Flow of foams is studied in a model porous medium, in a large range of capillary numbers Ca and relative gas flow rates $f_g$. From pressure measurements, we find that the effective viscosity is a decreasing power-law function of Ca, with the exponent ranging from $-1$ to $-0.75$. Direct observation reveals that the flow is heterogeneous. The fraction of preferential paths increases with both $f_g$ and Ca. In a straight channel of varying cross section, a bubble train behaves as a shear-thinning yield stress fluid. This feature accounts quantitatively for the effective viscosity in the micromodel.

Particles suspended in a fluid exert feedback forces that can significantly impact the flow, altering the turbulent drag and velocity fluctuations. We study flow modulation induced by small spherical particles heavier than the carrier fluid in the framework of an Eulerian two-way coupled model, where particles are represented by a continuum density transported by a compressible velocity field, exchanging momentum with the fluid phase. We implement the model in direct numerical simulations of the turbulent Kolmogorov flow, a simplified setting allowing for studying the momentum balance and the turbulent drag in the absence of boundaries. We show that the amplitude of the mean flow and the turbulence intensity are reduced by increasing particle mass loading with the consequent enhancement of the friction coefficient. Surprisingly, turbulence suppression is stronger for particles of smaller inertia. We understand such a result by mapping the equations for dusty flow, in the limit of vanishing inertia, to a Newtonian flow with an effective forcing reduced by the increase in fluid density due to the presence of particles. We also discuss the negative feedback produced by turbophoresis, which mitigates the effects of particles, especially with larger inertia, on the turbulent flow.

Periodically driven flows are known to generate nonzero, time-averaged fluxes of heat or solute species, due to the interactions of out-of-phase velocity and temperature/concentration fields, respectively. Herein, we investigate such transport (a form of the well-known Taylor-Aris dispersion) in the gap between two parallel plates, one of which oscillates vertically, generating a time-periodic squeeze flow of either a Newtonian or a Maxwell fluid. Using the method of multiple time-scale homogenization, the mass/heat balance equation describing transport in this flow is reduced to a one-dimensional advection-diffusion-reaction equation. This result indicates three effective mechanisms in the mass/heat transfer in the system: an effective diffusion that spreads mass/heat along the concentration/temperature gradient, an effective advective flux, and an effective reaction that releases or absorbs mass/heat—in the time-averaged frame. Our results demonstrate that there exist resonant modes under which the velocity peaks when the dimensionless plate oscillation frequency (embodied by the Womersley number, the ratio of the transient inertia to viscous forces) approaches specific values. As a result, transport in this flow is significantly influenced by the dimensionless frequency. On the one hand, the effective, time-averaged dispersion coefficient is always larger than the molecular diffusivity and is sharply enhanced near resonance. The interaction between the fluid elasticity and the oscillatory forcing enhances the efficiency of transport in the system. On the other hand, the identified effective advection and reaction mechanisms may transport mass/heat from regions of high concentration/temperature to those of low concentration/temperature, or vice versa, depending on the value of the dimensionless frequency. Ultimately, it is shown that the oscillatory squeeze flow can either enhance or diminish transport, depending on the interplay of these three effective (homogenized) mechanisms.

In this article, we provide a methodology to reconstruct high Reynolds number turbulent mean-flows from few time-averaged measurements. A turbulent flow over a backward-facing step at $\text{Re}=28275$ is considered to illustrate the potential of the approach. The data-assimilation procedure, based on a variational approach, consists in correcting a given baseline model by tuning space-dependent source terms such that the corresponding solution matches available measurements (obtained here from direct-numerical simulations). The baseline model chosen here consists in Reynolds-averaged Navier-Stokes equations closed with the turbulence Spalart-Allmaras model. We investigate two possible tuning functions: a source term in the momentum equations, which is able to compensate for the deficiencies in the modeling of the Reynolds stresses by the Boussinesq approximation and a source term in the turbulence equation, which modifies the balance between the eddy-viscosity production and dissipation. The quality of the mean-flow reconstruction strongly depends on the baseline model and on the quantity of measurements. In the case of many measurements, very accurate reconstructions of the mean-flow are obtained with the model corrected by the source term in the momentum equations, while the reconstruction is more approximate when tuning the source term in the turbulence model. In the case of few measurements, this “rigidity” of the corrected turbulence model is favorably used and allows the best mean-flow reconstruction. The flexibility/rigidity of a model is further discussed in the light of a singular-value decomposition of the linear input/output operator between source term and measurements.

