Standard Eulerian–Lagrangian (EL) methods generally employ drag force models that only represent the mean hydrodynamic force acting upon a particle-laden suspension. Consequently, higher-order drag force statistics, arising from neighbor-induced flow perturbations, are not accounted for; this has implications on the predictions for particle velocity variance and dispersion. We develop a force Langevin model that treats neighbor-induced drag fluctuations as a stochastic force within an EL framework. The stochastic drag force follows an Ornstein-Uhlenbeck process and requires closure of the integral timescale for the fluctuating hydrodynamic force and the standard deviation in drag. The former is closed using the mean-free time between successive collisions, derived from the kinetic theory of nonuniform gases. For the latter, particle-resolved direct numerical simulation (PR-DNS) of fixed particle assemblies is utilized to develop a correlation. The stochastic EL framework specifies unresolved drag force statistics, leading to the correct evolution and sustainment of particle velocity variance over a wide range of Reynolds numbers and solids volume fractions, when compared to PR-DNS of freely evolving homogeneous suspensions. By contrast, standard EL infers drag statistics from variations in the resolved flow and thus underpredicts the growth and steady particle velocity variance in homogeneous suspensions. Velocity statistics from standard EL approaches are found to depend on the bandwidth of the projection function used for two-way momentum coupling, while results obtained from the stochastic EL approach are insensitive to the projection bandwidth.

Surface-driven flows are ubiquitous in nature, from subcellular cytoplasmic streaming to organ-scale ciliary arrays. Here we model how confined geometries can be used to engineer complex hydrodynamic patterns driven by activity prescribed solely on the boundary. Specifically, we simulate light-controlled surface-driven active matter, probing the emergent properties of a suspension of active colloids that can bind and unbind from surfaces of a closed microchamber, together creating an active carpet. The attached colloids generate large-scale flows that in turn can advect detached particles toward the walls. Switching the particle velocities with light, we program the active suspension and demonstrate a rich design space of flow patterns characterized by topological defects. We derive the possible mode structures and use this theory to optimize different microfluidic functions including hydrodynamic compartmentalization and chaotic mixing. Our results pave the way toward designing and controlling surface-driven active fluids.

With the continuing progress in large eddy simulations (LES), and ever increasing computational resources, it is currently possible to numerically solve the time-dependent and anisotropic large scales of turbulence in a wide variety of flows. For some applications this large-scale resolution is satisfactory. However, a wide range of engineering problems involve flows at very large Reynolds numbers where the subgrid-scale dynamics of a practical LES are critically important to design and yet are out of reach given the computational demands of solving the Navier Stokes equations; this difficulty is particularly relevant in wall-bounded turbulence where even the large scales are often below the implied filter width of modest cost wall modeled LES. In this paper we briefly introduce a scale enrichment procedure which leverages spatially and spectrally localized Gabor modes. The method provides a physically consistent description of the small-scale velocity field without solving the full nonlinear equations. The enrichment procedure is appraised against its ability to predict small-scale contributions to the pressure field. We find that the method accurately extrapolates the pressure spectrum and recovers pressure variance of the full field remarkably well when compared to a computationally expensive, highly resolved LES. The analysis is conducted both in a priori and a posteriori settings for the case of homogeneous isotropic turbulence.

