Volume 26, Issue 1, January 2014

We report experimental observations of the controlled deformation of a dielectric liquid jet subjected to a local highvoltage electrostatic field in the direction normal to the jet. The jet deforms to the shape of an elliptic cylinder upon application of a normal electrostatic field. As the applied electric field strength is increased, the elliptic cylindrical jet deforms permanently into a flat sheet, and eventually breaksup into droplets. We interpret this observation—the stretch of the jet is in the normal direction to the applied electric field—qualitatively using the TaylorMelcher leaky dielectric theory, and develop a simple scaling model that predicts the critical electric field strength for the jettosheet transition. Our model shows a good agreement with experimental results, and has a form that is consistent with the classical drop deformation criterion in the TaylorMelcher theory. Finally, we statistically analyze the resultant droplets from sheet breakup, and find that increasing the applied electric field strength improves droplet uniformity and reduces droplet size.
 ANNOUNCEMENTS


Announcement: The 2013 François Naftali Frenkiel Award for Fluid Mechanics
View Description Hide Description 
Referee Acknowledgment for 2013
View Description Hide Description  Top

 LETTERS


Propulsion by a helical flagellum in a capillary tube
View Description Hide DescriptionWe study the microscale propulsion of a rotating helical filament confined by a cylindrical tube, using a boundaryelement method for Stokes flow that accounts for helical symmetry. We determine the effect of confinement on swimming speed and power consumption. Except for a small range of tube radii at the tightest confinements, the swimming speed at fixed rotation rate increases monotonically as the confinement becomes tighter. At fixed torque, the swimming speed and power consumption depend only on the geometry of the filament centerline, except at the smallest pitch angles for which the filament thickness plays a role. We find that the “normal” geometry of Escherichia coli flagella is optimized for swimming efficiency, independent of the degree of confinement. The efficiency peaks when the arc length of the helix within a pitch matches the circumference of the cylindrical wall. We also show that a swimming helix in a tube induces a net flow of fluid along the tube.

Effect of the computational domain on direct simulations of turbulent channels up to Re _{τ} = 4200
View Description Hide DescriptionThe effect of domain size on direct numerical simulations of turbulent channels with periodic boundary conditions is studied. New simulations are presented up to Re τ = 4179 in boxes with streamwise and spanwise sizes of 2πh × πh, where h is the channel halfheight. It is found that this domain is large enough to reproduce the onepoint statistics of larger boxes. A simulation in a box of size 60πh × 6πh is used to show that a contour of the twodimensional premultiplied spectrum of the streamwise velocity containing 80% of the kinetic energy closes at λ x ≈ 100h.

Powerlaw versus loglaw in wallbounded turbulence: A largeeddy simulation perspective
View Description Hide DescriptionThe debate whether the mean streamwise velocity in wallbounded turbulent flows obeys a loglaw or a powerlaw scaling originated over two decades ago, and continues to ferment in recent years. As experiments and direct numerical simulation can not provide sufficient clues, in this study we present an insight into this debate from a largeeddy simulation (LES) viewpoint. The LES organically combines stateoftheart models (the stretchedvortex model and inflow rescaling method) with a virtualwall model derived under different scaling law assumptions (the loglaw or the powerlaw by George and Castillo [“Zeropressuregradient turbulent boundary layer,” Appl. Mech. Rev.50, 689 (1997)]). Comparison of LES results for Re θ ranging from 10^{5} to 10^{11} for zeropressuregradient turbulent boundary layer flows are carried out for the mean streamwise velocity, its gradient and its scaled gradient. Our results provide strong evidence that for both sets of modeling assumption (log law or power law), the turbulence gravitates naturally towards the loglaw scaling at extremely large Reynolds numbers.
 Top