The flame length of a plume in incompressible cross-flow is analyzed and the results are compared with those obtained in a chemically reacting water tunnel experiment. It is argued that the axial vortex pair in the flow arises from the plume momentum normal to the free stream, the momentum flux being equivalent to the impulse from the buoyant force.

In recent decades, jet impingement cooling has gained significant attention due to its ability to remove large thermal loads from local heating zones. This study demonstrates the performance of pulsed jet impingement cooling on a Ti-coated glass window. Infrared (IR) thermography data are analyzed to generate heat transfer coefficient (HTC) maps for a range of heat fluxes ($q{}^{\prime \prime }\approx 20$–60 W/${\mathrm{cm}}^2$) and jet pulsation frequencies ($f_p\approx$ 7–25 Hz). Heat transfer coefficients are observed to scale as $h\propto \sqrt{2f_p}$ with local maximum values at the center of the jet stagnation zone. For reference, $h^{\max }\approx 15\mathrm{kW}/{\mathrm{m}}^2\mathrm{K}$ is found for $q{}^{\prime \prime }\approx$ 60 $\mathrm{W}/{\mathrm{cm}}^2$ and $f_p\approx 25$ Hz. Moreover, a jet pulsation frequency of $f_p\approx 15$ Hz matches well with both the bubble release rate and dry-out occurrence rate within 50 and 80 ms, respectively, at $q{}^{\prime \prime }=60 \mathrm{W}/{\mathrm{cm}}^2$. At heat fluxes $>40$ $\mathrm{W}/{\mathrm{cm}}^2$, boiling regimes were captured in terms of cyclic events of bubble growth, bubble collapse, dry-out, partial rewetting, and full rewetting. Finally, a theoretical model is proposed based on both the HTC expected for a steady jet and HTC augmentation due instantaneous heat flux matching for a pulsed jet at the jet-wall interface. The correlation between experiments and theory are reasonable, yet there are still unresolved complexities associated with thermofluid instabilities, decoupling the transient latent heat and sensible heat transfer mechanisms, and first-principles modeling of the spatiotemporal surface temperature and flow-field oscillations induced by a pulsed jet.

We experimentally inject silicone oil into the mixture of oil and noncolloidal particles inside a Hele-Shaw cell, to investigate the connection between miscible fingering and the interfacial structure that develops inside the thin gap. Previous studies with pure fluids have demonstrated that the onset of miscible fingering coincides with the transition from a smooth tonguelike structure to a sharp front between invading and defending fluids inside the gap. Our current experiments with suspensions reveal the same general behavior at the onset of miscible fingering, which we capture qualitatively using a lubrication model. However, distinct from the pure liquid counterpart, we observe changes in the interfacial structures inside the gap as the ratio of the gap thickness to particle diameter is systematically varied. We demonstrate that the particle dynamics inside the thin gap may alter interfacial structures even within the continuum limit, which lead to changes in morphologies of miscible fingering. The results of our study suggest a potential use of the wall confinement to control hydrodynamic instabilities in suspensions.

