The geometric structures and chemical properties of solid substrates are crucial in determining the dynamic behavior of nanobubbles. In this study, we designed a series of nanostructured substrates with alternating hydrophobic and hydrophilic domains based on the thickness and charge dependences of the hydrophobicity of graphene. We then systematically investigated the effects of these nanotrench structures on the dynamic behavior of nanobubbles using molecular-dynamics simulations. The nanotrench structures significantly enhanced the stability of bulk nanobubbles compared to homogeneous, flat graphene, and bulk nanobubble stability increased as the sizes of the hydrophilic domains increased. The mobility paths of the bulk nanobubbles were affected by the positions of the hydrophobic domains. The formation and positions of surface nanobubbles were also controlled by the properties of the nanostructured substrates; the nanobubbles were preferably located on the hydrophobic regions of the substrates. The morphologies of the surface nanobubbles depended on both the sizes of the hydrophobic regions and the degree of hydrophobicity. Under compression strain, the deformed hydrophilic domains of the solid graphene substrate prevented interactions between neighboring surface nanobubbles, resulting in stable nanobubbles. The findings provide insight into the effects of solid substrates on the dynamic behavior of nanobubbles.

We focus on the behaviors of the low-Stokes-number particles in a thermocapillary-induced convection within a closed geometry with a free surface, known as a half-zone liquid bridge. The motions of the spherical particles suspended by the bridge of a high-Prandtl-number liquid ($\mathrm{Pr}=28.6$) are tracked via two-dimensional and three-dimensional particle tracking velocimetry. Special attention is paid to the behaviors of the suspended particles in the flow regime in which coherent structures by the particles are realized; so-called particle accumulation structures (PASs). Through the experiments, we succeed in reconstructing three-dimensional trajectories of particles that form PASs, the toroidal core, and a structure wrapping the toroidal core. We illustrate the spatial and temporal correlations between the particles forming such three different coherent structures and corresponding regular flow structures; so-called Kolmogorov-Arnold-Moser (KAM) tori. It is found that the particles on the toroidal core exhibit helical motion through extracting the paths of the particles in azimuthal-axial planes with a small depth in the radial direction, which qualitatively corresponds to a Poincaré section.

This work aims at investigating three-dimensional finite-amplitude traveling wave solutions of the asymptotic suction boundary layer, as well as their role in state space, based on direct numerical simulations. Using a body forcing and allowing wall-normal perturbations at the wall to be nonzero and linked to the pressure gradient through a wall permeability $a$, nonlinear invariant solutions of the Navier-Stokes equations are found and continued towards low values of the Reynolds number. The solutions, having a reflect symmetry in the spanwise coordinate, set a new threshold in state space for the onset of exact coherent flow structures. The obtained traveling waves emerge from a saddle-node bifurcation at ${\text{Re}}_{SN}=225$ (based on the displacement thickness) for vanishing wall permeability. Increasing $a$ to small but finite values changes but slightly the value of ${\text{Re}}_{SN}$. In all cases, the obtained ${\text{Re}}_{SN}$ is below the lowest Reynolds number at which sustained turbulence is observed, namely, $\text{Re}\approx 270$ according to recent works. The corresponding waves in the Blasius boundary layer flow without suction exist from ${\text{Re}}_{SN}=496$, meaning that the asymptotic suction boundary layer might be more nonlinearly unstable (although more linearly stable) than the Blasius one. In the interval of Re studied it is found that the traveling waves occupy a region extending from the wall to the log-law region, with maximum root-mean-square velocities approaching those obtained by direct numerical simulations in the turbulent regime, especially for nonvanishing permeability. These solutions are found to be unstable, with steady leading modes, whose growth rate increases with the permeability and with the Reynolds number. When the trajectory escapes from these traveling waves along their unstable directions, transition to turbulence is observed even at Reynolds number as low as $\text{Re}=240$, suggesting that these solutions may play an important role in turbulent transition at low Reynolds numbers.