 ARTICLES

 Biofluid Mechanics

Mechanism of transient force augmentation varying with two distinct timescales for interacting vortex rings
View Description Hide DescriptionThe dynamics of dual vortex ring flows is studied experimentally and numerically in a model system that consists of a pistoncylinder apparatus. The flows are generated by double identical strokes which have the velocity profile characterized by the sinusoidal function of half the period. By calculating the total wake impulse in two strokes in the experiments, it is found that the average propulsive force increases by 50% in the second stroke for the sufficiently small stroke length, compared with the first stroke. In the numerical simulations, two types of transient force augmentation are revealed, there being the transient force augmentation for the small stroke lengths and the absolute transient force augmentation for the large stroke lengths. The relative transient force augmentation increases to 78% for L/D = 1, while the absolute transient force augmentation for L/D = 4 is twice as much as that for L/D = 1. Further investigation demonstrates that the force augmentation is attributed to the interaction between vortex rings, which induces transport of vortex impulse and more evident fluid entrainment. The critical situation of vortex ring separation is defined and indicated, with vortex spacing falling in a narrow gap when the stroke lengths vary. A new model is proposed concerning the limiting process of impulse, further suggesting that apart from vortex formation timescale, vortex spacing should be interpreted as an independent timescale to reflect the dynamics of vortex interaction.

Expansions at small Reynolds numbers for the locomotion of a spherical squirmer
View Description Hide DescriptionThe locomotion of a spherical squirmer — a model organism that achieves selfpropulsion via steady tangential movement of its surface — is quantified at small Reynolds number R. Matched asymptotic expansions are employed to calculate the swimming velocity of the squirmer through O(R ^{2}). Approximations to the velocity and vorticity fields around the squirmer that are uniformly valid to O(R) are also constructed.
 Micro and Nanofluid Mechanics

Sample distribution in peak mode isotachophoresis
View Description Hide DescriptionWe present an analytical study of peak mode isotachophoresis (ITP), and provide closed form solutions for sample distribution and electric field, as well as for leading, trailing, and counterion concentration profiles. Importantly, the solution we present is valid not only for the case of fully ionized species, but also for systems of weak electrolytes which better represent real buffer systems and for multivalent analytes such as proteins and DNA. The model reveals two major scales which govern the electric field and buffer distributions, and an additional length scale governing analyte distribution. Using wellcontrolled experiments, and numerical simulations, we verify and validate the model and highlight its key merits as well as its limitations. We demonstrate the use of the model for determining the peak concentration of focused sample based on known buffer and analyte properties, and show it differs significantly from commonly used approximations based on the interface width alone. We further apply our model for studying reactions between multiple species having different effective mobilities yet cofocused at a single ITP interface. We find a closed form expression for an effectiveon rate which depends on reactants distributions, and derive the conditions for optimizing such reactions. Interestingly, the model reveals that maximum reaction rate is not necessarily obtained when the concentration profiles of the reacting species perfectly overlap. In addition to the exact solutions, we derive throughout several closed form engineering approximations which are based on elementary functions and are simple to implement, yet maintain the interplay between the important scales. Both the exact and approximate solutions provide insight into sample focusing and can be used to design and optimize ITPbased assays.

Vortex flows induced by droplike aggregate drift in magnetic fluids
View Description Hide DescriptionThe paper reports a new phenomenon—vortex flows in isothermal magnetic fluids in the vicinity of the localized source of magnetic field (magnetized iron sphere) induced by the drift of droplike aggregates. Although the observed magnetic precipitation of droplike aggregates resembles an ordinary rainfall in the Earth atmosphere, its origin and nature are quite different. In magnetic fluids this “rain” is induced by the nonuniform magnetic field and occurs at the scale of 1 mm, not at the scale of several kilometers as in the Earth atmosphere. The reason of this phenomenon is that the applied magnetic field initiates phase transition of “gasliquid” type which is accompanied by formation of condensed phase represented by droplike aggregates with the characteristic dimension of about tens of micrometers elongated along the field lines. Inhomogeneous spatial distribution of droplike aggregates leads to deviation of the ponderomotive force, which is responsible for the formation of vortex flows in the fluid. The “rain” is the primary reason for the vortex flows and it lasts until all magnetic particles capable of condensing into droplike aggregates precipitate at the surface of the condensation core (iron sphere). Thus, vortex flows induced by droplike aggregate magnetophoresis represent one variant of “gasliquid” phase transition. Hydrodynamic flows intensify mass transfer in vicinity of magnetic condensation core and considerably speed it up.

