A common realization of superhydrophobic surfaces makes use of a mesh-like geometry, where pockets of air are trapped in a periodic array of holes in a no-slip solid substrate. We consider the small-solid-fraction limit where the ribs of the mesh are narrow. In this limit, we obtain a simple leading-order approximation for the slip-length tensor of an arbitrary mesh geometry. This approximation scales as the solid-fraction logarithm, as anticipated by Ybert et al. [Phys. Fluids 19, 123601 (2007)]; in the special case of a square mesh it agrees with the analytical results obtained by Davis and Lauga [Phys. Fluids 21, 113101 (2009)].

The interactions between vortex tubes and magnetic-flux rings in incompressible magnetohydrodynamics are investigated at high kinetic and magnetic Reynolds numbers, and over a wide range of the interaction parameter. The latter is a measure of the turnover time of the large-scale fluid motions in units of the magnetic damping time, or of the strength of the Lorentz force in units of the inertial force. The small interaction parameter results, which are related to kinematic turbulent dynamo studies, indicate the evolution of magnetic rings into flattened spirals wrapped around the vortex tubes. This process is also observed at intermediate interaction parameter values, only now the Lorentz force creates new vortical structures at the magnetic spiral edges, which have a striking solenoid vortex-line structure, and endow the flattened magnetic-spiral surfaces with a curvature. At high interaction parameter values, the decisive physical factor is Lorentz force effects. The latter create two (adjacent to the magnetic ring) vortex rings that reconnect with the vortex tube by forming an intriguing, serpentinelike, vortex-line structure, and generate, in turn, two new magnetic rings, adjacent to the initial one. In this regime, the morphologies of the vorticity and magnetic field structures are similar. The effects of these structures on kinetic and magnetic energy spectra, as well as on the direction of energy transfer between flow and magnetic fields, are also indicated.

The response of a laminar separation bubble to synthetic jet forcing with various modulation schemes is investigated via direct numerical simulations. A simple sinusoidal waveform is considered as a reference case, and various amplitude modulation schemes, including the square-wave “burst” modulation, are employed in the simulations. The results indicate that burst modulation is less effective at reducing the length of the flow separation than the sinusoidal forcing primarily because burst modulation is associated with a broad spectrum of input frequencies that are higher than the target frequency for the flow control. It is found that such high-frequency forcing delays vortex roll-up and promotes vortex pairing and merging, which have an adverse effect on reducing the separation bubble length. A commonly used amplitude modulation scheme is also found to have reduced effectiveness due to its spectral content. A new amplitude modulation scheme which is tailored to impart more energy at the target frequency is proposed and shown to be more effective than the other modulation schemes. Experimental measurements confirm that modulation schemes can be preserved through the actuator and used to enhance the energy content at the target modulation frequency. The present study therefore suggests that the effectiveness of synthetic jet-based flow control could be improved by carefully designing the spectral content of the modulation scheme.

We present models for single-particle dispersion in vertical and horizontal directions of stably stratified flows. The model in the vertical direction is based on the observed Lagrangian spectrum of the vertical velocity, while the model in the horizontal direction is a combination of a continuous-time eddy-constrained random walk process with a contribution to transport from horizontal winds. Transport at times larger than the Lagrangian turnover time is not universal and dependent on these winds. The models yield results in good agreement with direct numerical simulations of stratified turbulence, for which single-particle dispersion differs from the well-studied case of homogeneous and isotropic turbulence.

