Miscible viscous fingering is studied experimentally in the presence of a nonmonotonic viscosity profile due to nonideal mixing properties in a porous medium consisting in a micropillar array column used for chromatographic applications. In this setup, a mobile phase composed of an aqueous solution of methanol displaces a miscible finite-size sample containing mainly water. Due to a local buildup by nonideal mixing of maxima in the viscosity profile, fingering is observed at both the frontal and rear miscible interfaces of the sample phase, however with different spatial extents. The influence on the fingering dynamics of the pressure in the column and of the viscosity of the mobile or sample phases is analyzed.

Buoyant spheres released below the free surface can rise well above the surface in a phenomenon known as pop-up. Contrary to intuition, increasing the release depth sometimes results in a lower pop-up height. We present the pop-up height of rising buoyant spheres over a range of release depths (1–12.5 diameters) and Reynolds numbers $(4\times {10}^4$ to $6\times {10}^5)$. While the dynamics of rising buoyant spheres and bubbles has been thoroughly investigated for Reynolds numbers below ${10}^4$, pop-up in these larger-Reynolds-number regimes has not been studied. Yet the underwater motions of the sphere for the Reynolds numbers we study are the key to understanding the pop-up height. Two major regimes are apparent: vertical and oscillatory. The vertical regime exhibits a nearly vertical underwater trajectory and results in the largest pop-up heights. The oscillatory regime exhibits an underwater trajectory with periodic lateral motions and results in lower pop-up heights; this periodic lateral motion is modulated by unsteady vortex shedding in the wake of the sphere. Despite these complex fluid structure interactions, the experiments presented herein yield extremely repeatable results.

Confinement-guided coalescence of drops in microfluidic devices is an effective means to manipulate the composition of individual droplets. Recently, Sun et al. [Lab Chip 11, 3949 (2011)] have shown that coalescence between a long moving plug and an array of parked droplets in a microfluidic network can be used to flexibly manipulate the composition of the static droplet arrays. However, the transport mechanisms underlying this complex dilution process have not been elucidated. In this study, we develop phenomenological models and perform particle-based numerical simulations to identify the key mass transfer mechanisms influencing the concentration profiles of drops during coalescence-induced drop dilution. Motivated by experimental observations, in the simulations we consider (i) advection within the moving plug, (ii) diffusion in the moving plug and parked droplets, (iii) fluid advection due to initiation of coalescence, and (iv) advection in the coalesced plug due to the continuous phase flowing through the gutters in noncircular microchannels. We find that the dilution process is dominated by diffusion, recirculation in the moving plug, and gutter-flow-induced advection, but is only weakly affected by coalescence-induced advection. We show that the control parameters regulating dilution can be divided into those influencing the duration of mass transfer (e.g., plug length and velocity) and those affecting the rate of mass transfer (e.g., diffusion and gutter-flow-induced advection). Finally, we demonstrate that our simulations are able to predict droplet concentration profiles in experiments. The results from this study will allow better design of drop dilution microfluidic devices. Furthermore, the identification of gutter-flow-induced advection as an alternative mass transfer mechanism in two-phase flows could potentially lead to more efficient means of oil recovery from droplets trapped in porous media.

We propose a recipe to calculate accurately the Nusselt number $\text{Nu}$ in turbulent Rayleigh-Bénard convection, using the measured total heat flux $q$ and known parameters of the fluid and convection cell. More precisely, we present a method to compute the conductive heat flux $\widehat{q}$, which is a normalization of $q$ in the definition of $\text{Nu}$, for conditions where the fluid parameters may vary strongly across the fluid layer. We show that in the Oberbeck-Boussinesq approximation and also when the thermal conductivity depends exclusively on the temperature, the value of $\widehat{q}$ is determined by simple explicit formulas. For a general non-Oberbeck-Boussinesq (NOB) case we propose an iterative procedure to compute $\widehat{q}$. Using our procedure, we critically analyze some already conducted and some hypothetical experiments and show how $\widehat{q}$ is influenced by the NOB effects.

