Induced charge electrophoresis of a conducting cylinder suspended in a nonconducting cylindrical pore is theoretically analyzed and a micromotor is proposed that utilizes the cylinder rotation. The cylinder velocities are analytically obtained in the Dirichlet and the Neumann boundary conditions of the electric field on the cylindrical pore. The results show that the cylinder not only translates but also rotates when it is eccentric with respect to the cylindrical pore. The influences of a number of parameters on the cylinder velocities are characterized in detail. The cylinder trajectories show that the cylinder approaches and becomes stationary at certain positions within the cylindrical pore. The proposed micromotor is capable of working under a heavy load with a high rotational velocity when the eccentricity is large and the applied electric field is strong.

The description of hydrodynamic interactions between a particle and the surrounding liquid, down to the nanometer scale, is of primary importance since confined liquids are ubiquitous in many natural and technological situations. In this paper we combine three nonconventional atomic force microscopes to study hydrodynamics around micro- and nanocylinders. These complementary methods allow the independent measurement of the added mass and friction terms over a large range of probe sizes, fluid viscosities, and solicitation conditions. A theoretical model based on an analytical description of the velocity field around the probe shows that the friction force depends on a unique parameter, the ratio of the probe radius to the thickness of the viscous boundary layer. We demonstrate that the whole range of experimental data can be gathered in a master curve, which is well reproduced by the model. This validates the use of these atomic force microscopy modes for a quantitative study of hydrodynamics and opens the way to the investigation of other sources of dissipation in simple and complex fluids down to the submicron scale.

We present a complete theoretical framework for the axial dispersion of a Brownian colloidal suspension confined in a parallel plate channel, extending the Taylor-Aris treatment to particles with diameters comparable to the channel width. The theoretical model incorporates the effects of confinement on the colloid distribution, corrections to the velocity profile due to the effects of colloid concentration on the suspension viscosity, and position-dependent diffusivities. We test the theoretical model using explicit-solvent molecular dynamics simulations that fully incorporate hydrodynamic correlations and thermal fluctuations and obtain good quantitative agreement between theory and simulations. We find that the nonuniform colloid distributions that arise in confinement due to excluded volume between the colloids and channel walls significantly impact the axial dispersion.

In rarefied gases, mass and heat transport processes interfere with each other, leading to the mechano-caloric effect and thermo-osmotic effect, which are of interest to both theoretical study and practical applications. We employ the unified gas-kinetic scheme to investigate these cross coupling effects in gas flows in micro-channels. Our numerical simulations cover channels of planar surfaces and also channels of ratchet surfaces, with Onsager's reciprocal relation verified for both cases. For channels of planar surfaces, simulations are performed in a wide range of Knudsen number, and our numerical results show good agreement with the literature results. For channels of ratchet surfaces, simulations are performed for both the slip and transition regimes, and our numerical results not only confirm the theoretical prediction [Phys. Rev. Lett. 107, 164502 (2011)] for the Knudsen number in the slip regime but also show that the off-diagonal kinetic coefficients for cross coupling effects are maximized at a Knudsen number in the transition regime. Finally, a preliminary optimization study is carried out for the geometry of Knudsen pump based on channels of ratchet surfaces.

This study presents a direct numerical simulation analysis of the force distribution within a cluster of monodisperse spherical particles. A direct forcing immersed boundary method is used to calculate the forces on individual particles for a volume fraction range of $0.11\le \varphi \le 0.44$ and a Reynolds number range of $1.47\le \mathrm{Re}\le 636$. The hydrodynamic streamwise force is shown to have a normal distribution with a standard deviation ratio to the mean drag that decreases with increasing volume fraction and ranges between 17% and 26%. The lift forces also follow a normal distribution that has a significant standard deviation to mean drag ratio of around 14.5%, which does not vary significantly with the Reynolds number and volume fraction. A model is introduced that adds the identified normal distribution of the forces to the quasisteady force used in point-particle models. A nonisotropic method of defining spatial parameters is presented. It highlights the contribution of each parameter to the variation of the forces on each particle. The results show that the drag is influenced by the closest four to eight neighboring spheres. The drag force is highly dependent on the streamwise distances of the spheres located upstream. For low volume fractions and Reynolds number, the lateral distances of the spheres located downstream also have a significant contribution to those variations. The results also show that the lateral force variation is mostly dictated by the lateral distance of one to two spheres located upstream of each sphere.

