Physics of Fluids (PHYS FLUIDS)

We experimentally investigated molecular effects of the slip/no-slip boundary condition of Newtonian liquids in micro-and nanochannels as small as 350 nm. The slip was measurable for channels smaller than approximately 2 mu m. The amount of slip is found to be independent of the channel size, but is a function of the shear rate, the type of liquid (polar or nonpolar molecular structure), and the morphology of the solid surface (molecular-level smoothness). (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3006031]

In the present work, we revisit the temporal and the spatio-temporal stability of confined plane wakes under the perspective of the counterpropagating Rossby waves (CRWs). Within the context of broken line velocity profiles, each vorticity discontinuity can be associated to a counterpropagating Rossby wave. In the case of a wake modeled by a broken line profile, the interaction of two CRWs is shown to originate in a shear instability. Following this description, we first recover the stability results obtained by Juniper [J. Fluid Mech. 590, 163-185 (2007)]10.1017/S0022112007007975 and Biancofiore and Gallaire [Phys. Fluids 23, 034103 (2011)]10.1063/1.3554764 by means of the classical normal mode analysis. In this manner, we propose an explanation of the stabilizing influence of the confinement on the temporal stability properties. The CRW description further allows us to propose a new interpretation of the counterintuitive spatio-temporal destabilization in wake flows at moderate confinement noticed by Juniper [J. Fluid Mech. 565, 171-195 (2006)]10.1017/S0022112006001558: it is well predicted by the mean group velocity of the uncoupled CRWs.

This article covers several aspects of respiratory fluid mechanics that have been actively investigated by our group over the years. For the most part, the topics involve two-phase flows in the respiratory system with applications to normal and diseased lungs, as well as therapeutic interventions. Specifically, the topics include liquid plug flow in airways and at airway bifurcations as it relates to surfactant, drug, gene, or stem cell delivery into the lung; liquid plug rupture and its damaging effects on underlying airway epithelial cells as well as a source of crackling sounds in the lung; airway closure from "capillary-elastic instabilities," as well as nonlinear stabilization from oscillatory core flow which we call the "oscillating butter knife;" liquid film, and surfactant dynamics in an oscillating alveolus and the steady streaming, and surfactant spreading on thin viscous films including our discovery of the Grotberg-Borgas-Gaver shock.

An acoustic field is used to increase the critical heat flux (CHF) of a flat-boiling-heat-transfer surface. The increase is a result of the acoustic effects on the vapor bubbles. Experiments are performed to explore the effects of an acoustic field on vapor bubbles in the vicinity of a rigid-heated wall. Work includes the construction of a novel heater used to produce a single vapor bubble of a prescribed size and at a prescribed location on a flat-boiling surface for better study of an individual vapor bubble's reaction to the acoustic field. Work also includes application of the results from the single-bubble heater to a calibrated-copper heater used for quantifying the improvements in CHF.

We comment on the paper by Van Gorder ["Motion of a helical vortex filament in superfluid ${}^4$He under the extrinsic form of the local induction approximation", Phys. Fluids 25, 085101 (2013)]. We point out that the flow of the normal fluid component parallel to the vortex will often lead into the Donnelly-Glaberson instability, which will cause the amplification of the Kelvin wave. We explain why the comparison to local nonlinear equation is unreasonable, and remark that neglecting the motion in the $x$-direction is not reasonable for a Kelvin wave with an arbitrary wave length and amplitude. The correct equations in the general case are also derived.

This paper describes the creation, by temporal direct numerical simulation and the analysis based on the Reynolds stress transport equations, of a high-quality data set that represents the laminar-turbulent transition of a high-speed boundary-layer flow. Following Pruett and Zang (1992), and with the help of algorithmic refinements, the evolution of an axial, Mach 4.5 boundary-layer flow along a hollow cylinder is simulated numerically. Favre-averaged Reynolds stress transport equations are derived in generalized curvilinear coordinates and are then specialized to the cylindrical geometry at hand. Reynolds stresses and various turbulence quantities, such as turbulent kinetic energy and turbulent Mach number, are calculated from the numerical data at various stages of the transition process. The kinetic energy 'budgets' are constructed from the transport equations. Various contributing terms for the evolution of kinetic energy, like the rates of production and dissipation, transport, and diffusion, are presented. The compressible dissipation rate is small in comparison with the solenoidal dissipation rate for all times. The pressure-dilatation term is of the same order of magnitude as the compressible dissipation rate.

Viscous flow past a finite flat plate accelerating in the direction normal to itself is studied numerically. The plate moves with nondimensional speed tp , where p = 0, 1/2, 1, 2. The work focuses on resolving the flow at early to moderately large times and determining the dependence on the acceleration parameter p. Three stages in the vortex evolution are identified and quantified. The first stage, referred to as the Rayleigh stage [Luchini and Tognaccini, “The start-up vortex issuing from a semi-infinite flat plate,” J. Fluid Mech. 455, 175–193 (2002)], consists of a vortical boundary layer of roughly uniform thickness surrounding the plate and its tip, without any separating streamlines. This stage is present only for p > 0, for a time-interval that scales like p 3, as p → 0. The second stage is one of self-similar growth. The vortex trajectory and circulation satisfy inviscid scaling laws, the boundary layer thickness satisfies viscous laws. The self-similar trajectory starts immediately after the Rayleigh stage ends and lasts until the plate has moved a distance d = 0.5 to 1 times its length. Finally, in the third stage, the image vorticity due to the finite plate length becomes relevant and the flow departs from self-similar growth. The onset of an instability in the outer spiral vortex turns is also observed, however, at least for the zero-thickness plate considered here, it is shown to be easily triggered numerically by underresolution. The present numerical results are compared with experimental results of Pullin and Perry [“Some flow visualization experiments on the starting vortex,” J. Fluid Mech. 97, 239–255 (1980)], and numerical results of Koumoutsakos and Shiels [“Simulations of the viscous flow normal to an impulsively started and uniformly accelerated flat plate,” J. Fluid Mech. 328, 177–227 (1996)].