We present an experimental study of a two-dimensional liquid foam, composed of a confined monolayer of bubbles, forced to flow within a model porous medium that mimics an inhomogeneous open fracture. It consists of a Hele-Shaw cell with a single localized constriction-like defect that reduces locally its gap and thus its permeability. Taking advantage of the possibility to directly visualize and follow the bubbles, we compute the bubble velocity field by image correlation analysis, as well as the bubble deformation field, through eccentricity measurements obtained by fitting each bubble with an ellipse. The defect acting as a permeable obstacle can strongly disturb the foam flow; we investigate here the influence of its geometry (height, size, and shape) on the average steady-state flow of foams of various liquid content, and specifically the motion and deformation of their elementary components, the bubbles. In the frame of the flowing foam, we can observe a recirculation around the obstacle, characterized by a multipolar velocity field. Its complex structure displays a strong fore-aft asymmetry, with an extended region downstream the constriction, where the foam velocity can be much larger than the imposed driving one. This overshoot was already revealed for nonpermeable obstacles, but here we show that its extent and intensity are associated to the bubble deformation and depend strongly and nontrivially on both the geometry of the constriction as well as the liquid fraction of the foam.

Rotating spiral patterns in Rayleigh-Bénard convection are known to induce azimuthal flows, which raises the question of how different neighboring spirals interact with each other in spiral chaos and the role of hydrodynamics in this regime. Far from the core, we show that spiral rotations lead to an azimuthal body force that is irrotational and of magnitude proportional to the topological index of the spiral and its angular frequency. The force, although irrotational, cannot be included in the pressure field as it would lead to a nonphysical multivalued pressure. We calculate the asymptotic dependence of the resulting flow and show that it leads to a logarithmic dependence of the azimuthal velocity on distance $r$ away from the spiral core in the limit of negligible damping coefficient. This solution dampens to approximately $1/r$ when accounting for no-slip boundary conditions for the convection cell's plate. This flow component can provide additional hydrodynamic interactions among spirals including those observed in spiral defect chaos. We show that the analytic prediction for the azimuthal velocity agrees with numerical results obtained from both two-dimensional generalized Swift-Hohenberg and three-dimensional Boussinesq models and find that the velocity field is affected by the size and charges of neighboring spirals. Numerically, we identify a correlation between the appearance of spiral defect chaos and the balancing between the mean-flow advection and the diffusive dynamics related to roll unwinding.

We have used high-speed video and interferometry to investigate the impact, spreading, and eventual contraction of superfluid ${}^4\mathrm{He}$ drops on a sapphire substrate in a saturated atmosphere of helium vapor. We find that the short-term kinetic spreading of superfluid drops (time $t<10$ ms) is qualitatively similar to both normal helium and conventional fluids at room temperature. In contrast, the contraction phase of the superfluid drops is highly unusual. Superfluid drops survive for only a few seconds on the substrate due to superflow out of the drop into the surrounding helium film. The drop lifetime is strongly dependent on temperature and diverges at the superfluid transition temperature $T_{\lambda }\sim 2.17$ K. The contracting drops undergo a geometry-dependent two-phase contraction, which includes a toroidal phase where the radius decreases linearly in time and subsequently a spherical cap phase where the radius decreases with the square root of time. The receding contact angle is temperature dependent and becomes small near $T_{\lambda }$. We also observe that the superfluid outflow causes surprising edge effects, including the emergence of satellite droplets on the perimeter of the expanding drop, as well as ragged and frayed drop edges at lower temperatures.

We report that an electro-osmotic instability of concentration enrichment in curved geometries for an aqueous electrolyte, as opposed to the well-known one, is initiated exclusively at the enriched interface (anode), rather than at the depleted one (cathode). For this instability, the limitation of an unrealistically high material Peclet number in planar geometry is eliminated by the strong electric field arising from the line charge singularity. In a model setup of concentric circular electrodes, we show by stability analysis, numerical simulation, and experimental visualization that instability occurs at the inner anode, below a critical radius of curvature. The stability criterion is also formulated in terms of a critical electric field and extended to arbitrary (two-dimensional) geometries by conformal mapping. This discovery suggests that transport may be enhanced in processes limited by salt enrichment, such as reverse osmosis, by triggering this instability with needlelike electrodes.