We present an experimental study of the gravitational instability triggered by dissolution of carbon dioxide through a water-gas interface. We restrict the study to vertical parallelepipedic Hele-Shaw geometries, for which the thickness is smaller than the other dimensions. The partial pressure of carbon dioxide is quickly increased, leading to a denser layer of ${\mathrm{CO}}_2$-enriched water underneath the surface. This initially one-dimensional diffusive layer destabilizes through a convection-diffusion process. The concentration field of carbon dioxide, which is visualized by means of a pH-sensitive dye, shows a fingering pattern whose characteristics (wavelength and amplitude growth rate) are functions of the Rayleigh ($\text{Ra}$) and the Darcy ($\text{Da}$) numbers. At low Rayleigh numbers, the growth rate and the wave numbers are independent of the Rayleigh number and in excellent agreement with the classical results obtained numerically and theoretically in the Darcy regime. However, above a threshold of $\text{Ra}\sqrt{\text{Da}}$ of the order of 10, the growth rate and the wave number strongly decrease due to the Brinkman term associated with the viscous diffusion in the vertical and longitudinal directions. In this Darcy-Brinkman regime, the growth rate and the wave number depend only on the thickness-based Rayleigh number $\text{Ra}\sqrt{\text{Da}}$. The classical Rayleigh-Taylor theory including the Brinkman term has been extended to this diffusive gravitational instability and gives an excellent prediction of the growth rate over four decades of Rayleigh numbers. However, the Brinkman regime seems to be valid only until $\text{Ra}\sqrt{\text{Da}}=1000$. Above this threshold, the transverse velocity profile is no longer parabolic, which leads to an overestimation of the wave number by the theory.

We investigate the anisotropy in turbulent convection in a three-dimensional (3D) box using direct numerical simulation. We compute the anisotropic parameter $A=u_{\perp }^2/\left(2u_{\parallel }^2\right)$, where $u_{\perp }$ and $u_{\parallel }$ are the components of velocity perpendicular and parallel to the buoyancy direction, the shell and ring spectra, and shell-to-shell energy transfers. We observe that the flow is nearly isotropic for the Prandtl number $\mathrm{Pr}\approx 1$, but the anisotropy increases with the Prandtl number. For $\mathrm{Pr}=\infty ,A\approx 0.3$, anisotropy is not very significant even in extreme cases. We also observe that $u_{\parallel }$ feeds energy to $u_{\perp }$ via pressure. The computation of shell-to-shell energy transfers reveals that the energy transfer in turbulent convection is local and forward, similar to hydrodynamic turbulence. These results are consistent with the Kolmogorov's spectrum observed by Kumar et al. [Phys. Rev. E 90, 023016 (2014)] for turbulent convection.

We study the decay of high-Reynolds-number Taylor-Couette turbulence, i.e., the turbulent flow between two coaxial rotating cylinders. To do so, the rotation of the inner cylinder (${Re}_i=2\times {10}^6$, the outer cylinder is at rest) is stopped within 12 s, thus fully removing the energy input to the system. Using a combination of laser Doppler anemometry and particle image velocimetry measurements, six decay decades of the kinetic energy could be captured. First, in the absence of cylinder rotation, the flow-velocity during the decay does not develop any height dependence in contrast to the well-known Taylor vortex state. Second, the radial profile of the azimuthal velocity is found to be self-similar. Nonetheless, the decay of this wall-bounded inhomogeneous turbulent flow does not follow a strict power law as for decaying turbulent homogeneous isotropic flows, but it is faster, due to the strong viscous drag applied by the bounding walls. We theoretically describe the decay in a quantitative way by taking the effects of additional friction at the walls into account.

We present an experimental study of nonhomogeneous turbulence using a Rayleigh-Bénard convection cell. The fluid motion is forced by a temperature difference between two horizontal plates. Using Lagrangian tracking on a large volume we can capture part of the large-scale circulation. The velocity statistics are strongly affected by the inhomogeneous mean flow, but we recover the typical homogeneous isotropic turbulence statistics by removing the local average. We discuss and explain a Lagrangian unsteadiness which persists because of the large-scale circulation oscillations. Our Lagrangian approach is a way to study specificities of the convective roll motions in turbulent thermal convection. We propose a model based on the convolution between the large-scale circulation oscillations and the turbulent fluctuations to explain the shape of the velocity PDFs. However, the acceleration statistics are not affected by the mean flow.