(Abridged) A series of three-dimensional numerical simulations is used to study the intrinsic stability of high-speed turbulent flames. Calculations model the interaction of a fully-resolved premixed flame with a highly subsonic, statistically steady, homogeneous, isotropic turbulence. We consider a wide range of turbulent intensities and system sizes, corresponding to the Damk\"ohler numbers Da = 0.1-6.0. These calculations show that turbulent flames in the regimes considered are intrinsically unstable. In particular, we find three effects. 1) Turbulent flame speed develops pulsations with the observed peak-to-peak amplitude > 10 and a characteristic time scale close to a large-scale eddy turnover time. Such variability is caused by the interplay between turbulence, which continuously creates the flame surface, and highly intermittent flame collisions, which consume the flame surface. 2) Unstable burning results in the periodic pressure build-up and the formation of pressure waves or shocks, when the flame speed approaches or exceeds the speed of a Chapman-Jouguet deflagration. 3) Coupling of pressure gradients formed during pulsations with density gradients across the flame leads to the anisotropic amplification of turbulence inside the flame volume and flame acceleration. Such process, which is driven by the baroclinic term in the vorticity transport equation, is a reacting-flow analog of the mechanism underlying the Richtmyer-Meshkov instability. With the increase in turbulent intensity, the limit-cycle instability discussed here transitions to the regime described in our previous work, in which the growth of the flame speed becomes unbounded and produces a detonation.

Recent experiments showed that standing acoustic waves could be exploited to induce self-propulsion of rigid metallic particles in the direction perpendicular to the acoustic wave. We propose in this paper a physical mechanism for these observations based on the interplay between inertial forces in the fluid and the geometrical asymmetry of the particle shape. We consider an axisymmetric rigid near-sphere oscillating in a quiescent fluid along a direction perpendicular to its symmetry axis. The kinematics of oscillations can be either prescribed or can result dynamically from the presence of an external oscillating velocity field. Steady streaming in the fluid, the inertial rectification of the time-periodic oscillating flow, generates steady stresses on the particle which, in general, do not average to zero, resulting in a finite propulsion speed along the axis of the symmetry of the particle and perpendicular to the oscillation direction. Our derivation of the propulsion speed is obtained at leading order in the Reynolds number and the deviation of the shape from that of a sphere. The results of our model are consistent with the experimental measurements, and more generally explains how time periodic forcing from an acoustic field can be harnessed to generate autonomous motion.

The evolution of large-scale density perturbations is studied in a stably stratified, two-dimensional flow governed by the Boussinesq equations. As is known, intially smooth density (or temperature) profiles develop into fronts in the very early stages of evolution. This results in a frontally dominated $k^{-1}$ potential energy spectrum. The fronts, initially characterized by a relatively simple geometry, spontaneously develop into severely distorted sheets that possess structure at very fine scales, and thus there is a transfer of energy from large to small scales. It is shown here that this process culminates in the establishment of a $k^{-5/3}$ kinetic energy spectrum, although its scaling extends over a shorter range as compared to the $k^{-1}$ scaling of the potential energy spectrum. The establishment of the kinetic energy scaling signals the onset of enstrophy decay which proceeds in a mildly modulated exponential manner and possesses a novel self-similarity. Specifically, the self-similarity is seen in the time invariant nature of the probability density function (\pdf{}) associated with the normalized vorticity field. Given the rapid decay of energy at this stage, the spectral scaling is transient and fades with the emergence of a smooth, large-scale, very slowly decaying, (almost) vertically sheared horizontal mode with most of its energy in the potential component -- i.e. the Pearson-Linden regime.

The stationary-state spatial structure of reacting scalar fields, chaotically advected by a two-dimensional large-scale flow, is examined for the case for which the reaction equations contain delay terms. Previous theoretical investigations have shown that, in the absence of delay terms and in a regime where diffusion can be neglected (large P\'eclet number), the emergent spatial structures are filamental and characterized by a single scaling regime with a H\"older exponent that depends on the rate of convergence of the reactive processes and the strength of the stirring measured by the average stretching rate. In the presence of delay terms, we show that for sufficiently small scales all interacting fields should share the same spatial structure, as found in the absence of delay terms. Depending on the strength of the stirring and the magnitude of the delay time, two further scaling regimes that are unique to the delay system may appear at intermediate length scales. An expression for the transition length scale dividing small-scale and intermediate-scale regimes is obtained and the scaling behavior of the scalar field is explained. The theoretical results are illustrated by numerical calculations for two types of reaction models, both based on delay differential equations, coupled to a two-dimensional chaotic advection flow. The first corresponds to a single reactive scalar and the second to a nonlinear biological model that includes nutrients, phytoplankton and zooplankton. As in the no-delay case, the presence of asymmetrical couplings among the biological species results in a non-generic scaling behavior.

Forced advection of passive tracer, $\theta $, in nonlinear relaxational medium by large scale (Batchelor problem) incompressible velocity field at scales less than the correlation length of the flow and larger than the diffusion scale is considered. Effective theory explaining small scale scalar fluctuations is proven to be linear, asymptotic free (downscales from the scale of the pumping) and universal. Only three parameters are required to decribe exhaustively the small scale statistics of scalar difference: two velocity-dependent ones, average and dispersion ($\bar{\lambda}$ and $\Delta $ respectively) of the exponential stretching rate of a trial line element, and $\alpha $, standing for average rate of linear damping of small scale scalar fluctuations. $\alpha $ is an explicit functional of potential chracterized medium nonlinearity and amplitude of $\theta ^{2}$ flux pumped into the system. Structure functions show an extremely anomalous, intermittent behavior: $<|\delta \theta_{r}|^{q}> \sim r^{\xi_{q}}, \xi_{q} = \min {q,\sqrt{[ \frac{\bar{\lambda}}{\Delta}] ^{2} + \frac{2\alpha q}{\Delta}} - \frac{\bar{\lambda}}{\Delta}}$. No dissipative anomaly is found in the problem. Comment: 7 pages, RevTeX

Forced advection of passive scalar by a smooth $d$-dimensional incompressible velocity in the presence of a linear damping is studied. Acting separately advection and dumping do not lead to an essential intermittency of the steady scalar statistics, while being mixed together produce a very strong non-Gaussianity in the convective range: $q$-th (positive) moment of the absolute value of scalar difference, $<|\theta (t;{\bf r})-\theta (t;0)|^{q}> $ is proportional to $r^{\xi_{q}}$, $\xi _{q}=\sqrt{d^{2}/4+\alpha dq/[ (d-1)D]}-d/2$, where $\alpha /D$ measures the rate of the damping in the units of the stretching rate. Probability density function (PDF) of the scalar difference is also found. Comment: 4 pages, RevTex, Submitted to Phys. Fluids