We study the dynamics of evaporating ethanol films deposited by a receding liquid meniscus. The films are surrounded by pure vapor in a capillary heated above the saturation temperature. We observe the substrate dewetting with the dewetting ridge in spite of the complete wetting at equilibrium. The dewetting is caused by a high contact angle ($\sim {30}^{\circ }$) induced by evaporation. The obtained values agree with a theory proposed earlier. The film shape is measured with both grid deflection technique and interferometry. The phenomenon is convenient to observe inside a capillary with an axial thermal gradient. When the capillary is closed at one end and open at another to a constant pressure reservoir, the meniscus oscillations are known to appear spontaneously. Such a system is the simplest version of an industrial device called a pulsating heat pipe. The effect is general and can be used in any system to control the wetting properties.

A simplified model is developed for intrusive gravity currents propagating along the interface of a two-layer stratified ambient. The model is based on the conservation of mass and vorticity and it does not require any empirical closure assumptions. A parametric study conducted with this model reproduces the correct behavior in various limits and is consistent with previously reported experimental observations. Specifically, it predicts the formation of equilibrium intrusions when the intrusion density equals the depth-weighted mean density of the two ambient layers. It furthermore demonstrates the existence of nonsmooth limits under certain conditions. An energy analysis shows that under nonequilibrium conditions the intrusion gains energy. The predictions by the parametric study are furthermore compared to two-dimensional direct numerical simulation results and very good agreement is observed with regard to all flow properties.

Wind tunnel measurements in the wake of an axial flow miniature wind turbine provide evidence of large-scale motions characteristic of wake meandering [Howard et al., Phys. Fluids 27, 075103 (2015)]. A numerical investigation of the wake, using immersed boundary large eddy simulations able to account for all geometrical details of the model wind turbine, is presented here to elucidate the three-dimensional structure of the wake and the mechanisms controlling near and far wake instabilities. Similar to the findings of Kang et al. [Kang et al., J. Fluid Mech. 744, 376 (2014)], an energetic coherent helical hub vortex is found to form behind the turbine nacelle, which expands radially outward downstream of the turbine and ultimately interacts with the turbine tip shear layer. Starting from the wake meandering filtering used by Howard et al., a three-dimensional spatiotemporal filtering process is developed to reconstruct a three-dimensional meandering profile in the wake of the turbine. The counterwinding hub vortex undergoes a spiral vortex breakdown and the rotational component of the hub vortex persists downstream, contributing to the rotational direction of the wake meandering. Statistical characteristics of the wake meandering profile, along with triple decomposition of the flow field separating the coherent and incoherent turbulent fluctuations, are used to delineate the near and far wake flow structures and their interactions. In the near wake, the nacelle leads to mostly incoherent turbulence, while in the far wake, turbulent coherent structures, especially the azimuthal velocity component, dominate the flow field.

Available high-quality numerical simulation data are used to investigate and characterize the kinetic energy budgets for fully developed turbulent flow in pipes and channels, and in the zero-pressure gradient turbulent boundary layer. The mean kinetic energy equation in these flows is empirically and analytically shown to respectively exhibit the same four-layer leading-order balance structure as the mean momentum equation. This property of the mean kinetic energy budget provides guidance on how to group terms in the more complicated turbulence and total kinetic energy budgets. Under the suggested grouping, the turbulence budget shows either a two- or three-layer structure (depending on channel or pipe versus boundary layer flow), while the total kinetic energy budget exhibits a clear four-layer structure. These layers, however, differ in position and size and exhibit variations with friction Reynolds number (${\delta }^{+}$) that are distinct from the layer structure associated with the mean dynamics. The present analyses indicate that each of the four layers is characterized by a predominance of a reduced set of the grouped terms in the governing equation. The width of the third layer is mathematically reasoned to scale like ${\delta }^{+}-\sqrt{{\delta }^{+}}$ at finite Reynolds numbers. In the boundary layer the upper bounds of both the second and third layers convincingly merge under this normalization, as does the width of the third layer. This normalization also seems to be valid for the width of the third layer in pipes and channels, but only for ${\delta }^{+}>1000$. The leading-order balances in the total kinetic energy budget are shown to arise from a nontrivial interweaving of the mean and turbulence budget contributions with distance from the wall.

