Recent experimental data on a fuel-cell-like system revealed insights into the fluid flow in both free and porous media. A computational model is used to investigate the momentum and species transport in such a system, solved using the finite element method. The model consists of a stationary, isothermal, diluted species transport in free and porous media flow. The momentum transport is treated using different formulations, namely, Stokes-Darcy, Darcy-Brinkman, and hybrid Stokes-Brinkman formulations. The species transport is given by the advection equation for a reactant diluted in air. The formulations are compared to each other and to the available experimental data, where it is concluded that the Darcy-Brinkman formulation reproduces the data appropriately. The validated model is used to investigate the contribution of convection in reactant transport in porous media of fuel cells. Convective transport provides a major contribution to reactant distribution in the so-called diffusion media. For a serpentine channel and flow with $\mathrm{Re}=260\text{–}590$, convection accounts for 29–58% of total reactant transport to the catalyst layer.

We investigate the dynamical behavior of deformable filaments experimentally using a tunable model system consisting of linked paramagnetic colloidal particles, where the persistence length $l_p$, the contour length $l_c$, and the strength and frequency of the external driving force are controlled. We find that upon forcing by an external magnetic field, a variety of structural and conformational regimes exist. Depending on the competition of forces and torques on the chain, we see classic rigid rotator behavior, as well as dynamically rich wagging, coiling, and folding behavior. Through a combination of experiments, computational models, and theoretical calculations, we are able to observe, classify, and predict these dynamics as a function of the dimensionless Mason and magnetoelastic numbers.

In this work we present numerical simulations of ${10}^5$ sub-Kolmogorov deformable bubbles dispersed in Taylor-Couette flow (a wall-bounded shear system) with rotating inner cylinder and outer cylinder at rest. We study the effect of deformability of the bubbles on the overall drag induced by the carrier fluid in the two-phase system. We find that an increase in deformability of the bubbles results in enhanced drag reduction due to a more pronounced accumulation of the deformed bubbles near the driving inner wall. This preferential accumulation is induced by an increase in the resistance to the motion of the bubbles in the wall-normal direction. The increased resistance is linked to the strong deformation of the bubbles near the wall which makes them prolate (stretched along one axis) and orient along the streamwise direction. A larger concentration of the bubbles near the driving wall implies that they are more effective in weakening the plume ejections which results in stronger drag reduction effects. These simulations which are practically impossible with fully resolved techniques are made possible by coupling a subgrid deformation model with two-way coupled Euler-Lagrangian tracking of sub-Kolmogorov bubbles dispersed in a turbulent flow field which is solved through direct numerical simulations. The bubbles are considered to be ellipsoidal in shape and their deformation is governed by an evolution equation which depends on the local flow conditions and their surface tension.

Viscous fingering is a flow instability that is induced at the displacement front when a less-viscous fluid (LVF) displaces a more-viscous fluid (MVF). Because of the opaque nature of porous media, most experimental investigations of the structure of viscous fingering and its development in time have been limited to two-dimensional porous media or Hele–Shaw cells. In this study, we investigate the three-dimensional characteristics of viscous fingering in porous media using a microfocused x-ray computer tomography (CT) scanner. Similar to two-dimensional experiments, characteristic events such as tip-splitting, shielding, and coalescence were observed in three-dimensional viscous fingering as well. With an increase in the Péclet number at a fixed viscosity ratio, $M$, the fingers appearing on the interface tend to be fine; however, the locations of the tips of the fingers remain the same for the same injected volume of the LVF. The finger extensions increase in proportion to ln $M$, and the number of fingers emerging at the initial interface increases with $M$. This fact agrees qualitatively with linear stability analyses. Within the fingers, the local concentration of NaI, which is needed for the x-ray CT scanner, linearly decreases, whereas it sharply decreases at the tips of the fingers. A locally high Péclet number as well as unsteady motions in lateral directions may enhance the dispersion at the tips of the fingers. As the viscosity ratio increases, the efficiency of each sweep monotonically decreases and reaches an asymptotic state; in addition, the degree of mixing increases with the viscosity ratio. For high flow rates, the asymptotic value of the sweep efficiency is low for high viscosity ratios, while there is no clear dependence of the asymptotic value on the Péclet number.