Electrowetting-induced detachment of liquid droplets has application prospects in self-cleaning and digital microfluidics. Although several models have been provided to estimate the critical condition for jumping droplet, there is still a lack of a comprehensive understanding of the energy conversion during detachment process and an accurate prediction of the jumping velocity. In this study, an analytical model adopting the energy balance approach is derived to predict the jumping velocity of an electrowetting-actuated droplet. Our main contribution is to reformulate the models of four energy components including the surface energy, kinetic energy, gravitational potential energy at detachment, as well as the viscous dissipation of entire recoiling. The necessity to correct these energy components has also been physically explained. On the one hand, the droplet morphology at detachment is not spherical but a balloonlike shape, leading to the underestimated surface energy and gravitational potential energy. On the other hand, the previous model that assumes a constant velocity gradient in the bulk results in the overestimated viscous dissipation. Moreover, the kinetic energy of jumping droplet cannot be simply characterized by a rigid body model because of the non-negligible radial velocity. According to the statistics, the correction of the viscous dissipation term contributes the most to reducing prediction error, approaching $\sim 90\%$, while the relative errors introduced from other three energy terms are comparable, approaching $\sim 20\%$. By testing the prediction results against both present simulations and the experiments in the literature, it is validated that the present model successfully identifies the influence of liquid properties, droplet size, surface wettability, and applied voltage on jumping velocity. The results indicate that the increase in the droplet size causes a nonmonotonic change in jumping velocity, which first increases due to the weakened viscous dissipation, then decreases due to the prominent influence of gravity.

Coordinated cilia are used throughout the natural world for micronscale fluid transport. They are often modeled with regular filament arrays on fixed planar surfaces. Here we simulate hundreds of interacting active filaments on spherical surfaces, where defects in the cilia displacement field must be present. We see synchronized beating towards or about two defects for spheres held fixed. Defects alter filament beating, which causes the sphere to move once released. This motion feeds back to the filaments, resulting in a whirling state with metachronal behavior along the equator.

We use laboratory experiments to investigate the entrainment of ambient fluid into an axisymmetric turbulent plume containing dense particles with a settling velocity that is considerably smaller than the plume velocity. We consider the effect of particle size, particle concentration, and the orientation of the plume buoyancy flux—in either the same or opposite direction to the particle buoyancy flux. When the plume buoyancy flux is in the opposite direction to the particle buoyancy flux, entrainment into the plume increases by up to 40%. The rate of entrainment increases linearly with the ratio of particle buoyancy flux to fluid buoyancy flux but does not depend on the particle size for the range of particle sizes investigated here. In contrast, when the plume buoyancy flux is in the same direction as the particle buoyancy flux, entrainment into the plume is unaffected by the addition of particles. The observed increase in entrainment, when the plume and particle buoyancy fluxes are in opposite directions, is consistent with inertial clustering whereby particles are ejected from regions of relatively high vorticity and accumulate in regions of relatively high strain rate within the turbulent flow field. Regions with high particle concentration can then experience convective instabilities that affect the entrainment of ambient fluid into the plume. The differing behavior observed based on the plume buoyancy flux orientation is also consistent with the above mechanism. Finally, based on the laboratory findings, we propose an expression for the entrainment coefficient to take into account the effect of suspended particles of opposing buoyancy flux to the plume buoyancy flux.

Fluidic interfaces disintegrate under sufficiently strong electric fields, leading to electrohydrodynamic (EHD) tip streaming. Taylor cones, which emit charged droplets from the tip of a conical cusp, are among the most prominent and well-studied examples of EHD instabilities. In liquid-liquid systems, more complex interface deformation modes than simple Taylor cones can be observed, with the interface being pushed away from the electrode, and additional cone structures emerging from the rim of the dimple. In this paper, we investigate the mechanisms behind these deformation modes experimentally and numerically, and demonstrate that the presence of droplets triggers the dimple at the interface. To characterize the underlying processes, we replace the pin electrode by a hollow metallic needle with a prescribed electrolyte volume flow. The submerged electrospray introduces droplets of an aqueous KCl solution with varying ion concentrations into silicone oils with varying viscosities. By measuring the corresponding electric current and by optical investigation of the interface deformation, we study the system response to variations of the ionic concentration, viscosity, and applied voltage as well as flow rate. The voltage between the needle and liquid-liquid interface has a strong influence on the deformation, whereas the electrolyte flow rate only has a small influence. In addition, we observe that both the deflection as well as the current reach limiting values with increasing ion concentration and viscosity, which we explain based on a scaling relationship for the size of the droplets. In addition to the experiments, we use a finite element solver and compute the charge transport due to the droplets in the oil phase as an advection-diffusion process. Further, we compute the electric potential distribution, flow field, and interface deformation. After calibration of our model with particle tracking velocimetry data of the flow inside the oil phase, we reproduce the experimentally observed dimple at the liquid-liquid interface. By including a relationship between the electric field at the pin electrode and the emitted electrospray current, we are able to identify the space charge as the cause of the experimentally observed limiting behavior of the interface deflection and the electric current. In summary, this paper highlights the importance of charged droplets for the complex dynamic modes observed when a liquid-liquid interface is exposed to a local electric field.