Nonequilibrium turbulent wake scalings are not the preserve of irregular (fractal-like/multiscale) plates but appear to be universal, as they also hold for regular plates over a very substantial downstream distance.

From experiments of axially homogeneous turbulent convection in a vertical tube using heat (Prandtl number $\text{Pr}\simeq 6$) and brine ($\text{Pr}\simeq 600$) we show that at sufficiently high Rayleigh numbers (${\text{Ra}}_g$), the Nusselt number ${\text{Nu}}_g\sim {\left({\text{Ra}}_g\text{Pr}\right)}^{1/2}$, which corresponds to the so-called ultimate regime scaling. In heat experiments below certain ${\text{Ra}}_g$, however, there is transition to a new regime, ${\text{Nu}}_g\sim {\left({\text{Ra}}_g\text{Pr}\right)}^{0.3}$. This transition also seems to exist in earlier reported data for $\text{Pr}=1$ and $\text{Pr}\simeq 600$, at different ${\text{Ra}}_g$. However, the transition occurs at a single Grashof number, ${\text{Gr}}_{gc}\simeq 1.6\times {10}^5$, and unified flux scalings for $\text{Pr}\ge 1$, ${\text{Nu}}_g/\text{Pr}\sim {\text{Gr}}_g^{0.3}$, and ${\text{Nu}}_g/\text{Pr}\sim {\text{Gr}}_g^{1/2}$ can be given for the two regimes.

The hydrodynamic stability of stratifications made between miscible fluids having large differences in viscosity is experimentally investigated in square microchannels. Parallel fluid layers with a fast central stream and a slow sheath flow are produced by focusing a low-viscosity fluid into a high-viscosity fluid in a straight microchannel. Three regimes are identified and include diffusive, stable, and unstable flow patterns. In the unstable regime, coupled interfacial waves are seen to significantly disrupt strata when the Reynolds number associated with the low-viscosity stream is above 90. Several functional relationships are developed for the stratification width, propagating celerity, wavelength, amplitude, and frequency of interfacial waves over a range of viscosities and flow rates. We demonstrate, in particular, the wave phase locking for small central streams and show the production of high-viscosity fluid ligaments at the wave crests. In this case, a minute amount of high-viscosity fluid is entrained and blended into the low-viscosity fluid stream, thereby providing an original in-line mixing method for continuously adding a viscosifier to a thin fluid in microchannels.

We present a study of inertial modes in a differentially rotating spherical shell (spherical Couette flow) experiment with a radius ratio of $\eta =1/3$. Inertial modes are Coriolis-restored linear wave modes which often arise in rapidly rotating fluids. Recent experimental work has shown that inertial modes exist in a spherical Couette flow for ${\mathrm{\Omega }}_i<{\mathrm{\Omega }}_o$, where ${\mathrm{\Omega }}_i$ and ${\mathrm{\Omega }}_o$ are the inner and outer sphere rotation rate. A finite number of particular inertial modes has previously been found. By scanning the Rossby number from $-2.5<\text{Ro}=({\mathrm{\Omega }}_i-{\mathrm{\Omega }}_o)/{\mathrm{\Omega }}_o<0$ at two fixed ${\mathrm{\Omega }}_o$, we report the existence of similar inertial modes. However, the behavior of the flow described here differs significantly from previous spherical Couette experiments. We show that the kinetic energy of the dominant inertial mode dramatically increases with decreasing Rossby number, which eventually leads to a wave breaking and an increase of small-scale structures at a critical Rossby number. Such a transition in a spherical Couette flow has not been described before. The critical Rossby number scales with the Ekman number as $E^{1/5}$. Additionally, the increase of small-scale features beyond the transition transfers energy to a massively enhanced mean flow around the tangent cylinder. In this context, we discuss an interaction between the dominant inertial modes with a geostrophic Rossby mode exciting secondary modes whose frequencies match the triadic resonance condition.