Molecules at the air-water interface often form inhomogeneous layers in which domains of different densities are separated by sharp interfaces. Complex interfacial pattern formation may occur through the competition of short- and long-range forces acting within the monolayer. The overdamped hydrodynamics of such interfacial motion is treated here in a general manner that accounts for dissipation both within the monolayer and in the subfluid. Previous results on the linear stability of interfaces are recovered and extended, and a formulation applicable to the nonlinear regime is developed. A simplified dynamical law valid when dissipation in the monolayer itself is negligible is also proposed. Throughout the analysis, special attention is paid to the dependence of the dynamical behavior on a characteristic length scale set by the ratio of the viscosities in the monolayer and in the subphase. Comment: 12 pages, RevTeX, 4 ps figures, accepted in Physics of Fluids A

Recent experiments showed that standing acoustic waves could be exploited to induce self-propulsion of rigid metallic particles in the direction perpendicular to the acoustic wave. We propose in this paper a physical mechanism for these observations based on the interplay between inertial forces in the fluid and the geometrical asymmetry of the particle shape. We consider an axisymmetric rigid near-sphere oscillating in a quiescent fluid along a direction perpendicular to its symmetry axis. The kinematics of oscillations can be either prescribed or can result dynamically from the presence of an external oscillating velocity field. Steady streaming in the fluid, the inertial rectification of the time-periodic oscillating flow, generates steady stresses on the particle which, in general, do not average to zero, resulting in a finite propulsion speed along the axis of the symmetry of the particle and perpendicular to the oscillation direction. Our derivation of the propulsion speed is obtained at leading order in the Reynolds number and the deviation of the shape from that of a sphere. The results of our model are consistent with the experimental measurements, and more generally explains how time periodic forcing from an acoustic field can be harnessed to generate autonomous motion.

The evolution of large-scale density perturbations is studied in a stably stratified, two-dimensional flow governed by the Boussinesq equations. As is known, intially smooth density (or temperature) profiles develop into fronts in the very early stages of evolution. This results in a frontally dominated $k^{-1}$ potential energy spectrum. The fronts, initially characterized by a relatively simple geometry, spontaneously develop into severely distorted sheets that possess structure at very fine scales, and thus there is a transfer of energy from large to small scales. It is shown here that this process culminates in the establishment of a $k^{-5/3}$ kinetic energy spectrum, although its scaling extends over a shorter range as compared to the $k^{-1}$ scaling of the potential energy spectrum. The establishment of the kinetic energy scaling signals the onset of enstrophy decay which proceeds in a mildly modulated exponential manner and possesses a novel self-similarity. Specifically, the self-similarity is seen in the time invariant nature of the probability density function (\pdf{}) associated with the normalized vorticity field. Given the rapid decay of energy at this stage, the spectral scaling is transient and fades with the emergence of a smooth, large-scale, very slowly decaying, (almost) vertically sheared horizontal mode with most of its energy in the potential component -- i.e. the Pearson-Linden regime.

The stationary-state spatial structure of reacting scalar fields, chaotically advected by a two-dimensional large-scale flow, is examined for the case for which the reaction equations contain delay terms. Previous theoretical investigations have shown that, in the absence of delay terms and in a regime where diffusion can be neglected (large P\'eclet number), the emergent spatial structures are filamental and characterized by a single scaling regime with a H\"older exponent that depends on the rate of convergence of the reactive processes and the strength of the stirring measured by the average stretching rate. In the presence of delay terms, we show that for sufficiently small scales all interacting fields should share the same spatial structure, as found in the absence of delay terms. Depending on the strength of the stirring and the magnitude of the delay time, two further scaling regimes that are unique to the delay system may appear at intermediate length scales. An expression for the transition length scale dividing small-scale and intermediate-scale regimes is obtained and the scaling behavior of the scalar field is explained. The theoretical results are illustrated by numerical calculations for two types of reaction models, both based on delay differential equations, coupled to a two-dimensional chaotic advection flow. The first corresponds to a single reactive scalar and the second to a nonlinear biological model that includes nutrients, phytoplankton and zooplankton. As in the no-delay case, the presence of asymmetrical couplings among the biological species results in a non-generic scaling behavior.

Forced advection of passive tracer, $\theta $, in nonlinear relaxational medium by large scale (Batchelor problem) incompressible velocity field at scales less than the correlation length of the flow and larger than the diffusion scale is considered. Effective theory explaining small scale scalar fluctuations is proven to be linear, asymptotic free (downscales from the scale of the pumping) and universal. Only three parameters are required to decribe exhaustively the small scale statistics of scalar difference: two velocity-dependent ones, average and dispersion ($\bar{\lambda}$ and $\Delta $ respectively) of the exponential stretching rate of a trial line element, and $\alpha $, standing for average rate of linear damping of small scale scalar fluctuations. $\alpha $ is an explicit functional of potential chracterized medium nonlinearity and amplitude of $\theta ^{2}$ flux pumped into the system. Structure functions show an extremely anomalous, intermittent behavior: $<|\delta \theta_{r}|^{q}> \sim r^{\xi_{q}}, \xi_{q} = \min {q,\sqrt{[ \frac{\bar{\lambda}}{\Delta}] ^{2} + \frac{2\alpha q}{\Delta}} - \frac{\bar{\lambda}}{\Delta}}$. No dissipative anomaly is found in the problem. Comment: 7 pages, RevTeX

Forced advection of passive scalar by a smooth $d$-dimensional incompressible velocity in the presence of a linear damping is studied. Acting separately advection and dumping do not lead to an essential intermittency of the steady scalar statistics, while being mixed together produce a very strong non-Gaussianity in the convective range: $q$-th (positive) moment of the absolute value of scalar difference, $<|\theta (t;{\bf r})-\theta (t;0)|^{q}> $ is proportional to $r^{\xi_{q}}$, $\xi _{q}=\sqrt{d^{2}/4+\alpha dq/[ (d-1)D]}-d/2$, where $\alpha /D$ measures the rate of the damping in the units of the stretching rate. Probability density function (PDF) of the scalar difference is also found. Comment: 4 pages, RevTex, Submitted to Phys. Fluids