Consistently with observations from recent experiments and DNS, we focus on the effects of strong velocity increments at small spatial scales for the simulation of the drag force on particles in high Reynolds number flows. In this paper, we decompose the instantaneous particle acceleration in its systematic and residual parts. The first part is given by the steady-drag force obtained from the large-scale energy-containing motions, explicitly resolved by the simulation, while the second denotes the random contribution due to small unresolved turbulent scales. This is in contrast with standard drag models in which the turbulent microstructures advected by the large-scale eddies are deemed to be filtered by the particle inertia. In our paper, the residual term is introduced as the particle acceleration conditionally averaged on the instantaneous dissipation rate along the particle path. The latter is modeled from a log-normal stochastic process with locally defined parameters obtained from the resolved field. The residual term is supplemented by an orientation model which is given by a random walk on the unit sphere. We propose specific models for particles with diameter smaller and larger size than the Kolmogorov scale. In the case of the small particles, the model is assessed by comparison with direct numerical simulation (DNS). Results showed that by introducing this modeling, the particle acceleration statistics from DNS is predicted fairly well, in contrast with the standard LES approach. For the particles bigger than the Kolmogorov scale, we propose a fluctuating particle response time, based on an eddy viscosity estimated at the particle scale. This model gives stretched tails of the particle acceleration distribution and dependence of its variance consistent with experiments.

We analyze theoretically and experimentally the wake behind a horizontal cylinder of diameter $d$ horizontally translated at constant velocity $U$ in a fluid rotating about the vertical axis at a rate $\mathrm{\Omega }$. Using particle image velocimetry measurements in the rotating frame, we show that the wake is stabilized by rotation for Reynolds number $\mathrm{Re}=Ud/\nu$ much larger than in a nonrotating fluid. Over the explored range of parameters, the limit of stability is $\mathrm{Re}\simeq (275\pm 25)/\mathrm{Ro}$, with $\mathrm{Ro}=U/2\mathrm{\Omega }d$ the Rossby number, indicating that the stabilizing process is governed by the Ekman pumping in the boundary layer. At low Rossby number, the wake takes the form of a stationary pattern of inertial waves, similar to the wake of surface gravity waves behind a ship. We compare this steady wake pattern to a model, originally developed by Johnson [E. R. Johnson, J. Fluid Mech. 120, 359 (1982)], assuming a free-slip boundary condition and a weak streamwise perturbation. Our measurements show quantitative agreement with this model for $\mathrm{Ro}\lesssim 0.3$. At larger Rossby number, the phase pattern of the wake is close to the prediction for an infinitely small line object. However, the wake amplitude and phase origin are not correctly described by the weak-streamwise-perturbation model, calling for an alternative model for the boundary condition at moderate rotation rate.

A granular layer can form regular patterns, such as squares, stripes, and hexagons, when it is fluidized with a pulsating gas flow. These structures are reminiscent of the well-known patterns found in granular layers excited through vibration, but, contrarily to them, they have been hardly explored since they were first discovered. In this work, we investigate experimentally the conditions leading to pattern formation in pulsed fluidized beds and the dimensionless numbers governing the phenomenon. We show that the onset to the instability is universal for Geldart B (sandlike) particles and governed by the hydrodynamical parameters $\mathrm{\Gamma }=u_{\mathrm{a}}/\left(u_{\mathrm{t}}\overline{\varphi }\right)$ and $f/f_{\mathrm{n}}$, where $u_{\mathrm{a}}$ and $f$ are the amplitude and frequency of the gas velocity, respectively, $u_{\mathrm{t}}$ is the terminal velocity of the particles, $\overline{\varphi }$ is the average solids fraction, and $f_{\mathrm{n}}$ is the natural frequency of the bed. These findings suggest that patterns emerge as a result of a parametric resonance between the kinematic waves originating from the oscillating gas flow and the bulk dynamics. Particle friction plays virtually no role in the onset to pattern formation, but it is fundamental for pattern selection and stabilization.