Dynamics of a nanodroplet under a transmission electron microscope
View Description Hide DescriptionWe investigate the cyclical stickslip motion of water nanodroplets on a hydrophilic substrate viewed with and stimulated by a transmission electron microscope. Using a continuum long wave theory, we show how the electrostatic stress imposed by nonuniform charge distribution causes a pinned convex drop to deform into a toroidal shape, with the shape characterized by the competition between the electrostatic stress and the surface tension of the drop, as well as the charge density distribution which follows a Poisson equation. A horizontal gradient in the charge density creates a lateral driving force, which when sufficiently large, overcomes the pinning induced by surface heterogeneities in the substrate disjoining pressure, causing the drop to slide on the substrate via a cyclical stickslip motion. Our model predicts steplike dynamics in drop displacement and surface area jumps, qualitatively consistent with experimental observations.

Flows and torques in Brownian ferrofluids subjected to rotating uniform magnetic fields in a cylindrical and annular geometry
View Description Hide DescriptionFerrofluid flow in cylindrical and annular geometries under the influence of a uniform rotating magnetic field was studied experimentally using aqueous ferrofluids consisting of low concentrations (<0.01 v/v) of cobalt ferrite nanoparticles with Brownian relaxation to test the ferrohydrodynamic equations, elucidate the existence of couple stresses, and determine the value of the spin viscosity in these fluids. An ultrasound technique was used to measure bulk velocity profiles in the spinup (cylindrical) and annular geometries, varying the intensity and frequency of the rotating magnetic field generated by a two pole stator winding. Additionally, torque measurements in the cylindrical geometry were made. Results show rigidbody like velocity profiles in the bulk, and no dependence on the axial direction. Experimental velocity profiles were in quantitative agreement with the predictions of the spin diffusion theory, with a value of the spin viscosity of ∼10^{−8} kg m/s, two orders of magnitude larger than the value estimated earlier for iron oxide based ferrofluids, and 12 orders of magnitude larger than estimated using dimensional arguments valid in the infinite dilution limit. These results provide further evidence of the existence of couple stresses in ferrofluids and their role in driving the spinup flow phenomenon.

Subadditive ionic transport across arrays of solidstate nanopores
View Description Hide DescriptionNanopores, either biological, solidstate, or ultrathin pierced graphene, are powerful tools which are central to many applications, from sensing of biological molecules to desalination and fabrication of ion selective membranes. However, the interpretation of transport through low aspectratio nanopores becomes particularly complex as 3D access effects outside the pores are expected to play a dominant role. Here, we report both experiments and theory showing that, in contrast to naïve expectations, longrange mutual interaction across an array of nanopores leads to a nonextensive, sublinear scaling of the global conductance on the number of pores N. A scaling analysis demonstrates that the Ndependence of the conductance depends on the topology of the network. It scales like G ∼ N/log N for a 1D line of pores, and like for a 2D array, in agreement with experimental measurements. Our results can be extended to alternative transport phenomena obeying Laplace equations, such as diffusive, thermal, or hydrodynamic transport. Consequences of this counterintuitive behavior are discussed in the context of transport across thin membranes, with applications in energy harvesting.