Molecules at the air-water interface often form inhomogeneous layers in which domains of different densities are separated by sharp interfaces. Complex interfacial pattern formation may occur through the competition of short- and long-range forces acting within the monolayer. The overdamped hydrodynamics of such interfacial motion is treated here in a general manner that accounts for dissipation both within the monolayer and in the subfluid. Previous results on the linear stability of interfaces are recovered and extended, and a formulation applicable to the nonlinear regime is developed. A simplified dynamical law valid when dissipation in the monolayer itself is negligible is also proposed. Throughout the analysis, special attention is paid to the dependence of the dynamical behavior on a characteristic length scale set by the ratio of the viscosities in the monolayer and in the subphase. Comment: 12 pages, RevTeX, 4 ps figures, accepted in Physics of Fluids A

In this fluid dynamics video, we present the first time-resolved measurements of the oscillatory velocity field induced by swimming unicellular microorganisms. Confinement of the green alga C. reinhardtii in stabilized thin liquid films allows simultaneous tracking of cells and tracer particles. The measured velocity field reveals complex time-dependent flow structures, and scales inversely with distance. The instantaneous mechanical power generated by the cells is measured from the velocity fields and peaks at 15 fW. The dissipation per cycle is more than four times what steady swimming would require.

We study the properties and symmetries governing the hydrodynamic interaction between two identical, arbitrarily shaped objects, driven through a viscous fluid. We treat analytically the leading (dipolar) terms of the pair-mobility matrix, affecting the instantaneous relative linear and angular velocities of the two objects at large separation. We find that the ability to align asymmetric objects by an external time-dependent drive [Moths and Witten, Phys. Rev. Lett. 110, 028301 (2013)] is degraded by the hydrodynamic interaction. The effects of hydrodynamic interactions are explicitly demonstrated through numerically calculated time-dependent trajectories of model alignable objects composed of four stokeslets. In addition to the orientational effect, we find that the two objects generally repel each other, thus restoring full alignment at long times.

The alignment of vorticity and scalar gradient with the eigendirections of the rate of strain tensor is investigated in turbulent buoyant nonpremixed horizontal and vertical flames. The uniqueness of a buoyant nonpremixed flame is that it contains regions with distinct alignment characteristics. The strain-enstrophy angle Psi is used to identify these regions. Examination of the vorticity field and the vorticity production in these different regions indicates that Psi and consequently the alignment properties near the flame surface identified by the mixture fraction band F approximately equals F(sub st) differ from those in the fuel region, F > F(sub st) and the oxidizer region, F < F(sub st). The F approximately equals F(sub st) band shows strain-dominance resulting in vorticity/alpha alignment while F > F(sub st) (and F < F(sub st) for the vertical flame) band(s) show(s) vorticity/beta alignment. The implication of this result is that the scalar dissipation, epsilon(sub F), attains its maximum value always near F approximately equals F(sub st). These results are also discussed within the framework of recent dynamical results [Galanti et al., Nonlinearity 10, 1675 (1997)] suggesting that the Navier-Stokes equations evolved towards an attracting solution. It is shown that the properties of such an attracting solution are also consistent with our results of buoyant turbulent nonpremixed flames.

Motivated by results from recent particle tracking experiments in turbulence (Xu et al., Nat. Phys. 7, 709 (2011)), we study the Lagrangian time correlations of vorticity alignments with the three eigenvectors of the deformation-rate tensor. We use data from direct numerical simulations (DNS), and explore the predictions of a Lagrangian model for the velocity gradient tensor. We find that the initial increase of correlation of vorticity direction with the most extensive eigen-direction observed by Xu et al. is reproduced accurately using the Lagrangian model, as well as the evolution of correlation with the other two eigendirections. Conversely, time correlations of vorticity direction with the eigen-frame of the pressure Hessian tensor show differences with the model.

A dynamic procedure for the Lagrangian Averaged Navier-Stokes-$\alpha$ (LANS-$\alpha$) equations is developed where the variation in the parameter $\alpha$ in the direction of anisotropy is determined in a self-consistent way from data contained in the simulation itself. The dynamic model is initially tested in forced and decaying isotropic turbulent flows where $\alpha$ is constant in space but it is allowed to vary in time. It is observed that by using the dynamic LANS-$\alpha$ procedure a more accurate simulation of the isotropic homogeneous turbulence is achieved. The energy spectra and the total kinetic energy decay are captured more accurately as compared with the LANS-$\alpha$ simulations using a fixed $\alpha$. In order to evaluate the applicability of the dynamic LANS-$\alpha$ model in anisotropic turbulence, a priori test of a turbulent channel flow is performed. It is found that the parameter $\alpha$ changes in the wall normal direction. Near a solid wall, the length scale $\alpha$ is seen to depend on the distance from the wall with a vanishing value at the wall. On the other hand, away from the wall, where the turbulence is more isotropic, $\alpha$ approaches an almost constant value. Furthermore, the behavior of the subgrid scale stresses in the near wall region is captured accurately by the dynamic LANS-$\alpha$ model. The dynamic LANS-$\alpha$ model has the potential to extend the applicability of the LANS-$\alpha$ equations to more complicated anisotropic flows. Comment: 17 pages, 17 figures

We analyze the mechanism that determines the boundary of stability in Taylor-Couette flow. By simple physical argument we derive an analytic expression to approximate the stability line for all radius ratios and all speed ratios, for co- and counterrotating cylinders. The expression includes viscosity and so generalizes Rayleigh's criterion. We achieve agreement with linear stability theory and with experiments in the whole parameter space. Explicit formulae are given for limiting cases. Comment: 6 pages (LaTeX with REVTEX) including 4 figures (Postscript) Revised, discussion of two additional references. See also http://staff-www.uni-marburg.de/~esser

We discuss the equilibrium condition for a liquid that partially wets a solid on the level of intermolecular forces. Using a mean field continuum description, we generalize the capillary pressure from variation of the free energy and show at what length scale the equilibrium contact angle is selected. After recovering Young's law for homogeneous substrates, it is shown how hysteresis of the contact angle can be incorporated in a self-consistent fashion. In all cases the liquid-vapor interface takes a nontrivial shape, which is compared to models using a disjoining pressure. Comment: 12 pages, 6 figures

The line tension of an electrolyte wetting a non-polar substrate is computed analytically and numerically. The results show that, depending on the value of the apparent contact angle, positive or negative line tension values may be obtained. Furthermore, a significant difference between Young's contact angle and the apparent contact angle measured several Debye lengths remote from the three-phase contact line occurs. When applying the results to water wetting highly charged surfaces, line tension values of the same order of magnitude as found in recent experiments can be achieved. Therefore, the theory presented may contribute to the understanding of line tension measurements and points to the importance of the electrostatic line tension. Being strongly dependent on the interfacial charge density, electrostatic line tension is found to be tunable via the pH value of the involved electrolyte. As a practical consequence, the stability of nanoparticles adsorbed at fluid-fluid interfaces is predicted to be dependent on the pH value. The theory is suited for future incorporation of effects due to surfactants where even larger line tension values can be expected.