We present a theory to describe the time evolution of the red blood cell (RBC) and platelet concentration distributions in pressure-driven flow through a straight channel. This model is based on our previous theory for the steady-state distributions [Qi and Shaqfeh, Phys. Rev. Fluids 2, 093102 (2017)] and captures the flow-induced nonuniformity of the concentrations of RBCs and platelets in the cross-flow direction. Starting with a uniform concentration, RBCs migrate away from the channel walls due to a shear-induced lift force and eventually reach steady state due to shear-induced diffusion, i.e., hydrodynamic “collisions” with other RBCs. On the other hand, platelets exit the cell-laden region due to RBC-platelet interactions and enter the cell-free layer, resulting in margination. To validate the theory, we also perform boundary integral simulations of blood flow in microchannels and directly compare various measureables between theory and simulation. The timescales associated with RBC migration and platelet margination are discussed in the context of the simulation and theory, and their importance in the function of microfluidic devices as well as the vascular network are elucidated. Due to the varying shear rate in pressure-driven flow and the wall-induced RBC lift, we report a separation of timescales for the transport in the near-wall region and in the bulk region. We also relate the transient problem to the axial variation of migration and margination, and we demonstrate how the relevant timescales can be used to predict corresponding entrance lengths. Our theory can serve as a fast and convenient alternative to large-scale simulations of these phenomena.

The collapse of voids in porous energetic materials leads to hot-spot formation and reaction initiation. This work advances the current knowledge of the dynamics of void collapse and hot-spot formation using 3D reactive void collapse simulations in HMX. Four different void shapes, i.e., sphere, cylinder, plate, and ellipsoid, are studied. For all four shapes, collapse generates complex three-dimensional (3D) baroclinic vortical structures. The hot spots are collocated with regions of intense vorticity. The differences in the vortical structures for the different void shapes are shown to significantly impact the relative sensitivity of the voids. Voids of high surface area generate hot spots of greater intensity; intricate, highly contorted vortical structures lead to hot spots of corresponding tortuosity and therefore enhanced growth rates of reaction fronts. In addition, all 3D voids are shown to be more sensitive than their two-dimensional (2D) counterparts. The results provide physical insights into hot-spot formation and growth and point to the limitations of 2D analyses of hot-spot formation.

We present a numerical study on inertial electrically charged particles suspended in a turbulent carrier phase. Fluid-particle interactions are accounted for in an Eulerian-Lagrangian (EL) framework and coupled to a Fourier-based Ewald summation method, referred to as the particle-particle-particle–mesh $\left({\mathrm{P}}^3\mathrm{M}\right)$ method, to accurately capture short- and long-range electrostatic forces in a tractable manner. The EL ${\mathrm{P}}^3\mathrm{M}$ method is used to assess the competition between drag and Coulomb forces for a range of Stokes numbers and charge densities. Simulations of like- and oppositely charged particles suspended in a two-dimensional Taylor-Green vortex and three-dimensional homogeneous isotropic turbulence are reported. It is found that even in dilute suspensions, the short-range electric potential plays an important role in flows that admit preferential concentration. Suspensions of oppositely charged particles are observed to agglomerate in the form of chains and rings. Comparisons between the particle-mesh method typically employed in fluid-particle calculations and ${\mathrm{P}}^3\mathrm{M}$ are reported, in addition to one-point and two-point statistics to quantify the level of clustering as a function of Reynolds number, Stokes number, and nondimensional electric settling velocity.

Length scales of eddies involved in the power generation of infinite wind farms are studied by analyzing the spectra of the turbulent flux of mean kinetic energy (MKE) from large eddy simulations (LES). Large-scale structures with an order of magnitude bigger than the turbine rotor diameter $\left(D\right)$ are shown to have substantial contribution to wind power. Varying dynamics in the intermediate scales $\left(D–10D\right)$ are also observed from a parametric study involving interturbine distances and hub height of the turbines. Further insight about the eddies responsible for the power generation have been provided from the scaling analysis of two-dimensional premultiplied spectra of MKE flux. The LES code is developed in a high Reynolds number near-wall modeling framework, using an open-source spectral element code Nek5000, and the wind turbines have been modelled using a state-of-the-art actuator line model. The LES of infinite wind farms have been validated against the statistical results from the previous literature. The study is expected to improve our understanding of the complex multiscale dynamics in the domain of large wind farms and identify the length scales that contribute to the power. This information can be useful for design of wind farm layout and turbine placement that take advantage of the large-scale structures contributing to wind turbine power.