The near-wake dynamics developed behind a horizontal cylinder with wall proximity effects are elucidated from laboratory experiments and large-eddy simulations (LES). Fixed vertical gap to diameter ($G/D$) ratios of 0.5 and 1.0 were investigated for Reynolds numbers equal to 6 666, 10 000, and 13 333. The LES results agreed well with the experimental measurements for the time-averaged flow quantities and captured the upward flow motion developed over the lower half of the flow depth as a consequence of the near-wall effect. The presence of a narrow gap between the cylinder and the bed, i.e., $G/D=0.5$, significantly influenced the dynamics of the vortex generation and shedding which, in consequence, led to an increasingly pronounced asymmetric wake distribution with increasing Reynolds number. In the wider gap case of $G/D=1.0$, the wake remained relatively symmetrical, with reduced impact of ground proximity. Kelvin-Helmholtz instabilities developed in the upper and lower shear layers were shown to be decoupled as their instantaneous laminar-to-turbulent transition occurred at different downstream distances at any given time. Spanwise rollers were shown to form with an undulating pattern and presented irregularly located vortex dislocations. Furthermore, a ground vortex induced during the early stages of the lower roller's generation in the wake lifted off the ground and merged with the von Kármán vortices to form a single vortical structure. For $G/D=0.5$, a positive upwards force was present, and experimental and LES Strouhal number values ranged between 0.28–0.32, while computed drag coefficient values were lower than those typical for unbounded cylinder flows. As for $G/D=1.0$, Strouhal numbers decrease to a 0.26–0.30 range while drag coefficient increases, further demonstrating the effects on the cylinder wake structure dynamics due to the proximity to a solid boundary.

Rheology of a confined suspension of vesicles (model for blood) is analyzed numerically in two dimensions as a function of the viscosity contrast $\lambda$ (defined as the ratio between the inner and the outer viscosities, ${\eta }_{\mathrm{in}}$ and ${\eta }_{\mathrm{out}}$). We consider both the dilute, semidilute, and more concentrated regimes up to about $35\%$ of vesicle area fraction. This paper is a follow-up of our recent work [Phys. Rev. Fluids 3, 123601 (2018)], where we found that, depending on $\lambda$, the vesicle can either be centered or off-centered in a channel. Here we analyze in particular how the existence of the new attractor (off-centered solution) affects rheology. In the dilute regime, it is found that the effective viscosity corresponding to the off-centered solution may have a lower value than that of the centered solution. Moreover, the effective viscosity shows a discontinuity as a function of $\lambda$. This discontinuity is traced back to the existence of a saddle-node bifurcation of the lateral position. When the flow strength is increased, the viscosity behavior becomes continuous, owing to the evolution of the transition of the off-centered solution from a saddle-node to a pitchfork bifurcation. We analyze then rheology as a function of the suspension concentration $\phi$ for different values of $\lambda$. For large enough $\lambda$ the viscosity may be lower or larger than that corresponding to small $\lambda$, depending on initial configuration. There is a critical concentration beyond which the initial configuration is irrelevant, but still the behavior of the suspension viscosity with $\phi$ for low and large $\lambda$ are quite different both qualitatively and quantitatively. This is traced back to special spatial organization of the confined suspensions, which depends on $\lambda$.

An exact reduction of parametrically and periodically forced linear dynamical systems to modal dynamics in low-dimensional subspaces is possible when the operators involved commute with one another. We describe how a modal analysis may still be possible in the noncommuting case. The approach is illustrated with the determination of neutral curves for a stably and linearly stratified fluid in a square cavity under harmonically modulated gravitational forcing. In this example, the noncommutation of operators in the resulting Mathieu system is a direct consequence of the combined action of diffusion and wall confinement effects. An ansatz for modal diffusion is proposed, which enables remarkably predictive estimates of neutral curves via superposition of modal responses.

Suppose that viscous fluid is contained in the space between a fixed sphere $S_2$ and an interior sphere $S_1$ which moves with time-periodic velocity $\mathbf{U}\left(t\right)$ and angular velocity $\mathrm{\Omega }\left(t\right)$, with $〈\mathbf{U}\left(t\right)〉=〈\mathrm{\Omega }\left(t\right)〉=0$. It is shown that, provided this motion is chiral in character, it can drive a flow that exerts a nonzero torque on $S_2$. Thus angular momentum can be transferred through this mechanism. In the Appendix, it is shown why lubrication theory does not apply to this problem, even in the limit when the spheres make instantaneous contact.