The scaling properties of correlation functions of non-scalar fields (constructed from velocity derivatives) in isotropic hydrodynamic turbulence are characterized by a set of universal exponents. It is explained that these exponents also characterize the rate of decay of the effects of anisotropic forcing in developed turbulence. This set has never been measured in either numerical or laboratory experiments. These exponents are important for the general theory of turbulence, but also for modeling anisotropic flows. We propose in this letter how to measure these exponents using existing data bases of direct numerical simulations and by designing new laboratory experiments. Comment: 10 pages, latex, no figures, online (html) version available at http://lvov.weizmann.ac.il/EXP/EXP.html

We discuss the equilibrium condition for a liquid that partially wets a solid on the level of intermolecular forces. Using a mean field continuum description, we generalize the capillary pressure from variation of the free energy and show at what length scale the equilibrium contact angle is selected. After recovering Young's law for homogeneous substrates, it is shown how hysteresis of the contact angle can be incorporated in a self-consistent fashion. In all cases the liquid-vapor interface takes a nontrivial shape, which is compared to models using a disjoining pressure. Comment: 12 pages, 6 figures

The line tension of an electrolyte wetting a non-polar substrate is computed analytically and numerically. The results show that, depending on the value of the apparent contact angle, positive or negative line tension values may be obtained. Furthermore, a significant difference between Young's contact angle and the apparent contact angle measured several Debye lengths remote from the three-phase contact line occurs. When applying the results to water wetting highly charged surfaces, line tension values of the same order of magnitude as found in recent experiments can be achieved. Therefore, the theory presented may contribute to the understanding of line tension measurements and points to the importance of the electrostatic line tension. Being strongly dependent on the interfacial charge density, electrostatic line tension is found to be tunable via the pH value of the involved electrolyte. As a practical consequence, the stability of nanoparticles adsorbed at fluid-fluid interfaces is predicted to be dependent on the pH value. The theory is suited for future incorporation of effects due to surfactants where even larger line tension values can be expected.

The scaling properties of correlation functions of non-scalar fields (constructed from velocity derivatives) in isotropic hydrodynamic turbulence are characterized by a set of universal exponents. It is explained that these exponents also characterize the rate of decay of the effects of anisotropic forcing in developed turbulence. This set has never been measured in either numerical or laboratory experiments. These exponents are important for the general theory of turbulence, but also for modeling anisotropic flows. We propose in this letter how to measure these exponents using existing data bases of direct numerical simulations and by designing new laboratory experiments. Comment: 10 pages, latex, no figures, online (html) version available at http://lvov.weizmann.ac.il/EXP/EXP.html

The mean-velicity and turbulence quantities in a few qualitatively different types of asymmetric two-dimensional turbulent near wakes in nearly zero-pressure gradient have been experimentally studied. In all cases, the log-law similarity of the boundary layers was found to continue into the initial part of the wake same similarity variables as in the boundary layers on the same side, provided the origin of the normal distance is taken at the smooth extension of the respective surfaces. The Reynolds stress profiles show sharp peaks just downstream of the trailing, edge, and the magnitudes of the peaks are found to be related to the values of the surface friction at the trailing edge. These peaks grow into the full width of the wake to form the far wake profiles. In this process, the turbulent diffusions of the Reynolds stresses are very important and when the size- asymmetry is severe, is not clearly of gradient-transport type.

Here we show that asymmetric fully-localized flexural-gravity lumps can propagate on the surface of an inviscid and irrotational fluid covered by a variable-thickness elastic material, provided that the thickness varies only in one direction and has a local minimum. We derive and present equations governing the evolution of the envelope of flexural-gravity wave packets allowing the flexing material to have small variations in the transverse (to propagation) direction. We show that the governing equation belongs to the general family of Davey-Stewartson equations, but with an extra term in the surface evolution equation that accounts for the variable thickness of the elastic cover. We then use an iterative Newton-Raphson scheme, with a numerical continuation procedure via Lagrange interpolation, in a search to find fully-localized solutions of this system of equations. We show that if the elastic sheet thickness has (at least) a local minimum, flexural-gravity lumps can propagate near the minimum thickness, and in general have an asymmetric bell-shape in the transverse to the propagation direction. In applied physics, flexural-gravity waves describe for instance propagation of waves over the ice-covered bodies of water. Ice is seldom uniform, nor is the seafloor, and in fact near the boundaries (ice-edges, shorelines) they typically vary only in one direction (toward to edge), and are uniform in the transverse direction. This research suggests that fully localized waves are not restricted to constant ice-thickness/water-depth areas and can exist under much broader conditions. Presented results may have implications in experimental generation and observation of flexural-gravity (as well as capillary-gravity) lumps.