The control over stationary liquid thread fragmentation in confined co-flows is a key issue for the processing and transport of fluids in (micro-)ducts. Confinement indeed strongly enhances the stability of capillary threads, and also induces steric and hydrodynamic feedback effects on diphasic flows. We investigate the thread-to-droplet transition within the confined environment of a microchannel by using optocapillarity, i.e., interface stresses driven by light, as a wall-free constriction to locally flow focus stable threads in a tunable way, pinch them, and force their fragmentation. Above some flow-dependent onset in optical forcing, we observe a dynamic transition alternating between continuous (thread) and fragmented (droplets) states and show a surprisingly gradual thread-to-droplet transition when increasing the amplitude of the thread constriction. This transition is interpreted as an evolution from a convective to an absolute instability. Depending on the forcing amplitude, we then identify and characterize several stable fragmented regimes of single and multiple droplet periodicity (up to period-8). These droplet regimes build a robust flow-independent bifurcation diagram that eventually closes up, due to the flow confinement, to a monodisperse droplet size, independent of the forcing and close to the most unstable mode expected from the Rayleigh-Plateau instability. This fixed monodispersity can be circumvented by temporally modulating the optocapillary coupling, as we show that fragmentation can then occur either by triggering again the Rayleigh-Plateau instability when the largest excitable wavelength is larger than that of the most unstable mode, or as a pure consequence of a sufficiently strong optocapillary pinching. When properly adjusted, this modulation allows us to avoid the transient reforming and multidisperse regimes, and thereby to reversibly produce stable monodisperse droplet trains of controlled size. By actuating local flow focusing in time and amplitude, optocapillarity thus proves to be an efficient way to characterize and understand the thread-to-droplet transition in microchannels and to advance channel constriction strategies for the production of tunable monodisperse droplets when the overall confinement is important.

The coupled interaction between a sloshing fluid in a partially filled container suspended as a bifilar pendulum is investigated. The sloshing fluid has a free surface upon which waves are generated; this fluid contributes a restoring force to the container motion by its weight through the wire suspensions and the free-surface waves may either enhance or diminish the restoring force through hydrodynamic interaction with the container walls. Results are presented for inviscid irrotational sloshing in both a two-dimensional hyperbolic container and a three-dimensional hyperboloid container. Frequency results for the coupled system are presented for various pendulum lengths and fluid fill heights. It is found that for long pendulum lengths the container and the fluid oscillate in a synchronous motion when the vessel is released with typical experimental initial conditions, but for pendulum lengths below a given threshold the container and fluid oscillate asynchronously from the same initial condition.

In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity fluctuations $〈exp\left(q{u}_z^{+}\right)〉$ develop power-law scaling as a function of the wall normal distance $z/\delta$. Here $u$ is the streamwise velocity fluctuation, $+$ indicates normalization in wall units (averaged friction velocity), $z$ is the distance from the wall, $q$ is an independent variable, and $\delta$ is the boundary layer thickness. Previous work has shown that this power-law scaling exists in the log-region $3{\text{Re}}_{\tau }^{0.5}\lesssim z^{+},z\lesssim 0.15\delta$ where ${\text{Re}}_{\tau }$ is the friction velocity-based Reynolds number. Here we present empirical evidence that this self-similar scaling can be extended, including bulk and viscosity-affected regions $30<z^{+},z<\delta$, provided the data are interpreted with the Extended-Self-Similarity (ESS), i.e., self-scaling of the MGFs as a function of one reference value, $q_o$. ESS also improves the scaling properties, leading to more precise measurements of the scaling exponents. The analysis is based on hot-wire measurements from boundary layers at ${\text{Re}}_{\tau }$ ranging from 2700 to $13000$ from the Melbourne High-Reynolds-Number-Turbulent-Boundary-Layer-Wind-Tunnel. Furthermore, we investigate the scalings of the filtered, large-scale velocity fluctuations $u_z^L$ and of the remaining small-scale component, $u_z^S=u_z-u_z^L$. The scaling of $u_z^L$ falls within the conventionally defined log region and depends on a scale that is proportional to $l^{+}\sim {\text{Re}}_{\tau }^{1/2}$; the scaling of $u_z^S$ extends over a much wider range from $z^{+}\approx 30$ to $z\approx 0.5\delta$. Last, we present a theoretical construction of two multiplicative processes for $u_z^L$ and $u_z^S$ that reproduce the empirical findings concerning the scalings properties as functions of $z^{+}$ and in the ESS sense.