In this work, Schlieren measurements are presented for the wake of an air bubble sliding under a heated, inclined surface in quiescent water to provide new insights into the intricate sliding bubble wake structure and the associated convective cooling process. This is a two-phase flow configuration that is pertinent to thermal management solutions, where the fundamental flow physics have yet to be fully described. In this work, we present an experimental apparatus that enables high-quality Schlieren images for different bubble sizes and measurement planes. By combining these visualizations with an advanced bubble tracking technique, we can simultaneously quantify the symbiotic relationship that exists between the sliding bubble dynamics and its associated wake. An unstable, dynamic wake structure is revealed, consisting of multiple hairpin-shaped vortex structures interacting within the macroscopic area affected by the bubble. As vorticity is generated in the near wake, the bubble shape is observed to recoil and rebound. This also occurs normal to the surface and is particularly noticeable for larger bubble sizes, with a periodic ejection of material from the near wake corresponding to significant shape changes. These findings, along with their implications from a thermal management perspective, provide information on the rich dynamics of this natural flow that cannot be obtained using alternate experimental techniques.

Continuum models that describe two-phase flow of immiscible fluids in porous media often treat momentum exchange between the two phases by simply generalizing the single-phase Darcy law and introducing saturation-dependent permeabilities. Here we study models of creeping flows that include an explicit coupling between both phases via the addition of cross terms in the generalized Darcy law. Using an extension of the Buckley-Leverett theory, we analyze the impact of these cross terms on saturation profiles and pressure drops for different couples of fluids and closure relations of the effective parameters. We show that these cross terms in the macroscale models may significantly impact the flow compared to results obtained with the generalized Darcy laws without cross terms. Analytical solutions, validated against experimental data, suggest that the effect of this coupling on the dynamics of saturation fronts and the steady-state profiles is very sensitive to gravitational effects, the ratio of viscosity between the two phases, and the permeability. Our results indicate that the effects of momentum exchange on two-phase flow may increase with the permeability of the porous medium when the influence of the fluid-fluid interfaces become similar to that of the solid-fluid interfaces.

Turbulent boundary layers with $\mathrm{R}{\mathrm{e}}_{\tau }=2500$ were perturbed by an array of cylinders projecting outward from the wall, and the flow organization downstream was investigated at multiple measurement heights in the logarithmic region. Two array heights were considered: $H=0.2\delta$, extending through the log region and $H=\delta$, extending to the top of the boundary layer. Results from instantaneous PIV in wall-parallel planes and a vortex packet identification algorithm clearly showed a bottom-up mechanism for packet recovery downstream of the $H=\delta$ array, even though streamwise velocity statistics remained strongly perturbed. In contrast, some indications of top-down recovery were observed for the flow perturbed by the shorter $H=0.2\delta$ $\left(H^{+}=500\right)$ array. In this case, however, packet structures closer to the wall at $z^{+}=125$ remained altered beyond the end of the measurement domain 7δ downstream of the cylinders even though streamwise velocity statistics relaxed nearly to the unperturbed values.

The rheology of dense granular flows is often seen as dependent on the nature of the energy landscape defining the modes of energy relaxation under shear. We investigate numerically the transition from soft to rigid particles, varying $S$, their stiffness compared to the confining pressure over three decades, and the inertial number $I$ of the shear flow over five decades. We show that the rheological constitutive relation, characterized by a dynamical friction coefficient of the form $\mu \left(I\right)={\mu }_c+a{I}^{\alpha }$, is marginally affected by the particle stiffness, with constitutive parameters being essentially dependent on the interparticle friction. Similarly, the distribution of local shear rate mostly depends on the inertial number $I$, which shows that the characteristic time scale of plastic events is primarily controlled by the confining pressure and is insensitive to $S$. By contrast, the form under which energy is stored between these events and also the contact network properties such as the coordination number and the distance to isostaticity are strongly affected by stiffness, allowing us to discuss the different regimes in the $(S,I)$ phase space.

