy of Schoppa and Hussain [W. Schoppa and F. Hussain, Phys. Fluids 10, 1049 (1998)] for low Reynolds numbers only, but found no drag reduction at high friction Reynolds numbers $\left({\text{Re}}_{\tau }=550\right)$. Here we show that the lack of drag reduction at high $\text{Re}$ observed by Canton et al. is remedied by the proper choice of the large-scale control flow. In this study, we apply near-wall opposed wall-jet forcing to achieve drag reduction at the same (high) Reynolds number where Canton et al. found no drag reduction. The steady excitation is characterized by three control parameters, namely, the wall-jet-forcing amplitude $A^{+}$, the spanwise spacing ${\mathrm{\Lambda }}^{+}$, and the wall jet height $y_c^{+}$ $(+$ indicates viscous scaling); the primary difference between Schoppa and Hussain's work (also that of Canton et al.) and this Rapid Communication is the emphasis on the explicit choice of $y_c^{+}$ here. We show as an example that with a choice of $A^{+}\approx 0.015,{\mathrm{\Lambda }}^{+}\approx 1200$, and $y_c^{+}\approx 30$ the flow control definitely suppresses the wall shear stress at a series of Reynolds numbers, namely, $19\%,14\%$, and $12\%$ drag reductions at ${\text{Re}}_{\tau }=180$, 395, and 550, respectively. Further study should explore optimization of these parameter values.

In this paper we focus on the turbulent transport of a scalar through a channel. The scalar flux and the corresponding scalar concentration gradient along the channel allow us to define a Nusselt number and a Grashof number. While the relation between the large-scale velocity field and the input energy rate show perfect inertial (turbulent) behavior, three different regimes can be distinguished, with different scalings between Nusselt and Grashof numbers.

When a cavitation bubble oscillates and collapses in the vicinity of a solid boundary (a substrate), it induces intense microconvection in the surrounding liquid and—of high practical importance—directly at the substrate. As the involved flows are fast, highly unsteady, and possess an impressive shear, experiments are difficult and data are scarce. Here, insight into the generation and dynamics of the liquid flows from individual cavitation bubbles collapsing in the vicinity of a solid boundary is provided. Single laser-induced cavitation bubbles (maximum radius around 375 μm) are seeded at precisely defined standoff distances to a substrate by a focused laser pulse. The bubble shape dynamics are imaged by synchronized high-speed cameras from two perpendicular viewing angles. Recording of the shape dynamics is combined with the simultaneous time-resolved measurement of the full flow field on a micrometer-resolution. Measurements employ a high-speed hybrid particle imaging velocimetry and particle tracking velocimetry technique, with a temporal sampling of up to 135 kHz, using fluorescent microparticles as tracers. The time evolution of the unsteady flow field induced by one and the same bubble over a time period much longer than the bubble lifetime is determined. The shear flow at the substrate is analyzed and a liquid transport toward and away from the substrate surface is demonstrated. Depending on the bubble standoff distance, very different flow patterns are observed. The dominant liquid displacement is caused by the long-lived vortex ring being produced during bubble collapse. Most peculiar, the bubble standoff distance determines the sense of direction of the circulation associated with the vortex ring and, consequently, whether the vortex is ejected from the substrate or radially stretches over it. The results are relevant for the understanding of cavitation effects, such as surface cleaning, erosion, and mixing or in biomedical context and may serve as basis for numerical simulations.

Turbulent thermal diffusion is a combined effect of the temperature stratified turbulence and inertia of small particles. It causes the appearance of a nondiffusive turbulent flux of particles in the direction of the turbulent heat flux. This nondiffusive turbulent flux of particles is proportional to the product of the mean particle number density and the effective velocity of inertial particles. The theory of this effect has been previously developed only for small temperature gradients and small Stokes numbers [Phys. Rev. Lett. 76, 224 (1996)]. In this study, a generalized theory of turbulent thermal diffusion for arbitrary temperature gradients and Stokes numbers has been developed. The laboratory experiments in the oscillating grid turbulence and in the multifan produced turbulence have been performed to validate the theory of turbulent thermal diffusion in strongly stratified turbulent flows. It has been shown that the ratio of the effective velocity of inertial particles to the characteristic vertical turbulent velocity for large Reynolds numbers is less than 1. The effective velocity of inertial particles as well as the effective coefficient of turbulent thermal diffusion increase with Stokes numbers reaching the maximum at small Stokes numbers and decreases for larger Stokes numbers. The effective coefficient of turbulent thermal diffusion also decreases with the mean temperature gradient. It has been demonstrated that the developed theory is in a good agreement with the results of the laboratory experiments.

In the present investigation, we report data from direct numerical simulations of elliptical, finite release, Boussinesq gravity currents propagating down a uniform slope. The study comprises a series of simulations of elliptical gravity currents on a range of slope angles. The shape parameters are varied to study the effects of the initial cross-sectional aspect ratio $\left({\mathrm{\Lambda }}_0\right)$ and mean height to lock radius ratio $\left(\mathrm{\Gamma }\right)$ on the dynamics of the gravity current. It is found that the long-time development of the current spatial mass distribution is influenced by its initial shape at smaller slope angles ($\theta =5^{\circ }$ and ${10}^{\circ }$) whereas the long-time motion of the gravity current is relatively insensitive to its initial shape but is sensitive to the slope angle. The switching of axes are observed for all the noncircular releases studied in the present work. Multiple acceleration phases are observed for the current center of mass in the case of the current with a small or moderate initial cross-sectional aspect ratio (${\mathrm{\Lambda }}_0=0.1$, 0.2, 0.5, 1, and 2) whereas one single acceleration phase exists for the current with a large initial cross-sectional aspect ratio (${\mathrm{\Lambda }}_0=5$ and 10). The Froude numbers $\left(\mathit{\text{Fr}}\right)$ for the currents released with the same slope angle but different initial shapes are observed to attain a similar constant value after the second acceleration phase. The mean Froude number $\left(\overline{\mathit{\text{Fr}}}\right)$ is seen to increase with increasing slope angles. The mean height to lock radius ratio is found to affect only the early development of the current with little influence on the long-time evolution.