Despite a substantial body of literature dealing with the effects of free-stream turbulence (FST) on two-dimensional square prism, there remain some open questions regarding the influence of the bluff body shear layer development in a highly perturbed environment and the resulting impact on bluff body flow characteristics. Accordingly, flows with ambient and enhanced FST were studied at ${\text{Re}}_D=5.0\times {10}^4$ using long-duration time-resolved particle image velocimetry (PIV). The data indicate a narrowing and lengthening of the mean wake and an accompanying rise in base pressure. Using triple decomposition, the underlying dynamics of the wake reveal a streamwise lengthening of the individual von Kármán vortex structures, complementing the increase in mean wake length. Close inspection of the shear layer region, in the presence of FST, indicates a substantial increase in curvature towards the body but no pronounced increase in the growth rate. The loci of maximum turbulent kinetic energy and spanwise vorticity in the shear layer region further reveal that the most pronounced changes occur during the very initial stages follow separation. Inspection of a series of instantaneous PIV fields of $Q$ criterion show that the conventional transition pathway, via the formation and subsequent pairing of the Kelvin-Helmholtz (KH) vortices, is bypassed. The KH vortices are observed to immediately cluster and amalgamate before breaking into smaller random eddies. The bypass transition is followed by shear layer reattachment in some cases. This is considered a primary mechanism responsible for the reported changes in the global flow characteristics and the altered wake dynamics. Furthermore, a quantitative definition of the diffusion length is implemented for the square prism wake and its relationship to the Strouhal number and wake formation length is considered.

We have used the vortex filament method to numerically investigate the interactions between pairs of quantized vortex rings that are initially traveling in the same direction but with their axes offset by a variable impact parameter. The interaction of two circular rings of comparable radii produces outcomes that can be categorized into four regimes, dependent only on the impact parameter; the two rings can either miss each other on the inside or outside or reconnect leading to final states consisting of either one or two deformed rings. The fraction of energy that went into ring deformations and the transverse component of velocity of the rings are analyzed for each regime. We find that rings of very similar radius only reconnect for a very narrow range of the impact parameter, much smaller than would be expected from the geometrical cross-section alone. In contrast, when the radii of the rings are very different, the range of impact parameters producing a reconnection is close to the geometrical value. A second type of interaction considered is the collision of circular rings with a highly deformed ring. This type of interaction appears to be a productive mechanism for creating small vortex rings. The simulations are discussed in the context of experiments on colliding vortex rings and quantum turbulence in superfluid helium in the zero-temperature limit.

We revisit Taylor's experiment investigating the evolution of a blob of dye in a periodically sheared suspension of non-Brownian particles. Above a critical strain amplitude, particulate suspensions are subject to phase transition where reversibility is lost and particles fail to return to their original positions. We investigate the effect of this transition on the dispersion of a blob of dye. Beyond the critical strain, the dispersion of the blob is found to increase significantly. The dispersion coefficient of the blob of dye is measured and compared to the self-diffusivity coefficient of the particles.

The linear dynamics of perturbations in smooth shear flows covers the transient exchange of energies between (1) the perturbations and the basic flow and (2) different perturbations modes. Canonically, the linear exchange of energies between the perturbations and the basic flow can be described in terms of the Orr and the lift-up mechanisms, correspondingly for two-dimensional (2D) and three-dimensional (3D) perturbations. In this paper the mechanical basis of the linear transient dynamics is introduced and analyzed for incompressible plane constant shear flows, where we consider the dynamics of virtual fluid particles in the framework of plane perturbations (i.e., perturbations with plane surfaces of constant phase) for the 2D and 3D case. It is shown that (1) the formation of a pressure perturbation field is the result of countermoving neighboring sets of incompressible fluid particles in the flow, (2) the keystone of the energy exchange mechanism between the basic flow and perturbations is the collision of fluid particles with the planes of constant pressure in accordance with the classical theory of elastic collision of particles with a rigid wall, making the pressure field the key player in this process, (3) the interplay of the collision process and the shear flow kinematics describes the transient growth of plane perturbations and captures the physics of the growth, and (4) the proposed mechanical picture allows us to reconstruct the linearized Euler equations in spectral space with a time-dependent shearwise wave number, the linearized Euler equations for Kelvin modes. This confirms the rigor of the presented analysis, which, moreover, yields a natural generalization of the proposed mechanical picture of the transient growth to the well-established linear phenomenon of vortex–wave-mode coupling.