Stability and pattern formation of a two-layer liquid system with large aspect ratio subjected to vertical harmonic oscillations is studied by means of an integrated boundary layer model. The lower layer rests on an oscillating solid substrate, the upper layer is separated by a deformable interface from the lower layer and bounded at the top with a second, free interface to the ambient passive air. The model is derived from the Navier-Stokes equations in long-wave approximation, including inertial terms. Applying a Floquet analysis, linear stability charts and dispersion relations are computed and compared with results from the full linearized Navier-Stokes equations and the long-wave approximation. Nonlinear Faraday patterns simultaneously occurring at the interface and at the film surface are studied by numerically solving the integrated boundary layer model in two and three spatial dimensions. For gravitationally stable two-layer films with a lighter fluid on top of the heavier fluid, we find squares, hexagons, quasiperiodic patterns with eightfold symmetry as well as localized states in the form of large scale depletion regions or finite depth holes, occurring at the interface and surface. For a Rayleigh-Taylor unstable combination (heavier fluid above the light one) we show that external vibration increases the lifetime of the film by delaying or completely suppressing the film rupture.

Multilayer film flow down an inclined plane in the presence of an insoluble surfactant is investigated with particular emphasis on determining flow stability and investigating the possibility of traveling-wave solutions. The investigation is conducted for two or three layers under conditions of Stokes flow and, separately, on the basis of a long-wave assumption. A normal mode linear stability analysis for Stokes flow shows that adding surfactant to one of the film surfaces can destabilize an otherwise stable flow configuration. For the long-wave system, periodic traveling-wave branches are detected and traced, revealing solutions with pulselike solitary waves on each film surface traveling in phase with each other, traveling waves with capillary ridge structures, and solutions with two of the film surfaces almost in contact. Time-periodic traveling-wave solutions are also found. The stability of the traveling waves is determined by solving initial-value problems and by computing eigenvalue spectra. Boundary element simulations for Stokes flow confirm the existence of traveling waves outside the long-wave regime.

In this study, large-eddy simulation combined with a turbine model is used to investigate the effect of vertical wind veer associated with the Coriolis force on the structure and evolution of wind turbine wakes. In order to isolate the Coriolis effect on the wake, two cases are considered. In the first case, atmospheric boundary-layer flow is driven by a geostrophic wind, including the effect of Earth's rotation and the Coriolis force. In the second case, the boundary-layer flow is unidirectional and is forced by an imposed pressure gradient. Both cases have the same mean horizontal velocity and turbulence intensity at the hub height. The simulation results show that the Coriolis force significantly affects the aerodynamics of the wake including the mean velocity deficit, turbulence statistics, and wake-meandering characteristics downwind of the turbine. In particular, when the flow is forced by a geostrophic wind, vertical wind veer causes a skewed spatial structure in the wake. Moreover, the presence of lateral wind shear, in addition to the vertical one, enhances the shear production of turbulent kinetic energy and the turbulent momentum flux. This leads to a larger flow entrainment and, thus, a faster wake recovery compared to the case forced by unidirectional pressure gradient. Consistent with this result, wake meandering is also stronger in both lateral and vertical directions in the case of geostrophic forcing compared to the case with pressure-gradient forcing.

The scale dependence of the statistical alignment tendencies of the eigenvectors of the strain-rate tensor ${\mathit{e}}_i$, with the vorticity vector $\mathbf{\omega }$, is examined in the self-preserving region of a planar turbulent mixing layer. Data from a direct numerical simulation are filtered at various length scales and the probability density functions of the magnitude of the alignment cosines between the two unit vectors $|{\mathit{e}}_i·\widehat{\mathbf{\omega }}|$ are examined. It is observed that the alignment tendencies are insensitive to the concurrent large-scale velocity fluctuations, but are quantitatively affected by the nature of the concurrent large-scale velocity-gradient fluctuations. It is confirmed that the small-scale (local) vorticity vector is preferentially aligned in parallel with the large-scale (background) extensive strain-rate eigenvector ${\mathit{e}}_1$, in contrast to the global tendency for $\mathbf{\omega }$ to be aligned in parallel with the intermediate strain-rate eigenvector [Hamlington et al., Phys. Fluids 20, 111703 (2008)]. When only data from regions of the flow that exhibit strong swirling are included, the so-called high-enstrophy worms, the alignment tendencies are exaggerated with respect to the global picture. These findings support the notion that the production of enstrophy, responsible for a net cascade of turbulent kinetic energy from large scales to small scales, is driven by vorticity stretching due to the preferential parallel alignment between $\mathbf{\omega }$ and nonlocal ${\mathit{e}}_1$ and that the strongly swirling worms are kinematically significant to this process.