We present the results of an experimental study of the standing waves produced on the surface of a vertically shaken fluid bath just above the Faraday threshold, when a row of equally spaced pillars protrudes from the surface. When the pillar spacing is twice the Faraday wavelength, the resulting wave field is marked by images of the pillars projected at integer multiples of a fixed distance from the row. This projection effect is shown to be analogous to the well-known Talbot or self-imaging effect in optics, and a Faraday-Talbot length is defined that rationalizes the location of the images. A simple model of point sources emitting circular waves captures the observed patterns. We demonstrate that the images may serve as traps for bouncing and walking droplets.

The settling velocity of inertial particles falling in homogeneous turbulence is investigated by making use of direct numerical simulation (DNS) at moderate Reynolds number that include momentum exchange between both phases (two-way coupling approach). Effects of particle volume fraction, particle inertia, and gravity are presented for flow and particle parameters similar to the experiments of Aliseda et al. [J. Fluid Mech. 468, 77 (2002)]. A good agreement is obtained between the DNS and the experiments for the settling velocity statistics, when overall averaged, but as well when conditioned on the local particle concentration. Both DNS and experiments show that the settling velocity further increases with increasing volume fraction and local concentration. At the considered particle loading the effects of two-way coupling is negligible on the mean statistics of turbulence. Nevertheless, the DNS results show that fluid quantities are locally altered by the particles. In particular, the conditional average on the local particle concentration of the slip velocity shows that the main contribution to the settling enhancement results from the increase of the fluid velocity surrounding the particles along the gravitational direction induced by the collective particle back-reaction force. Particles and the surrounding fluid are observed to fall together, which in turn results in an amplification of the sampling of particles in the downward fluid motion. Effects of two-way coupling on preferential concentration are also reported. Increase of both volume fraction and gravity is shown to lower preferential concentration of small inertia particles while a reverse tendency is observed for large inertia particles. This behavior is found to be related to an attenuation of the centrifuge effects and to an increase of particle accumulation along gravity direction, as particle loading and gravity become large.

A fundamental problem in heat transfer is the convective cooling of the heated walls of a channel. We find steady two-dimensional (2D) flows that maximize the heat removed from fixed-temperature walls for a given rate of energy used to drive the flow, ${\text{Pe}}^2$ (Pe is the Peclet number, a dimensionless flow speed). For parabolic (Poiseuille) flow, the heat transfer scales as ${\text{Pe}}^{1/3}$. Starting from Poiseuille flow, we compute a sequence of optima using Newton's method with continuation. Computed optimal flows are found to be approximately unidirectional and nearly uniform outside of sharp boundary layers at the channel walls. A linear approximation near Poiseuille flow shows how the thermal boundary layer generates a boundary layer in the optimal flow. We are thus led to compute optimal unidirectional flows with boundary layers, for which the heat transfer scales as ${\text{Pe}}^{2/5}$, an improvement over the ${\text{Pe}}^{1/3}$ Poiseuille flow scaling. The optimal flows have viscous dissipation concentrated in boundary layers of thickness $\sim {\text{Pe}}^{-2/5}$ at the channel walls, and have a uniform velocity $\sim {\text{Pe}}^{4/5}$ outside the boundary layers. We explain the scalings using physical and mathematical arguments. We also show that with channels of aspect ratio (length/height) $L$, the outer flow speed scales as $L^{-1/5}$ and the boundary layer thickness scales as $L^{3/5}$ in the unidirectional approximation. At the Reynolds numbers near the turbulent transition for 2D Poiseuille flow in air, we find a 60% increase in heat transferred over that of Poiseuille flow.

We present an explicit analysis of wave-resonant instability of swirling flows inside fast rotating cylindrical containers. The linear dynamics are decomposed into the interaction between the horizontal inner centrifugal edge waves and the outer vertical gravity waves with the aim of understanding the dynamics of the centrifugal waves. We show how the far field velocity induced respectively by the centrifugal and the gravity waves affect each other's propagation rates and amplitude growth. We follow this with an analysis of the instability in terms of a four-wave interaction, two centrifugal and two gravity ones, and explain why the resonant instability can be obtained only between a pair of two counterpropagating waves, one centrifugal and one gravity. Furthermore, a near resonant regime which does not yield instability is shown to result from a phase-locking configuration between a pair of a counterpropagating centrifugal wave and a propropagating gravity one, where the interaction affects the waves' propagation rates but not the amplitude growth.