A time-evolution of a slightly rarefied gas from a uniform equilibrium state at rest is investigated on the basis of the linearized Boltzmann equation under the acoustic time scaling. By a systematic asymptotic analysis, linearized Euler sets of equations and acoustic-boundary-layer equations are derived, together with their slip and jump boundary conditions, as well as the correction formula in the Knudsen layer. Analysis is done up to the first order of the Knudsen number ($\mathrm{Kn}$), with ${\mathrm{Kn}}^{1/2}$ being the small parameter. Several rarefaction effects, which are known as the effects of the second order in $\mathrm{Kn}$ in the diffusion scaling, are enhanced to be of the first order in $\mathrm{Kn}$. This is because the variation of the macroscopic quantities along the normal direction is steep in the boundary layer and the compressibility of the gas is comparatively strong. The occurrence of secular terms associated with the Hilbert expansion is pointed out and a remedy for it is also given. Finally, as an application example, a sound propagation in a half space caused by a sinusoidal oscillation of flat boundary is examined on the basis of the Bhatnagar–Gross–Krook equation. The asymptotic solution agrees well with the direct numerical solution.

We utilize the incompressible, Hall-magnetohydrodynamics (MHD) model for conducting fluids to investigate the effect of Hall current on the stability of an impulsively accelerated, perturbed density interface, or contact discontinuity (CD) separating two fluids in the presence of a background magnetic field. This is used as a simple model, in a conducting fluid, of a Richtmyer-Meshkov type flow that is characterized in a neutral fluid by a shock-wave-density-interface interaction. Two versions of the Hall-MHD equations are explored. In the first, the ions are treated as an incompressible fluid but the electron gas retains its compressibility, while for the second version the incompressible limit for both species is invoked. The linearized equations of motion are first formulated for a sinusoidal interface perturbation and then solved as an initial-value problem using a Laplace transform method with general numerical inversion but with analytical inversion for some limiting-parameter cases. While the field equations are identical for both Hall-MHD models, the CD-jump conditions differ leading to qualitatively similar but quantitatively different CD dynamics. For both models, the presence of the magnetic field is found to suppress the incipient interfacial growth associated with neutral-gas, Richtmyer-Meshkov instability (RMI). When the ion skin depth is finite, the vorticity dynamics that drive the suppression of the RMI differ markedly from the ideal MHD, RMI flow. On the interface, the Hall-MHD description allows the presence of a tangential slip velocity which leads to finite circulation deposition. Away from the interface, vorticity is produced by the perturbed magnetic fields and transported to infinity by a dispersive wave system. This leads to decay of the velocity slip at the interface with the effect that interface growth remains bounded but distorted by damped oscillations associated with the ion cyclotron effect. The flow behavior for several limits of the ion skin depth and the Larmor radius is explored. Specific comparisons with the results from both models against ideal MHD are presented.

All the methods which estimate the unperturbed fluid flow velocity relying on particle suspensions address the same question: How can the fluid velocity be computed measuring the particles' trajectory and/or their velocities? The tracking of a few large density-mismatched particles is here used to efficiently and accurately reconstruct the background fluid flow. Approximating the particulate phase space and taking the limit of vanishing Stokes number $\text{St}\to 0$, we retrieve the background flow for three test cases: a shear flow near a wall, a rigid-body vortex, and a strained vortex. The major advantages and the potentials of this approach are discussed in the end, highlighting how to overcome the classic shortcomings of experimental measurements faced for near-boundaries particle tracking.