Fluid flows induced by a flagellated bacterial swimmer are often modeled as a simple force dipole, valid in the far field. Such representations neglect the inherent rotation of these bacteria as they swim, driven by a spinning helical flagellum or fascicle. Here, we present a refined swimmer representation that makes use of regularized singularities, retaining simplicity while capturing details of the complex flow field near the swimmer that have previously been absent from basic models. We illustrate the significance of this representation via a study of bacterial predator-prey dynamics, highlighting the importance of detailed hydrodynamics in models of bacterial interactions and bacterial active matter.

Spiroplasma is a small helical bacterium that swims and performs chemotaxis in a nonconventional way. Equipped with a flexible flat ribbon cytoskeleton, Spiroplasma deforms its body into a helix that periodically changes its chirality. The helical transformation produces a kink that propagates along the cell body and propels the microorganism in the opposite direction. Based on experimental observations, we develop a hydrodynamic model to describe Spiroplasma motility. We obtain expressions for the total linear and angular displacements of the cell body per swimming stroke. We show mathematically that the cell body does not reorient at the end of one period, which allows us to define an effective swimming speed, $v_s$. We then use $v_s$ to calculate the energy dissipated in one stroke, $\dot{W}$, and to define a hydrodynamic efficiency, $\eta ={\dot{W}}_0/\dot{W}$, where ${\dot{W}}_0$ is the power spent by a straight filament moving at the same speed $v_s$. We show that the helical shape of the cytoskeleton that maximizes both $v_s$ and $\eta$ are helices of pitch angles $\varphi$ close to that of Spiroplasma, $\varphi \simeq {35}^{\circ }$, in agreement with experimental observations and with previous numerical simulations.

Respiratory-type flows facilitate the exchange of fluid through an orifice in many natural and engineered environments. The external flow dynamics for an idealized respiratory-type flow, consisting of periodic inhalation and exhalation of a fixed tidal volume of fluid through a circular orifice at the end of a tube, are investigated. In both numerical and experimental investigations, inertial effects produce asymmetric inhalant and exhalant flow structures, resulting in a dynamic exchange of fluid volume across the orifice. A Lagrangian approach is used to quantify the reinhalation ratio $r_I$, defined as the amount of exhaled fluid that is subsequently reinhaled. Results show that these flow structure asymmetries and hence $r_I$ are strongly sensitive to Reynolds number, and, to a lesser extent, Womersley number or Strouhal number. At low Reynolds number, where viscous effects dominate, we observe flow kinematics similar to an ideal source or sink and the exchange ratio asymptotes to an upper limit. As the inertial effects become more dominant with increasing Reynolds number, we instead observe jetlike flow structures and a rapid decrease in $r_I$. In the context of biological sensory and metabolic processes, these results suggest organisms can optimize the exchange of fluid with surrounding environment by modulating the asymmetries in the flow structures arising during olfactory and respiratory activity.

Numerical simulations of a drop crossing a plane liquid-liquid interface in a centrifugal field are performed using the level-set method. The objective is to characterize the hydrodynamical parameters controlling the coating volume of the droplet, which results from the rupture of the liquid column of the lighter phase entrained by the droplet during the crossing of the interface in the tailing regime. The numerical method is validated first in two-phase flow simulations of a drop rising in a stagnant liquid and then in three-phase flow configurations to reproduce the theoretical critical condition for a drop to cross an interface in static conditions (without initial velocity). Then, in inertial conditions, extensive simulations of crossing droplets are performed in a wide range of flow parameters and phase properties for two types of drop: solidlike droplets (mimicking rigid particles) and deformable drops. The crossing criterion is found to remain very close to that given by the theory in static conditions, for either a spherical or a deformed droplet. For each case studied, the crossing time, the maximum length of the column of liquid pulled by the droplet, and the volume encapsulating the drop after crossing are computed and scaled as a function of an inertia parameter, which is the ratio $F^{*}$ between the inertial stresses pushing on the interface, defined from the minimum drop velocity reached during crossing as the characteristic velocity, and the opposite stress pulling back the entrained column towards the interface. The maximal column length increases with $F^{*}$ (when rescaled by the minimal inertial required for crossing) under two distinct growth rates according to the flow regime in the column. For solidlike drops, the final coating volume is a unique function of $F^{*}$ and grows with $F^{*}$ at large inertia. In the case of deformable droplets, the coating volume evolution can also be well predicted by $F^{*}$ but corrected by the drop-to-film viscosity ratio, which strongly affects the drainage rate of the film along the drop surface during the encapsulation process.