We study the spatiotemporal two-point correlation function of passively advected scalar fields in the inertial-convective range in three-dimensional homogeneous isotropic turbulence by means of numerical simulations. Our aim is to make a precision test of analytical results recently obtained using functional renormalization group (FRG). We show that at small time delays $t$, the Eulerian correlations of the scalar decay as a Gaussian in the variable $tp$ where $p$ is the wave number, as established by FRG, and which is related to the sweeping effect. At large time delays, a crossover to an exponential decay in $t{p}^2$ is predicted by the FRG analysis, but not observable in simulations due to numerical noise. We then propose to study this regime for a scalar field advected by a Kraichnan synthetic velocity field, and accurately confirm the FRG result, including the precise form of the prefactor in the exponential. By introducing finite time correlations in the synthetic velocity field, we also uncover the crossover between the two regimes.

We study the direction-dependent drag acting on a cylindrical solid intruder with length $L$ and diameter $D$ as it moves in water-saturated granular beds at constant depth. Polysterene and hydrogel grains with diameter $d$ are used to investigate materials which have high contact friction and those which are nearly frictionless, respectively. The drag on the intruder is measured while oriented perpendicular $F_{\perp }$ and parallel $F_{\parallel }$ to its axis as a function of speed $U$ from the quasistatic to the rate-dependent regime. We find that the drag anisotropy $\xi =F_{\perp }/F_{\parallel }$ is not constant and increases significantly with driving rate and $L/D$ in both mediums. In particular for $L/D=40$, $\xi$ increases from 2.6 to 4.5, and from 7.0 to 8.2 in the high- and low-friction beds, respectively, as the nondimensional Froude number $\mathrm{Fr}=U/\sqrt{g(D+d)}$ is varied between ${10}^{-4}$ and $2\times {10}^{-2}$. On average, $\xi$ is observed to increase logarithmically with $L/D$ for $L/D\gg 1$. Exploiting the index-matched nature of hydrogel grains in water, we further show that the sediment flow around the cylinder in the two orientations is consistent with skin friction–dominated drag. The relative contributions of the cylindrical side and the circular flat-ends on $\xi$ are estimated with thin disks to understand the observed variation of drag with aspect ratio and surface friction.

This paper investigates the impact of radial mass flux on Taylor-Couette flow in counter-rotating configuration, in which a Hopf bifurcation gives rise to branches of nontrivial solutions. Using direct numerical simulation we elucidate structures, dynamics, stability, and bifurcation behavior in qualitative and quantitative detail as a function of inner Reynolds numbers (${\text{Re}}_i$) and radial mass flux ($\alpha$) spanning a parameter space with a rich variety of solutions. Both radial inflow and strong radial outflow stabilize the system, whereas weak radial outflow has a strong destabilizing effect. We detected the existence of stable ribbons and mixed ribbons with low azimuthal wave number without symmetry restriction. In addition, ribbon solutions and mixed-ribbon solutions can be stable or unstable saddles. Furthermore, in the case of unstable saddles alternations between two different symmetrically related saddles generate different heteroclinic cycles. For alternating stationary (in comoving frame) ribbons the persistence time in one saddle decreases with distance from the onset. The persistence time for the heteroclinic cycle of alternating mixed ribbons shows a more complicated dependence with variation in control parameters and seems to follow an intermittency scenario of type III. Depending on whether the symmetrically related solutions are stationary or time-dependent, the heteroclinic connection can be either of oscillatory or nonoscillatory type.