Previously we published a dynamical model (E. Brown and G. Ahlers, Phys. Fluids, 20, 075101 (2008)) for the large-scale-circulation (LSC) dynamics of Rayleigh-Benard convection in cylindrical containers. The model consists of a pair of stochastic ordinary differential equations, motivated by the Navier-Stokes equations, one each for the strength delta and the orientation theta_0 of the LSC. Here we extend it to cases where the rotational invariance of the system is broken by one of several physically relevant perturbations. As an example we present experimental measurements of the LSC dynamics for a container tilted relative to gravity. In that case the model predicts that the buoyancy of the thermal boundary layers encourages fluid to travel along the steepest slope, that it locks the LSC in this direction, and that it strengthens the flow, as seen in experiments. The increase in LSC strength is shown to be responsible for the observed suppression of cessations and azimuthal fluctuations. We predict and observe that for large enough tilt angles, the restoring force that aligns the flow with the slope is strong enough to cause oscillations of the LSC around this orientation. This planar oscillation mode is different from coherent torsional oscillations that have been observed previously. The model was applied also to containers with elliptical cross-sections and predicts that the pressure due to the side walls forces the flow into a preferred orientation in the direction of the longest diameter. When the ellipticity is large enough, then oscillations around this orientation are predicted. Comment: 16 pages, 12 figures

Thermal management is critical to a number of technologies used in a microgravity environment and in Earth-based systems. Examples include electronic cooling, power generation systems, metal forming and extrusion, and HVAC (heating, venting, and air conditioning) systems. One technique that can deliver the large heat fluxes required for many of these technologies is two-phase heat transfer. This type of heat transfer is seen in the boiling or evaporation of a liquid and in the condensation of a vapor. Such processes provide very large heat fluxes with small temperature differences. Our research program is directed toward the development of a new, two-phase heat transfer cell for use in a microgravity environment. In this paper, we consider the main technology used in this cell, a novel technique for the atomization of a liquid called vibration-induced droplet atomization. In this process, a small liquid droplet is placed on a thin metal diaphragm that is made to vibrate by an attached piezoelectric transducer. The vibration induces capillary waves on the free surface of the droplet that grow in amplitude and then begin to eject small secondary droplets from the wave crests. In some situations, this ejection process develops so rapidly that the entire droplet seems to burst into a small cloud of atomized droplets that move away from the diaphragm at speeds of up to 50 cm/s. By incorporating this process into a heat transfer cell, the active atomization and transport of the small liquid droplets could provide a large heat flux capability for the device. Experimental results are presented that document the behavior of the diaphragm and the droplet during the course of a typical bursting event. In addition, a simple mathematical model is presented that qualitatively reproduces all of the essential features we have seen in a burst event. From these two investigations, we have shown that delayed droplet bursting results when the system passes through a resonance condition. This occurs when the initial acceleration of the diaphragm is higher than the critical acceleration and the driving frequency is larger than the initial resonance frequency of the diaphragm-droplet system. We have incorporated this droplet atomization device into a design for a new heat transfer cell for use in a microgravity environment. The cell is essentially a cylindrical container with a hot surface on one end and a cold surface on the other. The vibrating diaphragm is mounted in the center of the cold surface. Heat transfer occurs through droplet evaporation and condensation on the hot and cold ends of the cell. A prototype of this heat transfer cell has been built and tested. It can operate continuously and provides a modest level of heat transfer, about 20 W/sq cm. Our work during the next few years will be to optimize the design of this cell to see if we can produce a device that has significantly better performance than conventional heat exchangers and heat pipes.

In this fluid dynamics video, we present a visualization of the primary atomization of a turbulent liquid jet injected into a turbulent gaseous crossflow. It is based on a detailed numerical simulation of the primary atomization region of the jet using a finite volume, balanced force, incompressible LES/DNS flow solver coupled to a Refined Level Set Grid (RLSG) solver to track the phase interface position. The visualization highlights the two distinct breakup modes of the jet: the column breakup mode of the main liquid column and the ligament breakup mode on the sides of the jet and highlights the complex evolution of the phase interface geometry.

Catalytic bimetallic Janus particles swim by a bipolar electrochemical propulsion mechanism that results from electroosmotic fluid slip around the particle surface. The flow is driven by electrical body forces which are generated from a coupling of a reaction-induced electric field and net charge in the diffuse layer surrounding the particle. This paper presents simulations, scaling, and physical descriptions of the experimentally observed trend that the swimming speed decays rapidly with increasing solution conductivity. The simulations solve the full Poisson-Nernst-Planck-Stokes equations with multiple ionic species, a cylindrical particle in an infinite fluid, and nonlinear Butler-Volmer boundary conditions to represent the electrochemical surface reactions. The speed of bimetallic particles is reduced in high-conductivity solutions because of reductions in the induced electric field in the diffuse layer near the rod, the total reaction rate, and the magnitude of the rod zeta potential. The results in this work suggest that the auto-electrophoretic mechanism is inherently susceptible to speed reductions in higher ionic strength solutions.

The results of an experimental investigation on the effect of vortex generators, in the form of small tabs at the nozzle exit on the evolution of a jet, are reported in this paper. Primarily tabs of triangular shape are considered, and the effect is studied up to a jet Mach number of 1.8. Each tab is found to produce a dominant pair of counter-rotating streamwise vortices having a sense of rotation opposite to that expected from the wrapping of the boundary layer. This results in an inward indentation of the mixing layer into the core of the jet. A triangular-shaped tab with its apex leaning downstream, referred to as a delta tab, is found to be the most effective in producing such vortices, with a consequential large influence on the overall jet evolution. Two delta tabs, spaced 180 deg apart, completely bifurcate the jet. Four delta tabs stretch the mixing layer into four 'fingers,' resulting in a significant increase in the jet mixing downstream. For six delta tabs the mixing layer distortion settles back to a three finger configuration through an interaction of the streamwise vortices. The tabs are found to be equally effective in jets with turbulent or laminar initial boundary layers. Two sources of streamwise vorticity are postulated for the flow under consideration. One is the upstream 'pressure hill,' generated by the tab, which constitutes the main contributor of vorticity to the dominant pair. Another is due to vortex filaments shed from the sides of the tab and reoriented downstream by the mean shear of the mixing layer. Depending on the orientation of the tab, the latter source can produce a vortex pair having a sense of rotation opposite to that of the dominant pair. In the case of the delta tab, vorticity from the two sources add, explaining the strong effect in that configuration.

Flagellated bacteria exploiting helical propulsion are known to swim along circular trajectories near surfaces. Fluid dynamics predicts this circular motion to be clockwise (CW) above a rigid surface (when viewed from inside the fluid) and counter-clockwise (CCW) below a free surface. Recent experimental investigations showed that complex physicochemical processes at the nearby surface could lead to a change in the direction of rotation, both at solid surfaces absorbing slip-inducing polymers and interfaces covered with surfactants. Motivated by these results, we use a far-field hydrodynamic model to predict the kinematics of swimming near three types of interfaces: clean fluid-fluid interface, slipping rigid wall, and a fluid interface covered by incompressible surfactants. Representing the helical swimmer by a superposition of hydrodynamic singularities, we first show that in all cases the surfaces reorient the swimmer parallel to the surface and attract it, both of which are a consequence of the Stokes dipole component of the swimmer flow field. We then show that circular motion is induced by a higher-order singularity, namely a rotlet dipole, and that its rotation direction (CW vs. CCW) is strongly affected by the boundary conditions at the interface and the bacteria shape. Our results suggest thus that the hydrodynamics of complex interfaces provide a mechanism to selectively stir bacteria.