The dynamics of an adhesive two-dimensional vesicle doublet under various flow conditions is investigated numerically using a high-order, adaptive-in-time boundary integral method. In a quiescent flow, two nearby vesicles move slowly toward each other under the adhesive potential, pushing out fluid between them to form a vesicle doublet at equilibrium. A lubrication analysis on such draining of a thin film gives the dependencies of draining time on adhesion strength and separation distance, which are in good agreement with numerical results. In a planar extensional flow, we find that a stable vesicle doublet forms only when two vesicles collide head-on around the stagnation point. In a microfluid trap where the stagnation of an extensional flow is dynamically placed in the middle of a vesicle doublet through an active control loop, novel dynamics of a vesicle doublet are observed. Numerical simulations show that there exists a critical extensional flow rate above which adhesive interaction is overcome by the diverging stream, thus providing a simple method to measure the adhesion strength between two vesicle membranes. In a planar shear flow, numerical simulations reveal that a vesicle doublet may form provided that the adhesion strength is sufficiently large at a given vesicle reduced area. Once a doublet is formed, its oscillatory dynamics is found to depend on the adhesion strength and their reduced area. Furthermore the effective shear viscosity of a dilute suspension of vesicle doublets is found to be a function of the reduced area. Results from these numerical studies and analysis shed light on the hydrodynamic and rheological consequences of adhesive interactions between vesicles in a viscous fluid.

We examine the transport in a homogeneous porous medium of a finite slice of a solute which adsorbs on the porous matrix following a Langmuir adsorption isotherm and can influence the dynamic viscosity of the solution. In the absence of any viscosity variation, the Langmuir adsorption induces the formation of a shock layer wave at the frontal interface and of a rarefaction wave at the rear interface of the sample. For a finite width sample, these waves interact after a given time that varies nonlinearly with the adsorption properties to give a triangle-like concentration profile in which the mixing efficiency of the solute is larger in comparison to the linear or no-adsorption cases. In the presence of a viscosity contrast such that a less viscous carrier fluid displaces the more viscous finite slice, viscous fingers are formed at the rear rarefaction interface. The fingers propagate through the finite sample to preempt the shock layer at the viscously stable front. In the reverse case, i.e., when the shock layer front features viscous fingering, the fingers are unable to intrude through the rarefaction zone and the qualitative properties of the expanding rear wave are preserved. A nonmonotonic dependence with respect to the Langmuir adsorption parameter $b$ is observed in the onset time of interaction between the nonlinear waves and viscous fingering. The coupled effect of viscous fingering at the rear interface and of Langmuir adsorption provides a powerful mechanism to enhance the mixing efficiency of the adsorbed solute.

We perform fully Eulerian numerical simulations of an initially spherical hyperelastic particle suspended in a Newtonian pressure-driven flow in a cylindrical straight pipe. We study the full particle migration and deformation for different Reynolds numbers and for various levels of particle elasticity, to disentangle the interplay of inertia and elasticity on the particle focusing. We observe that the particle deforms and undergoes a lateral displacement while traveling downstream through the pipe, finally focusing at the pipe centerline. We note that the migration dynamics and the final equilibrium position are almost independent of the Reynolds number, while they strongly depend on the particle elasticity; in particular, the migration is faster as the elasticity increases (i.e., the particle is more deformable), with the particle reaching the final equilibrium position at the centerline in shorter times. Our simulations show that the results are not affected by the particle initial conditions, position, and velocity. Finally, we explain the particle migration by computing the total force acting on the particle and its different components, viscous and elastic.

The self-oscillations observed in the single-branch pulsating heat pipe (SBPHP) are explained by showing the existence of a mechanical resonator excited by a self-driving force (feedback) through linear stability analysis, with experimental validation. The SBPHP is a tube closed at one end which is initially filled with water. The closed end is heated and a vapor bubble forms and reaches an equilibrium size. From this stable state, increasing the temperature of the heater temperature beyond a threshold leads to oscillations of the liquid plug sustained over time. We would like to understand where these oscillations come from and why they do not vanish over time due to the friction. A model of this system is formulated such that it can then be linearized and solved analytically for the motion over time. The solution shows that the coupling of the spring effect of the vapor and the inertia of the liquid plug leads to a spring-mass system, which can oscillate after a small perturbation. The evaporation and condensation taking place as the oscillations occur produce a change of the vapor pressure. The resulting force on the liquid plug is positive feedback; it injects energy into the spring-mass system and makes the oscillations unstable (startup) if greater than the friction. A criterion for startup is formally provided in the form of a dimensionless instability number derived from the model. An experimental apparatus is used to validate the theoretical prediction. The predicted effects of the tube's axial temperature gradient (destabilizing), of a thin film thermal resistance (stabilizing), and of the external pressure (stabilizing) are validated. The mass of the vapor and the friction force are measured during the startup and are shown to act as feedback and dissipation, respectively, as predicted by the theory. It is concluded that the main physical mechanism behind the instability in the SBPHP is now well understood. This provides a theoretical basis for the further development of pulsating heat pipes increasingly used for thermal management of electronics and harvesting of waste heat.