The excitation and further sustenance of large-scale magnetic fields in rotating astrophysical systems, including planets, stars, and galaxies, is generally thought to involve a fluid magnetic dynamo effect driven by helical magnetohydrodynamic turbulence. While this scenario is appealing on general grounds, it, however, currently remains largely unconstrained, notably because a fundamental understanding of the nonlinear asymptotic behavior of large-scale fluid magnetism in the astrophysically relevant but treacherous regime of large magnetic Reynolds number Rm is still lacking. We explore this problem using local high-resolution simulations of turbulent magnetohydrodynamics driven by an inhomogeneous helical forcing generating a sinusoidal profile of kinetic helicity, mimicking the hemispheric distribution of kinetic helicity in rotating turbulent fluid bodies. We identify a transition at large Rm to a nonlinear state, followed up to $\text{Rm}\simeq 3\times {10}^3$, consisting of strong, saturated small-scale magnetohydrodynamic turbulence and a weaker, traveling coherent large-scale field oscillation. This state is characterized by an asymptotically small resistive dissipation of magnetic helicity, by its spatial redistribution across the equator through turbulent fluxes driven by the hemispheric distribution of kinetic helicity, and by the tentative presence in the tangled dynamical magnetic field of plasmoids typical of reconnection at large Rm.

We numerically investigate the effect of rough boundaries on heat flux enhancement and flow structures in turbulent Rayleigh-Bénard convection of air ($\text{Pr}=0.7$) confined in a two-dimensional cell of aspect ratio 2 for the Rayleigh number $\text{Ra}$ in the range ${10}^6\le \text{Ra}\le 4.64\times {10}^9$. We consider three levels of roughness having maximum height as $5\%$, $10\%$, and $20\%$ of the cell height. The presence of rough surfaces induces a significant enhancement in heat flux beyond a critical Rayleigh number ${\text{Ra}}_c$, the value of which strongly depends on the roughness height. The probability density function of the temperature fluctuations exhibits a bi-Gaussian distribution below ${\text{Ra}}_c$, while it displays exponential nature in the enhanced heat flux regime. The distinct nature of large-scale flow patterns is observed in this regime. While a stable double-roll state persists for the smallest roughness setup, the effect of corner rolls emerges in the intermediate level. The breakdown of the stable double-roll structure into multiple rolls is seen to be linked to higher heat flux owing to the efficient washing out effect in the roughness grooves. While a stronger horizontal motion elevates the shear production for the smallest roughness case, direct injection of plumes into the bulk improves the buoyancy production, leading to larger heat flux for the tallest roughness. Roughness heights are seen not to have any discernible effect on the overall flow strength. A vertical distribution of mean temperature indicates the presence of multilayer characteristics with the roughness-invariant near-wall region identified by a weakly nonlinear profile. The variation of the mean temperature in the intermediate layer plays a crucial role in heat transfer enhancement as it reflects the quality of ventilation of the entrapped fluid.

Infants born with single-ventricle physiologies pose significant challenges for mechanical circulatory support devices. Their corresponding Fontan circulations consist of passive blood flow that returns to the lungs via direct connections to the pulmonary arteries without a pumping chamber. When Fontan patients reach adolescence or young adulthood, they tend to develop heart failure and may require heart transplants and/or mechanical assist devices. Mechanical supports often require a reservoir to attach, but no such blood reservoir exists in a closed Fontan circulation. This study was aimed to investigate the existence of a hemodynamically optimized geometry for an artificial right atrium (ARA) that can act as a reservoir for circulatory support in Fontan patients. Our hemodynamics-based criteria for an ARA were defined as minimum particle residence time (PRT) (to reduce the probability of blood clot formation) and maximum volume compliance (to prevent pressurization of cerebral and hepatic veins). A computational approach was used to complete this study. We utilized non-Newtonian fluid-solid interaction simulations constructed by lattice-Boltzmann and immersed boundary methods. Our results show that a hemodynamically optimum shape for an ARA with minimum PRT (relative to the cases considered in this study) is convex at the outlet (towards the lungs) and concave at the opposite side of the outlet. Additionally, the optimal ARA geometry well preserves the volume compliance that is needed to prevent pressurization of cerebral and/or hepatic veins. Interestingly, this shape resembles that of the healthy anatomical right atrium. Future implantation of our proposed ARA configuration may potentially lessen the risk of implementing biventricular supports in Fontan patients.