Monte Carlo simulation of nitrogen dissociation based on stateresolved cross sections
View Description Hide DescriptionStateresolved analyses of N + N2 are performed using the direct simulation Monte Carlo (DSMC) method. In describing the elastic collisions by a stateresolved method, a statespecific total cross section is proposed. The stateresolved method is constructed from the statespecific total cross section and the rovibrational statetostate transition cross sections for boundbound and boundfree transitions taken from a NASA database. This approach makes it possible to analyze the rotationaltotranslational, vibrationaltotranslational, and rotationaltovibrational energy transfers and the chemical reactions without relying on macroscopic properties and phenomenological models. In nonequilibrium heat bath calculations, the results of present stateresolved DSMC calculations are validated with those of the master equation calculations and the existing shocktube experimental data for boundbound and boundfree transitions. In various equilibrium and nonequilibrium heat bath conditions and 2D cylindrical flows, the DSMC calculations by the stateresolved method are compared with those obtained with previous phenomenological DSMC models. In these previous DSMC models, the variable soft sphere, phenomenological LarsenBorgnakke, quantum kinetic, and total collision energy models are considered. From these studies, it is concluded that the stateresolved method can accurately describe the rotationaltotranslational, vibrationaltotranslational, and rotationaltovibrational transfers and quasisteady state of rotational and vibrational energies in nonequilibrium chemical reactions by statetostate kinetics.
 Interfacial Flows

Transient growth of droplet instabilities in a stream
View Description Hide DescriptionDroplet deformation is the first stage of all aerodynamically inducedbreakups, considerably affecting the characteristics of the atomization. In the present study, using an adaptive volume of fluid method, two and threedimensional direct numerical simulations have been performed to understand droplet deformation. A high Reynolds number and a range of relatively high Weber numbers are chosen, addressing the shear breakup of droplets in a stream. The study is focused on the initiation and growth of instabilities over the droplet. The role of KelvinHelmholtz and RayleighTaylor instabilities in wave formation and azimuthal transverse modulation are shown and the obtained results for the most amplified wavenumbers are compared with instability theories for zero and nonzero vorticity layers. The present results for the most amplified wavenumbers and deformation topologies are in good agreement with the previous experimental results.

Numerical analysis of droplet impact onto liquid film
View Description Hide DescriptionNormal impingement of a single droplet on a thin liquid film is investigated numerically solving the axisymmetric NavierStokes equations. Gravity and viscosity are taken into account whereas compressibility effects are neglected. Two phases are tracked by means of volume of fluid method and adaptive mesh refinement is used to increase accuracy of the interface. Numerical results are validated both qualitatively and quantitatively using experimental measurements. Effects of gas density, gas viscosity, and film thickness on the crown behavior are studied. Influence of droplet deviation from spherical shape on the crown behavior is investigated. It is shown that increasing the gas density leads to reduction of crown radius evolution rate, while gas viscosity does not affect the rate of crown radius evolution. Development rate of crown height decreases by increasing the gas density. Reynolds number and splashing regime can change the effect of gas viscosity on the crown height evolution. Deviation of droplet from sphere can change behavior of crown completely as result of change in droplet mass center position. Difference between numerical results and experimental ones is justified using different droplet shapes.

Electric field induced sheeting and breakup of dielectric liquid jets
View Description Hide DescriptionWe report experimental observations of the controlled deformation of a dielectric liquid jet subjected to a local highvoltage electrostatic field in the direction normal to the jet. The jet deforms to the shape of an elliptic cylinder upon application of a normal electrostatic field. As the applied electric field strength is increased, the elliptic cylindrical jet deforms permanently into a flat sheet, and eventually breaksup into droplets. We interpret this observation—the stretch of the jet is in the normal direction to the applied electric field—qualitatively using the TaylorMelcher leaky dielectric theory, and develop a simple scaling model that predicts the critical electric field strength for the jettosheet transition. Our model shows a good agreement with experimental results, and has a form that is consistent with the classical drop deformation criterion in the TaylorMelcher theory. Finally, we statistically analyze the resultant droplets from sheet breakup, and find that increasing the applied electric field strength improves droplet uniformity and reduces droplet size.