Using a scaling analysis, we assess the impact of interfacial slip on the time required for the thin liquid film between two drops undergoing a head-on collision to drain to the critical thickness for rupture by van der Waals forces. Interfacial slip is included in our continuum development using a Navier slip boundary condition, with the slip coefficient modeled using previous theories [Helfand and Tagami, J. Chem. Phys. 57, 1812 (1972); Goveas and Fredrickson, Eur. Phys. J. B 2, 79 (1998)]. Slip decreases hydrodynamic resistance and speeds up film drainage. It renders the dependence of the drainage time on capillary number stronger in the spherical-film regime, but, interestingly, this dependence is altered only weakly in the dimpled-film regime. A subtle effect of slip is that it increases the range of capillary numbers in which the film remains predominantly spherical in shape during drainage (as opposed to being dimpled), leading to significantly faster drainage for these capillary numbers. Slip also leads to an increase in the critical capillary number beyond which coalescence is not possible in a head-collision.

The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the confines of a one-point model. In the original formulation [Kassinos and Reynolds, Center for Turbulence Research: Annual Research Briefs, 31–51 (1996)], the IPRM was developed in a Lagrangian setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is reformulated in an Eulerian framework, and evolution equations are developed for the marginal probability density functions (PDFs). Eulerian methods avoid the issues associated with statistical estimators used by Lagrangian approaches, such as slow convergence. A specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with Eulerian simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new Eulerian solution method are thoroughly analyzed. The sensitivity of the Eulerian simulations to parameters of the numerical scheme, such as the size of the time step and the shape parameter of the radial basis functions, is examined. A comparison between Eulerian and Lagrangian simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new Eulerian solution method and the original Lagrangian approach.

Liquid jets ultimately break up into droplets through an instability driven by surface tension. For highly viscous liquids, drops are connected by cylindrical liquid filaments whose radii linearly decrease with time, thus forming drops on a string structure. For a jet composed of two aqueous phases made in air by coaxial extrusion, we observe that, for moderate Weber and capillary numbers, drops slow down with different velocities, leading to drop coalescence. The origin of the traffic collision is linked to the spatial feature of the capillary instability where capillary and viscous forces acting on the drops evolve along the jet and ultimately amplify small velocity fluctuations. The emergence of such fluctuations is related to the unstable nature of the annular coflow of liquids having contrasting viscoelastic properties. From a practical point of view, flow and actuation conditions can be adjusted to inhibit drop collision and thus drop coalescence. These findings allow then the fabrication of monodisperse submillimeter core-shell objects based on the fragmentation of compound jets made of polymer solutions that find applications for three-dimensional cell culture.

We examine finite Reynolds number contributions to the inertial range solution of the third order structure functions $D_{3,0}$ and $D_{1,2}$ stemming from the unsteady and viscous terms. Under the assumption that the second order correlations $f$ and $g$ are self-similar under a coordinate change, we are able to rewrite the exact second order equations as a function of a normalized scale $\tilde{r}$ only. We close the resulting system of equations using a power law and an eddy-viscosity ansatz. If we further assume K41 scaling, we find the same Reynolds number dependence as previously in the literature. We proceed to extrapolate towards higher Reynolds numbers to examine the unsteady and viscous terms in more detail. We find that the intersection between the two terms, where their contribution to the solution of the structure function equations is relatively small, scales with the Taylor scale $\lambda$.