The dispersion and mixing of passive particles in a turbulent channel flow are investigated by means of a network-based representation of their motion. We employ direct numerical simulations at five different Reynolds numbers, from ${\text{Re}}_{\tau }=180$ up to ${\text{Re}}_{\tau }=950$, and obtain sets of particle trajectories via numerical integration. By dividing the channel domain into wall-normal levels, the motion of particles across these levels is used to build a time-varying complex network, which is able to capture the transient phase of the wall-normal mixing process and its dependence on the Reynolds number ${\text{Re}}_{\tau }$. Using network metrics, we observe that the dispersion of clouds of tracers depends highly on both their wall-normal starting position and the time elapsed from their release. We identify two main mechanisms that contribute to the long-lasting inhibition of the dispersion of particles released near the walls. We also show how the relative importance of these mechanisms varies with the Reynolds number. In particular, at low ${\text{Re}}_{\tau }$ the weaker velocity fluctuations appear dominant in inhibiting dispersion, while at higher Reynolds numbers a larger role is played by cyclic patterns of motion. At the higher Reynolds numbers employed in this work, we find that most network properties are Reynolds independent when scaled with outer-flow variables. Instead, at lower ${\text{Re}}_{\tau }$, the aforementioned scaling is not observed. We explore the meaning of the emergence of this scaling in relation to the features of dispersion and to the network definition.

The turbulent axisymmetric bluff body wake is studied with a large eddy simulation (LES). The effect of pulsed jet forcing on the wake is investigated. For completeness, the pulsed jet actuator is included in the computational domain. Spectral proper orthogonal decomposition (SPOD) is applied to analyze the wake and the effect of pulsed jet forcing. The numerical results show good agreement with the experimental results and successfully reproduce the dominant modes of the axisymmetric wake. SPOD identifies the axisymmetric bubble pumping mode (${\mathrm{St}}_D=0.06)$, axisymmetric-breaking vortex shedding mode $({\mathrm{St}}_D=0.22)$, and an axisymmetric-breaking mode close to the subharmonic of the shedding mode $({\mathrm{St}}_D=0.1)$. When the high-frequency pulsed jet $({\mathrm{St}}_{\theta }=0.107)$ is applied to the wake, the pressure fluctuation on the base and the azimuthal modes are globally weakened without any mode selection. The mean flow properties show that the inlet flow is driven towards the wake centerline by the high-frequency jet, and the shear layer deviates, forming a concave separation streamline. The entrainment in the wake is suppressed, and the wake is narrowed, leading to a global pressure rise. The high-frequency pulsed jet is concentric and greatly enhances the entrainment in the vicinity of the separation point. A low-pressure region is generated there, which drives the inlet flow towards the wake. Low-frequency forcing $({\mathrm{St}}_{\theta }=0.029$) generates a diffusive pulsed jet which enhances the mixing and entrainment in its trajectory. Low-frequency forcing reduces the wake length and accelerates recirculating flow near the base, leading to a reduction in base pressure, and the vortex shedding mode $({\mathrm{St}}_D=0.2)$ is amplified.