Simulations of Janus droplets at equilibrium and in shear
View Description Hide DescriptionJanus droplets are compound droplets that consist of two adhering drops of different fluids that are suspended in a third fluid. We use the ShanChen lattice Boltzmann method for multicomponent mixtures to simulate Janus droplets at rest and in shear. In this simulation model, interfacial tensions are not known a priori from the model parameters and must be determined using numerical experiments. We show that interfacial tensions obtained with the YoungLaplace law are consistent with those measured from the equilibrium geometry. The regimes of adhering, separated, and engulfing droplets were explored. Two different adhesion geometries were considered for twodimensional simulations of Janus droplets in shear. The first geometry resembles two adhering circles with small overlap. In the second geometry, the two halves are semicircular. For both geometries, the rotation rate of the droplet depends on its orientation. The width of the periodic simulation domain also affects the rotation rate of both droplet types up to an aspect ratio of 6:1 (width:height). While the droplets with the first geometry oscillated about the middle of the domain, the droplets of the second geometry did not translate while rotating. A fourpole vortex structure inside droplets of the second geometry was found. These simulations of single Janus droplets reveal complex behaviour that implies a rich range of possibilities for the rheology of Janus emulsions.

Analysis of interfacial instability and multimode bubble formation in saturated boiling using coupled level set and volumeoffluid approach
View Description Hide DescriptionThe dynamics of vaporliquid interface are important because interfacial instability determines bubble growth, detachment frequency, waiting time, shape of bubbles, and the interrelationship between bubble formation sites. In this study, a detailed numerical simulation has been performed to understand the transition in bubble release pattern and multimode bubble formation in saturated pool boiling. The interfaces drop down alternatively at the nodes and antinodes of the wavelengths dictated by RayleighTaylor instability and TaylorHelmholtz instability. Due to higher degrees of superheat, vapor jets emanate from nodes and antinodes. An attempt has been made to predict the maximum and minimum heat fluxes during saturated pool boiling.

Porescale dynamics of salt transport and distribution in drying porous media
View Description Hide DescriptionUnderstanding the physics of water evaporation from saline porous media is important in many natural and engineering applications such as durability of building materials and preservation of monuments, water quality, and mineralfluid interactions. We applied synchrotron xray microtomography to investigate the porescale dynamics of dissolved salt distribution in a three dimensional drying saline porous media using a cylindrical plastic column (15 mm in height and 8 mm in diameter) packed with sand particles saturated with CaI2 solution (5% concentration by mass) with a spatial and temporal resolution of 12 μm and 30 min, respectively. Every time the drying sand column was set to be imaged, two different images were recorded using distinct synchrotron xrays energies immediately above and below the Kedge value of Iodine. Taking the difference between pixel gray values enabled us to delineate the spatial and temporal distribution of CaI2 concentration at pore scale. Results indicate that during early stages of evaporation, air preferentially invades large pores at the surface while finer pores remain saturated and connected to the wet zone at bottom via capillaryinduced liquid flow acting as evaporating spots. Consequently, the salt concentration increases preferentially in finer pores where evaporation occurs. Higher salt concentration was observed close to the evaporating surface indicating a convectiondriven process. The obtained salt profiles were used to evaluate the numerical solution of the convectiondiffusion equation (CDE). Results show that the macroscale CDE could capture the overall trend of the measured salt profiles but fail to produce the exact slope of the profiles. Our results shed new insight on the physics of salt transport and its complex dynamics in drying porous media and establish synchrotron xray tomography as an effective tool to investigate the dynamics of salt transport in porous media at high spatial and temporal resolution.

The effect of a normal electric field on wave propagation on a fluid film
View Description Hide DescriptionLongwavelength, smallamplitude disturbances on the surface of a fluid layer subject to a normal electric field are considered. In our model, a dielectric medium lies above a layer of perfectly conducting fluid, and the electric field is produced by parallel plate electrodes. The Reynolds number of the fluid flow is taken to be large, with viscous effects restricted to a thin boundary layer on the lower plate. The effects of surface tension and electric field enter the governing equation through an inverse Bond number and an electrical Weber number, respectively. The thickness of the lower fluid layer is assumed to be much smaller than the disturbance wavelength, and a unified analysis is presented allowing for the full range of scalings for the thickness of the upper dielectric medium. A variety of different forms of modified Kortewegde Vries equation are derived, involving Hilbert transforms, convolution terms, higher order spatial derivatives, and fractional derivatives. Critical values are identified for the inverse Bond number and electrical Weber number at which the qualitative nature of the disturbances changes.