Many unanswered questions remain pertaining to droplet dynamics during impact on vibrating surfaces. Using optical high-speed imaging, we investigate the impact dynamics of macroscopic water droplets $\left(\approx 2.5\mathrm{mm}\right)$ on rigid and elastic superhydrophobic surfaces vibrating at 60–320 Hz and amplitudes of 0.2–2.7 mm. Specifically, we study the influence of the frequency, amplitude, rigidity, and substrate phase at the moment of impact on the contact time of impacting droplets. We show that a critical impact phase exists at which the contact time transitions from a minimum to a maximum greater than the theoretical contact time on a rigid, nonvibrating superhydrophobic surface. For impact at phases higher than the critical phase, contact times decrease until reaching a minimum of half the theoretical contact time just before the critical phase. The frequency of oscillation determines the phase-dependent variability of droplet contact times at different impact phases: higher frequencies (> 120 Hz) show less contact time variability and have overall shorter contact times compared to lower frequencies (60–120 Hz). The amplitude of vibration has little direct effect on the contact time. Through semiempirical modeling and comparison to experiments, we show that phase-averaged contact times can increase or decrease relative to a nonvibrating substrate for low $\left(<80\mathrm{Hz}\right)$ or high $\left(>100\mathrm{Hz}\right)$ vibration frequencies, respectively. This study not only provides new insights into droplet impact physics on vibrating surfaces, but also develops guidelines for the rational design of surfaces to achieve controllable droplet wetting in applications utilizing vibration.

Viscous fingering—the fluid-mechanical instability that takes place when a low-viscosity fluid displaces a high-viscosity fluid—has traditionally been studied under either fully miscible or fully immiscible fluid systems. Here we study the impact of partial miscibility (a common occurrence in practice) on the fingering dynamics. Through a careful design of the thermodynamic free energy of a binary mixture, we develop a phase-field model of fluid-fluid displacements in a Hele-Shaw cell for the general case in which the two fluids have limited (but nonzero) solubility into one another. We show, by means of high-resolution numerical simulations, that partial miscibility exerts a powerful control on the degree of fingering: fluid dissolution hinders fingering while fluid exsolution enhances fingering. We also show that, as a result of the interplay between compositional exchange and the hydrodynamic pattern-forming process, stronger fingering promotes the system to approach thermodynamic equilibrium more quickly.

Dynamics and rheology of a confined suspension of vesicles (a model for red blood cells) are studied numerically in two dimensions by using an immersed boundary lattice Boltzmann method. We pay particular attention to the link between the spatiotemporal organization and the rheology of the suspension. Besides confinement, we analyze the effect of concentration of the suspension, $\varphi$ (defined as the area fraction occupied by the vesicles in the simulation domain), as well as the viscosity contrast $\lambda$ (defined as the ratio between the viscosity of the fluid inside the vesicles, ${\eta }_{\mathrm{int}}$, and that of the suspending fluid, ${\eta }_{\mathrm{ext}}$). The hydrodynamic interaction between two vesicles is shown to play a key role in determining the spatial organization. For $\lambda =1$, the pair of vesicles settles into an equilibrium state with constant interdistance, which is regulated by the confinement. The equilibrium interdistance increases with the gap between walls, following a linear relationship. However, no stable equilibrium interdistance between two tumbling vesicles is observed for $\lambda =10$. A quite ordered suspension is observed concomitant with the existence of an equilibrium interdistance between a vesicle pair. However, a disordered suspension prevails when no pair equilibrium interdistance exists, as occurs for tumbling vesicles. We then analyze the rheology, focusing on the effective viscosity, denoted as $\eta$, as well as on normalized viscosity, defined as $\left[\eta \right]=(\eta -{\eta }_{\mathrm{ext}})/\left({\eta }_{\mathrm{ext}}\varphi \right)$. Ordering of the suspension is accompanied by a nonmonotonic behavior of $\left[\eta \right]$ with $\varphi$, while $\eta$ exhibits plateaus. The nonmonotonic behavior of $\left[\eta \right]$ is suppressed when a disordered pattern prevails.