We investigate ambient fluid entrainment and near-field flow characteristics of a free surface plunging jet for five Reynolds numbers ranging from 3000 to 10 000 using time-resolved stereo particle image velocimetry. We present time-averaged velocities, rms velocity fluctuations, mean entrainment, and instantaneous flow structures in the near-field for plunging jets, and compare the results with previous studies on free jets. It is found that additional instabilities accumulated from the free surface facilitate vortex development, leading to early initiation of bulk fluid entrainment, and finally result in expedited closure of the shear layer, which is absent for submerged free jets. These primary vortices are formed right below the free surface and disintegrate into secondary structures at axial locations that are upstream compared to those of free jets. As a result, plunging jets have a smaller potential core length, exhibit earlier decay of the mean centerline velocity and entrain more liquid from the ambient. Moreover, the peak rms velocity fluctuations occur at locations significantly more upstream than in free jets. For the plunging jet case at $\mathrm{Re}=3000$, faster jet decay, higher levels of turbulent intensity in the near field, and augmented mass entrainment result from strong primary vortices that give the turbulent-nonturbulent interface its convoluted shape, which facilitates both bulk entrapment of ambient fluid and small-scale nibbling because of larger surface area. At higher Reynolds numbers, primary vortices are smaller in size, weak in swirling strength, and disintegrate prematurely, resulting in suppressed mixing and reduced entrainment efficiency.

This paper investigates the thermal instability in a horizontal porous annulus with an external wavy wall. The porous matrix is supposed to be filled by an incompressible fluid. The model that we consider includes the heat equation and the hydrodynamics equations under the Darcy law and Boussinesq approximation. The derived model with the temperature-stream function is solved numerically using the alternating direction implicit method. Our numerical results indicate that the heat transfer and the convective instability depend strongly on the waviness of the external cylinder. The results of this paper confirm that the heat transfer is enhanced when the waviness amplitude increases. It is noticed that the thermoconvective instabilities are strongly affected by the undulation number.

The dynamics of a passive scalar plume in a turbulent boundary layer is experimentally investigated via vertical turbulent transport time series. Experimental data are acquired in a rough-wall turbulent boundary layer that develops in a recirculating wind tunnel setup. Two source sizes in an elevated position are considered in order to investigate the influence of the emission conditions on the plume dynamics. The analysis is focused on the effects of the meandering motion and the relative dispersion of the plume with respect to its center of mass. First, classical statistics are investigated. We found that (in accordance with previous studies) the meandering motion is the main factor responsible for differences in the variance and intermittency, as well as the kurtosis and power spectral density, between the two source sizes. On the contrary, the mean and the skewness are slightly affected by the emission conditions. With the aim to characterize the temporal structure of the turbulent transport series, the visibility algorithm is exploited to carry out a complex network-based analysis. In particular, two network metrics—the average peak occurrence and the assortativity coefficient—are analyzed, as they are able to capture the temporal occurrence of extreme events and their relative intensity in the series. The effects of the meandering motion and the relative dispersion of the plume are discussed in view of the network metrics, revealing that a stronger meandering motion is associated with higher values of both the average peak occurrence and the assortativity coefficient. The network-based analysis advances the level of information of classical statistics by characterizing the impact of the emission conditions on the temporal structure of the signals in terms of extreme events (namely, peaks and pits) and their relative intensity. In this way, complex networks provide—through the evaluation of network metrics—an effective tool for time-series analysis of experimental data.