We study the occurrence of a magnetoelastic fingering instability when a viscous ferrofluid is displaced by a nonmagnetic fluid of negligible viscosity in a horizontal, rectangular Hele-Shaw cell. Interfacial disturbances result from the interplay of viscous, elastic, and magnetic effects when the system is subjected to a uniform magnetic field, applied in the plane of the cell, and perpendicular to the initially flat interface separating the fluids. We approach the problem perturbatively through a third-order mode-coupling theory and investigate the development of interfacial patterns at early nonlinear stages of the flow. A representative collection of possible magnetoelastic fingering structures is presented which differ significantly from the classical Saffman-Taylor fingers that arise in such a rectangular cell setup in the absence of magnetic and elastic effects.

We report on the stability of thin liquid films overflowing single microstructures with sharp corners. The microstructures were of rectangular and triangular shape. Their heights and widths were 0.25, 0.5, and 0.75 times the Nusselt film thickness. To observe steady, wavy, and very unstable films we performed simulations with Reynolds numbers ranging from 10 to 70. The dynamics of the liquid film and the overflowing gas phase were described by the coupling between the Cahn-Hilliard and the Navier-Stokes equations. The resulting model forms a very tightly coupled and nonlinear system of equations. Therefore we carefully selected the solution strategy to enable efficient and accurate large-scale simulations. Our results showed that the formation of waves was shifted to higher Reynolds numbers compared to the film on a smooth surface. If waves were finally formed, the microstructures led to irregular waves. Our results indicate a great influence of the microstructure's shape and dimension on the stability of the overflowing liquid film.

Lagrangian stochastic models are widely used to predict and analyze turbulent dispersion in complex environments, such as in various terrestrial and marine canopy flows. However, due to a lack of empirical data, it is still not understood how particular features of highly inhomogeneous canopy flows affect the Lagrangian statistics. In this work, we study Lagrangian short-time statistics by analyzing empirical Lagrangian trajectories in subvolumes of space that are small in comparison with the canopy height. For the analysis we used 3D Lagrangian trajectories measured in a dense canopy flow model in a wind-tunnel, using an extended version of real-time 3D particle tracking velocimetry. One of our key results is that the random turbulent fluctuations due to the intense dissipation were more dominant than the flow's inhomogeneity in affecting the short-time Lagrangian statistics. This amounts to a so-called quasihomogeneous regime of Lagrangian statistics at small scales. Using the Lagrangian dataset, we calculate the Lagrangian autocorrelation function and the second-order Lagrangian structure-function and extract associated parameters, namely, a Lagrangian velocity decorrelation timescale, $T_i$, and the Kolmogorov constant, $C_0$. We demonstrate that in the quasihomogeneous regime, both these functions are well represented using a second-order Lagrangian stochastic model that was designed for homogeneous flows. Furthermore, we show that the spatial variations of the Lagrangian separation of scales, $T_i/{\tau }_{\eta }$, and the Kolmogorov constant, $C_0$, cannot be explained by the variation of the Reynolds number, ${\text{Re}}_{\lambda }$, in space, and that $T_i/{\tau }_{\eta }$ was small as compared with homogeneous turbulence predictions at similar ${\text{Re}}_{\lambda }$. We thus hypothesize that these characteristics occurred due to the injection of kinetic energy at small scales due to the so-called “wake-production” process, and we show empirical results supporting our hypothesis. These findings shed light on key features of Lagrangian statistics in flows with intense dissipation, and have direct implications for modeling short term dispersion in such complex environments.