The sedimentation and fluttering (angular oscillation of the axis) of straight cylinders are studied in a viscous fluid at rest filling a vertical Hele-Shaw cell for different density contrasts ${\rho }_s-{\rho }_f$ and fluid viscosities ${\mu }_f$ and for two cylinder densities ${\rho }_s$ and diameters $D$. The influence of confinement in the cell is studied by comparing the present results to those of the literature for nonconfined fluids. While the confinement and the cylinder length $L$ both influence strongly the mean sedimentation velocity $V_s$, the characteristics of the fluttering instability are much more similar in the confined and nonconfined cases. While the drag coefficient is nearly constant in a nonconfined fluid, it is larger here and depends both on $L$ (due to flow blockage) and on the Reynolds number ${\text{Re}}_D=V_{s}D{\rho }_f/{\mu }_f$; the inertial and viscous drag components have equal magnitudes for ${\text{Re}}_D\simeq 40$. For fluttering, instead, the key parameter is the Froude number $\text{Fr}=V_s/V_g [V_g=\sqrt{({\rho }_s-{\rho }_f)gL/{\rho }_f}]$, and the fluttering oscillations vanish below $\text{Fr}\sim 0.07$ for all cylinders and fluids investigated. Above this threshold, the angular amplitude increases with $\text{Fr}$ up to a plateau value, while that of the horizontal oscillations is, at first, very large and then decreases; both amplitudes are reduced when the viscous drag is dominant, but, if inertial drag is dominant, all data points follow a common trend. For all fluids and cylinders, too, the fluttering frequency varies as $f=0.102V_g/L$. These features of fluttering are generally qualitatively similar to those reported in nonconfined fluids, but this instability is observable down to lower ${\text{Re}}_D$ values ($\simeq 24$ instead of $\sim 200$).

Both surface tension and buoyancy force in stable stratification act to restore perturbed interfaces back to their initial positions. Hence, both are intuitively considered as stabilizing agents. Nevertheless, the Taylor-Caulfield instability is a counterexample in which the presence of buoyancy forces in stable stratification destabilize shear flows. An explanation for this instability lies in the fact that stable stratification supports the existence of gravity waves. When two vertically separated gravity waves propagate horizontally against the shear, they may become phase locked and amplify each other to form a resonance instability. Surface tension is similar to buoyancy but its restoring mechanism is more efficient at small wavelengths. Here, we show how a modification of the Taylor-Caulfield configuration, including two interfaces between three stably stratified immiscible fluids, supports interfacial capillary gravity whose interaction yields resonance instability. Furthermore, when the three fluids have the same density, an instability arises solely due to a pure counterpropagating capillary wave resonance. The linear stability analysis predicts a maximum growth rate of the pure capillary wave instability for an intermediate value of surface tension corresponding to ${\text{We}}^{-1}=5$, where $\text{We}$ denotes the Weber number. We perform direct numerical nonlinear simulation of this flow and find nonlinear destabilization when $2\le {\text{We}}^{-1}\le 10$, in good agreement with the linear stability analysis. The instability is present also when viscosity is introduced, although it is gradually damped and eventually quenched.

Log-layer mismatch refers to a chronic problem found in wall-modeled large-eddy simulation (WMLES) or detached-eddy simulation, where the modeled wall-shear stress deviates from the true one by approximately $15\%$. Many efforts have been made to resolve this mismatch. The often-used fixes, which are generally ad hoc, include modifying subgrid-scale stress models, adding a stochastic forcing, and moving the LES–wall-model matching location away from the wall. An analysis motivated by the integral wall-model formalism suggests that log-layer mismatch is resolved by the built-in physics-based temporal filtering. In this work we investigate in detail the effects of local filtering on log-layer mismatch. We show that both local temporal filtering and local wall-parallel filtering resolve log-layer mismatch without moving the LES–wall-model matching location away from the wall. Additionally, we look into the momentum balance in the near-wall region to provide an alternative explanation of how LLM occurs, which does not necessarily rely on the numerical-error argument. While filtering resolves log-layer mismatch, the quality of the wall-shear stress fluctuations predicted by WMLES does not improve with our remedy. The wall-shear stress fluctuations are highly underpredicted due to the implied use of LES filtering. However, good agreement can be found when the WMLES data are compared to the direct numerical simulation data filtered at the corresponding WMLES resolutions.

This paper is associated with a video winner of a 2016 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2016.GFM.V0055