Here we show that asymmetric fully-localized flexural-gravity lumps can propagate on the surface of an inviscid and irrotational fluid covered by a variable-thickness elastic material, provided that the thickness varies only in one direction and has a local minimum. We derive and present equations governing the evolution of the envelope of flexural-gravity wave packets allowing the flexing material to have small variations in the transverse (to propagation) direction. We show that the governing equation belongs to the general family of Davey-Stewartson equations, but with an extra term in the surface evolution equation that accounts for the variable thickness of the elastic cover. We then use an iterative Newton-Raphson scheme, with a numerical continuation procedure via Lagrange interpolation, in a search to find fully-localized solutions of this system of equations. We show that if the elastic sheet thickness has (at least) a local minimum, flexural-gravity lumps can propagate near the minimum thickness, and in general have an asymmetric bell-shape in the transverse to the propagation direction. In applied physics, flexural-gravity waves describe for instance propagation of waves over the ice-covered bodies of water. Ice is seldom uniform, nor is the seafloor, and in fact near the boundaries (ice-edges, shorelines) they typically vary only in one direction (toward to edge), and are uniform in the transverse direction. This research suggests that fully localized waves are not restricted to constant ice-thickness/water-depth areas and can exist under much broader conditions. Presented results may have implications in experimental generation and observation of flexural-gravity (as well as capillary-gravity) lumps.

Previously we published a dynamical model (E. Brown and G. Ahlers, Phys. Fluids, 20, 075101 (2008)) for the large-scale-circulation (LSC) dynamics of Rayleigh-Benard convection in cylindrical containers. The model consists of a pair of stochastic ordinary differential equations, motivated by the Navier-Stokes equations, one each for the strength delta and the orientation theta_0 of the LSC. Here we extend it to cases where the rotational invariance of the system is broken by one of several physically relevant perturbations. As an example we present experimental measurements of the LSC dynamics for a container tilted relative to gravity. In that case the model predicts that the buoyancy of the thermal boundary layers encourages fluid to travel along the steepest slope, that it locks the LSC in this direction, and that it strengthens the flow, as seen in experiments. The increase in LSC strength is shown to be responsible for the observed suppression of cessations and azimuthal fluctuations. We predict and observe that for large enough tilt angles, the restoring force that aligns the flow with the slope is strong enough to cause oscillations of the LSC around this orientation. This planar oscillation mode is different from coherent torsional oscillations that have been observed previously. The model was applied also to containers with elliptical cross-sections and predicts that the pressure due to the side walls forces the flow into a preferred orientation in the direction of the longest diameter. When the ellipticity is large enough, then oscillations around this orientation are predicted. Comment: 16 pages, 12 figures

Thermal management is critical to a number of technologies used in a microgravity environment and in Earth-based systems. Examples include electronic cooling, power generation systems, metal forming and extrusion, and HVAC (heating, venting, and air conditioning) systems. One technique that can deliver the large heat fluxes required for many of these technologies is two-phase heat transfer. This type of heat transfer is seen in the boiling or evaporation of a liquid and in the condensation of a vapor. Such processes provide very large heat fluxes with small temperature differences. Our research program is directed toward the development of a new, two-phase heat transfer cell for use in a microgravity environment. In this paper, we consider the main technology used in this cell, a novel technique for the atomization of a liquid called vibration-induced droplet atomization. In this process, a small liquid droplet is placed on a thin metal diaphragm that is made to vibrate by an attached piezoelectric transducer. The vibration induces capillary waves on the free surface of the droplet that grow in amplitude and then begin to eject small secondary droplets from the wave crests. In some situations, this ejection process develops so rapidly that the entire droplet seems to burst into a small cloud of atomized droplets that move away from the diaphragm at speeds of up to 50 cm/s. By incorporating this process into a heat transfer cell, the active atomization and transport of the small liquid droplets could provide a large heat flux capability for the device. Experimental results are presented that document the behavior of the diaphragm and the droplet during the course of a typical bursting event. In addition, a simple mathematical model is presented that qualitatively reproduces all of the essential features we have seen in a burst event. From these two investigations, we have shown that delayed droplet bursting results when the system passes through a resonance condition. This occurs when the initial acceleration of the diaphragm is higher than the critical acceleration and the driving frequency is larger than the initial resonance frequency of the diaphragm-droplet system. We have incorporated this droplet atomization device into a design for a new heat transfer cell for use in a microgravity environment. The cell is essentially a cylindrical container with a hot surface on one end and a cold surface on the other. The vibrating diaphragm is mounted in the center of the cold surface. Heat transfer occurs through droplet evaporation and condensation on the hot and cold ends of the cell. A prototype of this heat transfer cell has been built and tested. It can operate continuously and provides a modest level of heat transfer, about 20 W/sq cm. Our work during the next few years will be to optimize the design of this cell to see if we can produce a device that has significantly better performance than conventional heat exchangers and heat pipes.

In this fluid dynamics video, we present a visualization of the primary atomization of a turbulent liquid jet injected into a turbulent gaseous crossflow. It is based on a detailed numerical simulation of the primary atomization region of the jet using a finite volume, balanced force, incompressible LES/DNS flow solver coupled to a Refined Level Set Grid (RLSG) solver to track the phase interface position. The visualization highlights the two distinct breakup modes of the jet: the column breakup mode of the main liquid column and the ligament breakup mode on the sides of the jet and highlights the complex evolution of the phase interface geometry.

Catalytic bimetallic Janus particles swim by a bipolar electrochemical propulsion mechanism that results from electroosmotic fluid slip around the particle surface. The flow is driven by electrical body forces which are generated from a coupling of a reaction-induced electric field and net charge in the diffuse layer surrounding the particle. This paper presents simulations, scaling, and physical descriptions of the experimentally observed trend that the swimming speed decays rapidly with increasing solution conductivity. The simulations solve the full Poisson-Nernst-Planck-Stokes equations with multiple ionic species, a cylindrical particle in an infinite fluid, and nonlinear Butler-Volmer boundary conditions to represent the electrochemical surface reactions. The speed of bimetallic particles is reduced in high-conductivity solutions because of reductions in the induced electric field in the diffuse layer near the rod, the total reaction rate, and the magnitude of the rod zeta potential. The results in this work suggest that the auto-electrophoretic mechanism is inherently susceptible to speed reductions in higher ionic strength solutions.