Stratified turbulence shows scale- and direction-dependent anisotropy and the coexistence of weak turbulence of internal gravity waves and strong turbulence of eddies. Straightforward application of standard analyses developed in isotropic turbulence sometimes masks important aspects of the anisotropic turbulence. To capture detailed structures of the energy distribution in the wave-number space, it is indispensable to examine the energy distribution with nonintegrated spectra by fixing the codimensional wave-number component or in the two-dimensional domain spanned by both the horizontal and the vertical wave numbers. Indices which separate the range of the anisotropic weak-wave turbulence in the wave-number space are proposed based on the decomposed energies. In addition, the dominance of the waves in the range is also verified by the small frequency deviation from the linear dispersion relation. In the wave-dominant range, the linear wave periods given by the linear dispersion relation are smaller than approximately one third of the eddy-turnover time. The linear wave periods reflect the anisotropy of the system, while the isotropic Brunt-Väisälä period is used to evaluate the Ozmidov wave number, which is necessarily isotropic. It is found that the time scales in consideration of the anisotropy of the flow field must be appropriately selected to obtain the critical wave number separating the weak-wave turbulence.

The dissolution of minerals into water becomes significant in geomorphology when the erosion rate is controlled by the hydrodynamic transport of the solute. Even in the absence of an external flow, dissolution itself can induce a convective flow due to the action of gravity. Here we perform a study of the physics of solutal convection induced by dissolution. We simulate numerically the hydrodynamics and the solute transport in a two-dimensional geometry, corresponding to the case where a soluble body is suddenly immersed in a quiescent solvent. We identify three regimes. At a short timescale, a concentrated boundary layer grows by diffusion at the interface. After a finite onset time, the thickness and the density reach critical values, which starts the destabilization of the boundary layer. Finally, the destabilization is such that we observe the emission of intermittent plumes. This last regime is quasistationary: The structure of the boundary layer and the erosion rate fluctuate around constant values. Assuming that the destabilization of the boundary layer occurs at a specific value of the solutal Rayleigh number, we derive scaling laws for both fast and slow dissolution kinetics. Our simulations confirm this scenario by validating the scaling laws for both onset and the quasistationary regime. We find a constant value of the Rayleigh number during the quasistationary regime, showing that the structure of the boundary layer is well controlled by the solutal convection. We apply the scaling laws previously established to the case of real dissolving minerals. We predict the typical dissolution rate in the presence of solutal convection. Our results suggest that solutal convection could occur in more natural situations than expected. Even for minerals with a quite low saturation concentration, the erosion rate would increase as the dissolution would be controlled by the hydrodynamics.

We report an extensive theoretical and numerical study of gravitational settling of small particles in a stratified fluid at rest. The particle motion creates a flow that advects the stratified agent, which in turn impacts the velocity by buoyancy. A peculiar insulation flow also exists when a particle and fluid at infinity are at rest, screening the particle from the outside gradients. We derive an integral representation for the linear coupled flow that holds at low Reynolds and Péclet numbers. The representation demonstrates that the far flow contains a previously unnoticed term that is produced by the thermal component of the fundamental solution. We obtain nontrivial symmetry relations that constitute a form of the Onsager reciprocal relations. Stratification is a singular perturbation: however small it is, far from the particle the flow is fast decaying and does not obey the slow power-law decay of the Stokes flow at zero stratification. We derive the enhancement of the drag force due to the stratification by adopting the integral equation on the surface traction. This allows one to find the force directly, circumventing finding the flow whose calculation demands the matched asymptotic expansions that complicated previous studies. In this way we are able to extend the domain of validity of the drag formula by orders of magnitude. We confirm the predictions by numerical simulations at low Reynolds numbers. We also performed simulations for a range of non-small Reynolds numbers where the flow is nonlinear, but the Reynolds number is not too large. The considered range of parameters demonstrates that inclusion of stratification might be necessary for correct prediction of the sedimentation velocity of plankton particles and small organic particles of marine snow. We provide the settling velocity of Volvox as an example. We sum up our observations by deriving an empirical fitting formula for the drag coefficient. Finally, we discuss the observability of the insulating flow around a floating body.