A mechanistic model, derived from kinetic theory, is developed to describe segregation in confined multicomponent suspensions such as blood. It incorporates the two key phenomena arising in these systems at low Reynolds number: hydrodynamic pair collisions and hydrodynamic migration. Two flow profiles are considered: simple shear flow (plane Couette flow) and plane Poiseuille flow. The theory begins by writing the evolution of the number density of each component in the suspension as a master equation with contributions from migration and collisions. By making judicious approximations for the collisions, this system of integrodifferential equations is reduced to a set of drift-diffusion equations. We focus attention on the case of a binary suspension with a deformable primary component that completely dominates the collision dynamics in the system and a trace component that has no effect on the primary. The model captures the phenomena of depletion layer formation and margination observed in confined multicomponent suspensions of deformable particles. The depletion layer thickness of the primary component is predicted to follow a master curve relating it in a specific way to confinement ratio and volume fraction. Results from various sources (experiments, detailed simulations, master equation solutions) with different parameters (flexibility of different components in the suspension, viscosity ratio, confinement, among others) collapse onto the same curve. For sufficiently dilute suspensions the analytical form predicted by the drift-diffusion theory for this curve is in excellent agreement with results from these other sources with only one adjustable parameter. In a binary suspension, several regimes of segregation arise, depending on the value of a “margination parameter” $\mathrm{M}$. Most importantly, in both Couette and Poiseuille flows there is a critical value of $\mathrm{M}$ below which a sharp “drainage transition” occurs: one component is completely depleted from the bulk flow to the vicinity of the walls. Direct simulations also exhibit this transition as the size or flexibility ratio of the components changes. Finally, some prior studies suggest a nonmonotonic dependence of margination propensity on volume fraction. We formulate a hypothesis regarding this observation. Theory predictions support the hypothesis, providing further insights into the mechanisms behind margination and segregation phenomena.

The interface between the fluid environment and the surface of the body in swimming fishes is critical for both physiological and hydrodynamic functions. The skin surface in most species of fishes is covered with bony scales or toothlike denticles (in sharks). Despite the apparent importance of fish surfaces for understanding aquatic locomotion and near-surface boundary layer flows, relatively little attention has been paid to either the nature of surface textures in fishes or possible hydrodynamic effects of variation in roughness around the body surface within an individual and among species. Fish surfaces are remarkably diverse and in many bony fishes scales can have an intricate surface texture with projections, ridges, and comblike extensions. Shark denticles (or scales) are toothlike and project out of the skin to form a complexly textured surface that interacts with free-stream flow. Manufacturing biomimetic foils with fishlike surfaces allows hydrodynamic testing and we emphasize here the importance of dynamic test conditions where the effect of surface textures is assessed under conditions of self-propulsion. We show that simple two-dimensional foils with patterned cuts do not perform as well as a smooth control surface, but that biomimetic shark skin foils can swim at higher self-propelled speeds than smooth controls. When the arrangement of denticles on the foil surface is altered, we find that a staggered-overlapped pattern outperforms other arrangements. Flexible foils made of real shark skin outperform sanded controls when foils are moved with a biologically realistic motion program. We suggest that focus on the mechanisms of drag reduction by fish surfaces has been too limiting and an additional role of fish surface textures may be to alter leading edge vortices and flow patterns on moving surfaces in a way that enhances thrust. Analysis of water flow over an artificial shark skin foil under both static and dynamic conditions shows that a shear layer develops over the denticle surface and we propose that there is limited flow under the expanded surfaces of shark denticles. The diversity of fish scale types and textures and the effect of these surfaces on boundary layer flows and fish locomotor energetics is a rich area for future investigation.

The response of a soap film to the continuous deformation of its wire boundary is considered, with particular attention to the topological transitions that can occur at critical stages of the deformation process. Two well-known examples that have been studied by both theory and experiment are the catenoid suspended between circular wires in parallel planes, and the Möbius-strip soap film spanning a wire that is twisted and folded back on itself. In this latter case, we have shown in previous publications that, when the wire is unfolded, the soap film undergoes a topological transition through a boundary singularity to a two-sided film, with a corresponding jump in the linking number between the axis of the wire and the Plateau boundary on its surface. Here, we review this particular aspect of the problem, and propose a simplified model experiment through which the slipping adjustment of a Plateau border on a solid surface may be investigated.

A classic result due to Taylor is that a weakly conducting drop bearing zero net charge placed in a uniform electric field adopts a prolate or oblate spheroidal shape, the flow and shape being axisymmetrically aligned with the applied field. Here I overview some intriguing symmetry-breaking instabilities occurring in strong applied dc fields: Quincke rotation resulting in drop steady tilt or tumbling, and pattern formation on the surface of a particle-coated drop.