A new scaling is developed for the turbulent kinetic energy (TKE) and its dissipation in a turbulent wall-bounded flow. In the traditional dimensional analysis of wall-bounded turbulence, the control parameters for the near-wall region are the kinematic viscosity $\nu$ and the wall shear stress, resulting in the friction velocity $u_{\tau }$ as the characteristic velocity scale and the viscous length scale $\nu /u_{\tau }$ as the characteristic length scale. Although the mean streamwise velocity scales well with the friction velocity, the TKE, and, in particular, the TKE dissipation does not scale with the friction velocity. In the present paper, a new dimensional analysis is performed to identify a proper scaling for the TKE and its dissipation. The control parameters in the near-wall region are the kinematic viscosity and the TKE dissipation at the wall ${\epsilon }_{k,\mathrm{w}}$. The new inner velocity scale for the TKE budget equation is the Kolmogorov wall velocity $u_{\epsilon }\stackrel{def}{=}{\left(\nu {\epsilon }_{k,\mathrm{w}}\right)}^{1/4}$, and the proper length scale is the Kolmogorov wall length $\nu /u_{\epsilon }$. The profiles of the TKE and its dissipation in the near-wall region collapse well under the new scaling, and the TKE profiles in the outer layer also scale well with the new scaling. However, the TKE peak value $k_{\max }$ does not scale with the Kolmogorov wall velocity $u_{\epsilon }$ or the friction velocity $u_{\tau }$ but with a mixed scale. One mixed scale is $u_{\tau }{U}_{\infty }$ first proposed by DeGraaff and Eaton [J. Fluid Mech. 422, 319 (2000)], where $U_{\infty }$ is the mean velocity in the free stream or at the channel centerline. A new mixed scale developed in this paper for $k_{\max }$ is $\nu {\epsilon }_{k,\mathrm{w}}/u_{\tau }^2$, and justification is provided by adding a control parameter to the new dimensional analysis.

We perform a resolvent analysis to examine the perturbation dynamics over the laminar separation bubble (LSB) that forms near the leading edge of a NACA 0012 airfoil at a chord-based Reynolds number (Re) of 500 000 and an angle of attack of 8 degrees. While we focus on the LSB residing over $6\%$ of the chord length, the resolvent operator is constructed about the global mean flow over the airfoil, avoiding numerical issues arising from domain truncation. Moreover, randomized singular value decomposition is adopted in the present analysis to relieve the computational cost associated with the high-Re global base flow. To examine the local physics over the LSB, we consider the use of exponential discounting to limit the time horizon that allows for the instability to develop with respect to the base flow. With discounting, the gain distribution over frequency accurately captures the spectral content over the LSB obtained from flow simulation. The peak-gain frequency also agrees with previous flow control results on suppressing dynamic stall over a pitching airfoil. According to the gain distribution and the modal structures, we conclude that the dominant energy-amplification mechanism is the Kelvin-Helmholtz instability. In addition to discounting, we also examine the use of spatial windows for both the forcing and response. From the response-windowed analysis, we find that the LSB serves the main role of energy amplifier, with the amplification saturating at the reattachment point. The input window imposes the constraint of surface forcing, and the results show that the optimal actuator location is slightly upstream of the separation point. The surface-forcing mode also suggests the optimal momentum forcing in the surface-tangent direction, with strong unidirectionality that is ideal for synthetic-jet-type actuators. This study demonstrates the strength of randomized resolvent analysis in tackling high-Reynolds-number base flows, and it calls attention to the care needed for base-flow instabilities. The physical insights provided by the resolvent analysis can also support flow control studies that target the LSB for suppressing flow separation or dynamic stall.