The results of an experimental investigation on the effect of vortex generators, in the form of small tabs at the nozzle exit on the evolution of a jet, are reported in this paper. Primarily tabs of triangular shape are considered, and the effect is studied up to a jet Mach number of 1.8. Each tab is found to produce a dominant pair of counter-rotating streamwise vortices having a sense of rotation opposite to that expected from the wrapping of the boundary layer. This results in an inward indentation of the mixing layer into the core of the jet. A triangular-shaped tab with its apex leaning downstream, referred to as a delta tab, is found to be the most effective in producing such vortices, with a consequential large influence on the overall jet evolution. Two delta tabs, spaced 180 deg apart, completely bifurcate the jet. Four delta tabs stretch the mixing layer into four 'fingers,' resulting in a significant increase in the jet mixing downstream. For six delta tabs the mixing layer distortion settles back to a three finger configuration through an interaction of the streamwise vortices. The tabs are found to be equally effective in jets with turbulent or laminar initial boundary layers. Two sources of streamwise vorticity are postulated for the flow under consideration. One is the upstream 'pressure hill,' generated by the tab, which constitutes the main contributor of vorticity to the dominant pair. Another is due to vortex filaments shed from the sides of the tab and reoriented downstream by the mean shear of the mixing layer. Depending on the orientation of the tab, the latter source can produce a vortex pair having a sense of rotation opposite to that of the dominant pair. In the case of the delta tab, vorticity from the two sources add, explaining the strong effect in that configuration.

Flagellated bacteria exploiting helical propulsion are known to swim along circular trajectories near surfaces. Fluid dynamics predicts this circular motion to be clockwise (CW) above a rigid surface (when viewed from inside the fluid) and counter-clockwise (CCW) below a free surface. Recent experimental investigations showed that complex physicochemical processes at the nearby surface could lead to a change in the direction of rotation, both at solid surfaces absorbing slip-inducing polymers and interfaces covered with surfactants. Motivated by these results, we use a far-field hydrodynamic model to predict the kinematics of swimming near three types of interfaces: clean fluid-fluid interface, slipping rigid wall, and a fluid interface covered by incompressible surfactants. Representing the helical swimmer by a superposition of hydrodynamic singularities, we first show that in all cases the surfaces reorient the swimmer parallel to the surface and attract it, both of which are a consequence of the Stokes dipole component of the swimmer flow field. We then show that circular motion is induced by a higher-order singularity, namely a rotlet dipole, and that its rotation direction (CW vs. CCW) is strongly affected by the boundary conditions at the interface and the bacteria shape. Our results suggest thus that the hydrodynamics of complex interfaces provide a mechanism to selectively stir bacteria.

We study reduced-order models of three-dimensional perturbations in linearized channel flow using balanced proper orthogonal decomposition (BPOD). The models are obtained from three-dimensional simulations in physical space as opposed to the traditional single-wavenumber approach, and are therefore better able to capture the effects of localized disturbances or localized actuators. In order to assess the performance of the models, we consider the impulse response and frequency response, and variation of the Reynolds number as a model parameter. We show that the BPOD procedure yields models that capture the transient growth well at a low order, whereas standard POD does not capture the growth unless a considerably larger number of modes is included, and even then can be inaccurate. In the case of a localized actuator, we show that POD modes which are not energetically significant can be very important for capturing the energy growth. In addition, a comparison of the subspaces resulting from the two methods suggests that the use of a non-orthogonal projection with adjoint modes is most likely the main reason for the superior performance of BPOD. We also demonstrate that for single-wavenumber perturbations, low-order BPOD models reproduce the dominant eigenvalues of the full system better than POD models of the same order. These features indicate that the simple, yet accurate BPOD models are a good candidate for developing model-based controllers for channel flow. Comment: 35 pages, 20 figures

A particle dynamics-based hybrid model, consisting of monodisperse spherical solid particles and volume-averaged gas hydrodynamics, is used to study traveling planar waves (one-dimensional traveling waves) of voids formed in gas-fluidized beds of narrow cross sectional areas. Through ensemble-averaging in a co-traveling frame, we compute solid phase continuum variables (local volume fraction, average velocity, stress tensor, and granular temperature) across the waves, and examine the relations among them. We probe the consistency between such computationally obtained relations and constitutive models in the kinetic theory for granular materials which are widely used in the two-fluid modeling approach to fluidized beds. We demonstrate that solid phase continuum variables exhibit appreciable ``path dependence'', which is not captured by the commonly used kinetic theory-based models. We show that this path dependence is associated with the large rates of dilation and compaction that occur in the wave. We also examine the relations among solid phase continuum variables in beds of cohesive particles, which yield the same path dependence. Our results both for beds of cohesive and non-cohesive particles suggest that path-dependent constitutive models need to be developed.

Experimental measurements of properties of the large-scale circulation (LSC) in turbulent convection of a fluid heated from below in a cylindrical container of aspect ratio one are presented and used to test a model of diffusion in a potential well for the LSC. The model consists of a pair of stochastic ordinary differential equations motivated by the Navier-Stokes equations. The two coupled equations are for the azimuthal orientation theta_0, and for the azimuthal temperature amplitude delta at the horizontal midplane. The dynamics is due to the driving by Gaussian distributed white noise that is introduced to represent the action of the small-scale turbulent fluctuations on the large-scale flow. Measurements of the diffusivities that determine the noise intensities are reported. Two time scales predicted by the model are found to be within a factor of two or so of corresponding experimental measurements. A scaling relationship predicted by the model between delta and the Reynolds number is confirmed by measurements over a large experimental parameter range. The Gaussian peaks of probability distributions p(delta) and p(\dot\theta_0) are accurately described by the model; however the non-Gaussian tails of p(delta) are not. The frequency, angular change, and amplitude bahavior during cessations are accurately described by the model when the tails of the probability distribution of $\delta$ are used as experimental input. Comment: 17 pages, 17 figures