Controlling fluid flow is a fundamental problem with applications from biomedicine to environmental engineering. Contemporary solutions combine electromechanical sensors, valves, and pumps; however, these are expensive and difficult to maintain. We report an autonomous flow control principle inspired by vascular transport in plants. Combining experiments on real and biomimetic tissues, we show that networks of cells linked by nonlinear valves permit the physical programming of a nearly arbitrary pressure drop versus flow rate relation. The nonlinearity is a consequence of fluid-structure interactions that allow a flexible element to selectively block the valve aperture. We report four applications: parallel connections that function as (i) a nonlinear flow controller, (ii) a constant flow controller, (iii) a reverse Ohm flow controller, and a serial connection that acts as (iv) a fluidic on-off switch.

In supersonic turbulent boundary layers over isothermal walls, we investigate how the wall heat flux affects turbulent statistics and velocity scaling laws. To distinguish local Reynolds number and compressibility effects, we consider a conventional ideal gas with Sutherland's law and a fluid for which the dynamic viscosity is proportional to the square root of density, such that the semi-local Reynolds number is constant in the wall-normal direction. The results clearly indicate that the changes of the semi-local Reynolds number within the boundary layer affect the coherent turbulent structures, which induces the deviation of the viscous stress, Reynolds stress, and semi-local transformed mean velocity between different wall temperature conditions. For the cases with constant semi-local Reynolds number, we observe that the wall heat flux does not affect the turbulent structures and that the velocity profiles perfectly collapse among each other, indicating the importance of the semi-local Reynolds number, rather than the temperature or density themselves, on turbulent statistics and structures. Also, the conditional averaged analysis for the near-wall turbulent phenomena indicates a clear relationship between the turbulent structures and the mean velocity gradients. Additionally, an existing analytical temperature-velocity relation is verified based on the examinations of the applied equilibrium flow assumptions, and the results explain the disagreement between the present data and the analytical solutions in the outer boundary layer region, especially for isothermal wall cases.

A sixth-order compact finite differences scheme of the two-dimensional transport-Poisson equations in terms of vorticity-stream function is formulated to solve the motion of a flapping airfoil in a noninertial reference frame, fitting a NACA-0012 profile with the Kármán-Trefftz transformation. These numerical simulations have been used to estimate the validity range of the linear potential theories of Fernandez-Feria and the classical Garrick model on the propulsion of a pitching airfoil pivoting to a quarter chord length of the leading edge and a heaving airfoil in forward flight, in terms of the Reynolds, Re, and Strouhal number, St, compared with available numerical and experimental data. The Fernandez-Feria's propulsion theory shows better agreement with the numerical and experimental results than the Garrick model for the time-averaged thrust coefficient where it is found that the Fernandez-Feria's theory is limited to $\mathrm{Re}\gtrsim 4000$ and $\mathrm{St}\lesssim 0.25$ for pure pitching motions and $\mathrm{Re}\gtrsim 1000$ and $\mathrm{St}\lesssim 0.2$ for pure heaving motions.

We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer, and capillarity. The resulting long-wave evolution equation for the droplet thickness is treated analytically via the method of matched asymptotic expansions in the limit of slow mass transfer rates, quasistatic dynamics, and vanishingly small slip lengths to deduce a lower-dimensional system of integrodifferential equations for the two moving fronts. We demonstrate that the predictions of the deduced system agree excellently with simulations of the full model for a number of representative cases within the domain of applicability of the analysis. Specifically, we focus on situations where the mass of the drop changes periodically, to highlight a number of interesting features of the dynamics, which include stick-slip, hysteresislike effects, as well as the possibility for the droplet to alternate between the constant-radius and constant-angle stages which have been previously reported in related works. These features of the dynamics are further scrutinized by investigating how the bifurcation structure of droplet equilibria evolves as the mass of the droplet varies.

We consider a thin droplet that spreads over a flat, horizontal, and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes along the contact line. A matched asymptotics analysis is undertaken in the long-wave limit of the Stokes equations with slip to derive a set of evolution equations for the Fourier harmonics of nearly circular contact lines. Numerical experiments highlight the generally excellent agreement between the long-wave model and the derived equations, demonstrating that these are able to capture many of the features which characterize the intricate interplay between substrate heterogeneities and mass transfer on droplet motion.