Previous work reported that microvillus deformation has an important influence on dynamics of cell adhesion. However, the existing studies were limited to the extensional deformation of microvilli and did not consider the effects of their bending deformation on cell adhesion. This Rapid Communication investigates the effects of flexural stiffness of microvilli on the rolling process related to adhesion of leukocytes by using a lattice-Boltzmann lattice-spring method (LLM) combined with adhesive dynamics (AD) simulations. The simulation results reveal that the flexural stiffness of microvilli and their bending deformation have a profound effect on rolling velocity and adhesive forces. As the flexural stiffness of the microvilli decreases, their bending angles increase, resulting in an increase in the number of receptor-ligand bonds and adhesive bonding force and a decrease in the rolling velocity of leukocytes. The effects of flexural stiffness on deformation and adhesion represent crucial factors involved in cell adhesion.

Direct numerical simulations of closely interacting infinite circular cylinders in a Bingham fluid are presented, and results compared to asymptotic solutions based on lubrication theory in the gap. Unlike for a Newtonian fluid, the macroscopic flow outside of the gap between the cylinders is shown to have a large effect on the pressure profile within the gap and the resulting lubrication force on the cylinders. The presented results indicate that the asymptotic lubrication solution can be used to predict the lubrication pressure only if the surrounding viscoplastic matrix is yielded by a macroscopic flow. This has implications for the use of subgrid-scale lubrication models in simulations of noncolloidal particulate suspensions in viscoplastic fluids.

Flow through helical tubes and channels have been examined in different contexts, for facilitating heat and mass transfer at low Reynolds number flow, for generating plug flow to minimize reactor volume for many reactions. The curvature and torsion of the helices have been shown to engender secondary flow in addition to the primary axial flow, which enhances passive in-plane mixing between different fluid streams. Most of these studies, however, involve a single spiral with circular cross-section, which in essence is symmetric. It is not known, however, how the coupled effect of asymmetry of cross-section and the curvature and torsion of channel would affect the flow profile inside such tubes or channels. In this context, we have presented here the analysis of fluid flow at low Reynolds number inside a novel triple helical channel that consists of three helical flow paths joined along their contour length forming a single channel. We have carried out both microparticle image velocimetry (micro-PIV) and 3D simulation in FLUENT of flow of a Newtonian fluid through such channels. Our analysis shows that whereas in conventional single helices, the secondary flow is characterized by two counter-rotating vortices, in the case of triple helical channels, number of such vortices increases with the helix angle. Such flow profile is expected to enhance possibility of mixing between the liquids, yet diminish the pressure drop.

We investigate experimentally the impact of heterogeneity on the capillary pressure hysteresis in fluid invasion of model porous media. We focus on symmetric heterogeneity, where the contact angles the fluid interface makes with the oil-wet (${\theta }_1$) and the water-wet (${\theta }_2$) beads add up to $\pi$. While enhanced heterogeneity is usually known to increase hysteresis phenomena, we find that hysteresis is greatly reduced when heterogeneities in wettability are introduced. On the contrary, geometric heterogeneity (like bidisperse particle size) does not lead to such an effect. We provide a qualitative explanation of this surprising result, resting on rather general geometric arguments.

We study the effects of imposed three-dimensional flows on the trajectories and mixing of gyrotactic swimming microorganisms and identify phenomena not seen in flows restricted to two dimensions. Through numerical simulation of Taylor-Green and Arnold-Beltrami-Childress (ABC) flows, we explore the role that the flow and the cell shape play in determining the long-term configuration of the cells' trajectories, which often take the form of multiple sinuous and helical “plumelike” structures, even in the chaotic ABC flow. This gyrotactic suppression of Lagrangian chaos persists even in the presence of random noise. Analytical solutions for a number of cases reveal the how plumes form and the nature of the competition between torques acting on individual cells. Furthermore, studies of Lyapunov exponents reveal that, as the ratio of cell swimming speed relative to the flow speed increases from zero, the initial chaotic trajectories are first suppressed and then give way to a second unexpected window of chaotic trajectories at speeds greater than unity, before suppression of chaos at high relative swimming speeds.

Lock-release gravity current experiments are performed to examine the evolution of a particle bearing flow that propagates either in a uniform-density fluid or in a two-layer fluid. In all cases, the current is composed of fresh water plus micrometer-scale particles, the ambient fluid is saline, and the current advances initially either over the surface as a hypopycnal current or at the interface of the two-layer fluid as a mesopycnal current. In most cases the tank is tilted so that the ambient fluid becomes deeper with distance from the lock. For hypopycnal currents advancing in a uniform density fluid, the current typically slows as particles rain out of the current. While the loss of particles alone from the current should increase the current's buoyancy and speed, in practice the current's speed decreases because the particles carry with them interstitial fluid from the current. Meanwhile, rather than settling on the sloping bottom of the tank, the particles form a hyperpycnal (turbidity) current that advances until enough particles rain out that the relatively less dense interstitial fluid returns to the surface, carrying some particles back upward. When a hypopycnal current runs over the surface of a two-layer fluid, the particles that rain out temporarily halt their descent as they reach the interface, eventually passing through it and again forming a hyperpycnal current. Dramatically, a mesopycnal current in a two-layer fluid first advances along the interface and then reverses direction as particles rain out below and fresh interstitial fluid rises above.

The motion of three interacting point vortices in the plane can be thought of as the motion of three geometrical points endowed with a dynamics. This motion can therefore be reformulated in terms of dynamically evolving geometric quantities, viz., the circle that circumscribes the vortex triangle and the angles of the vortex triangle. In this study, we develop the equations of motion for the center, $Z$, and radius, $R$, of this circumcircle; and for the angles of the vortex triangle, $A,B$, and $C$; and for the triangle orientation given by ${\phi }_1$. The equations of motion for $R,A,B$, and $C$ form an autonomous dynamical system. A number of known results in the three-vortex problem follow readily from the equations, giving an alternate geometrical perspective on the problem.

A modeling framework is derived to predict the scour induced by marine hydrokinetic turbines installed on fluvial or tidal erodible bed surfaces. Following recent advances in bridge scour formulation, the phenomenological theory of turbulence is applied to describe the flow structures that dictate the equilibrium scour depth condition at the turbine base. Using scaling arguments, we link the turbine operating conditions to the flow structures and scour depth through the drag force exerted by the device on the flow. The resulting theoretical model predicts scour depth using dimensionless parameters and considers two potential scenarios depending on the proximity of the turbine rotor to the erodible bed. The model is validated at the laboratory scale with experimental data comprising the two sediment mobility regimes (clear water and live bed), different turbine configurations, hydraulic settings, bed material compositions, and migrating bedform types. The present work provides future developers of flow energy conversion technologies with a physics-based predictive formula for local scour depth beneficial to feasibility studies and anchoring system design. A potential prototype-scale deployment in a large sandy river is also considered with our model to quantify how the expected scour depth varies as a function of the flow discharge and rotor diameter.

We examine the potential of the nonlinear parabolized stability equations (PSE) to provide an accurate yet computationally efficient treatment of the growth of disturbances in H-type transition to turbulence. The PSE capture the nonlinear interactions that eventually induce breakdown to turbulence and can as such identify the onset of transition without relying on empirical correlations. Since the local PSE solution at the onset of transition is a close approximation of the Navier-Stokes equations, it provides a natural inflow condition for direct numerical simulations (DNS) and large-eddy simulations (LES) by avoiding nonphysical transients. We show that a combined PSE-DNS approach, where the pretransitional region is modeled by the PSE, can reproduce the skin-friction distribution and downstream turbulent statistics from a DNS of the full domain. When the PSE are used in conjunction with wall-resolved and wall-modeled LES, the computational cost in both the laminar and turbulent regions is reduced by several orders of magnitude compared to DNS.