Volume 28, Issue 5, May 2016
 LETTERS


Moderation of nearfield pressure over a supersonic flight model using laserpulse energy deposition
View Description Hide DescriptionThe impact of a thermal bubble produced by energy deposition on the nearfield pressure over a Mach 1.7 freeflight model was experimentally investigated using an aeroballistic range. A laser pulse from a transversely excited atmospheric (TEA) CO2 laser was sent into a test chamber with 68 kPa ambient pressure, focused 10 mm below the flight path of a conically nosed cylinder with a diameter of 10 mm. The pressure history, which was measured 150 mm below the flight path along the acoustic ray past the bubble, exhibited precursory pressure rise and roundoff peak pressure, thereby demonstrating the proofofconcept of sonic boom alleviation using energy deposition.

Limiting tensile strength of liquid nitrogen
View Description Hide DescriptionThe method of pulsed liquid superheating in a tension wave that forms when a compression pulse is reflected from the liquid free surface has been used to investigate the kinetics of spontaneous cavitation in liquid nitrogen. The limiting tensile stress pn of nitrogen corresponding to nucleation rates J = 10^{20} − 10^{22} s^{−1} m^{−3} and the slope of the temperature dependence of the nucleation rate GT = dlnJ/dT have been determined by experiment. The results of experiments are compared with classical nucleation theory (CNT) and a modified classical nucleation theory (MCNT), which takes into account the size dependence of the properties of a critical bubble. It has been noted that experimental data are in better agreement with the results of MCNT than with those of CNT.
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 ARTICLES

 Micro and Nanofluid Mechanics

Nearfield acousto monitoring shear interactions inside a drop of fluid: The role of the zeroslip condition
View Description Hide DescriptionA full understanding of nanometerrange (nearfield) interactions between two sliding solid boundaries, with a mesoscopic fluid layer sandwiched in between, remains challenging. In particular, the origin of the blueshift resonance frequency experienced by a laterally oscillating probe when approaching a substrate is still a matter of controversy. A simpler problem is addressed here, where a laterally oscillating solid probe interacts with a more sizable drop of fluid that rests on a substrate, aiming at identifying interaction mechanisms that could also be present in the nearfield interaction case. It is found that the inelastic component of the probefluid interaction does not constitute the main energydissipation channel and has a weak dependence on fluid’s viscosity, which is attributed to the zeroslip hydrodynamic condition. In contrast, the acoustic signal engendered by the fluid has a stronger dependence on the fluid’s viscosity (attributed also to the zeroslip hydrodynamic condition) and correlates well with the probe’s resonance frequency redshift. We propose a similar mechanism happens in near field experiments, but a blueshift in the probe’s resonance results as a consequence of the fluid molecules (subjected to the zeroslip condition at both the probe and substrate boundaries) exerting instead a spring type restoring force on the probe.

Electroosmosismodulated peristaltic transport in microfluidic channels
View Description Hide DescriptionWe analyze the peristaltic motion of aqueous electrolytes altered by means of applied electric fields. Handling electrolytes in typical peristaltic channel material such as polyvinyl chloride and Teflon leads to the generation of a net surface charge on the channel walls, which attracts counterions and repels coions from the aqueous solution, thus leading to the formation of an electrical double layer—a region of net charges near the wall. We analyze the spatial distribution of pressure and wall shear stress for a continuous wave train and single pulse peristaltic wave in the presence of an electrical (electroosmotic) body force, which acts on the net charges in the electrical double layer. We then analyze the effect of the electroosmotic body force on the particle reflux as elucidated through the net displacement of neutrally buoyant particles in the flow as the peristaltic waves progress. The impact of combined electroosmosis and peristalsis on trapping of a fluid volume (e.g., bolus) inside the travelling wave is also discussed. The present analysis goes beyond the traditional analysis, which neglects the possibility of coupling the net pumping of fluids due to peristalsis and allows us to derive general expressions for the pressure drop and flow rate in order to set up a general framework for incorporating flow control and actuation by simultaneous peristalsis and application of electric fields to aqueous solutions. It is envisaged that the results presented here may act as a model for the design of labonachip devices.

Highfrequency sound wave propagation in binary gas mixtures flowing through microchannels
View Description Hide DescriptionThe propagation of highfrequency sound waves in binary gas mixtures flowing through microchannels is investigated by using the linearized Boltzmann equation based on a BhatnagarGrossKrook (BGK)type approach and diffuse reflection boundary conditions. The results presented refer to mixtures whose constituents have comparable molecular mass (like NeAr) as well as to disparatemass gas mixtures (composed of very heavy plus very light molecules, like HeXe). The sound wave propagation model considered in the present paper allows to analyze the precise nature of the forcedsound modes excited in different gas mixtures.
 Interfacial Flows

Growth of sinuous waves on thin liquid sheets: Comparison of predictions with experiments
View Description Hide DescriptionA recent theory [M. S. Tirumkudulu and M. Paramati, “Stability of a moving radial liquidsheet: Time dependent equations,” Phys. Fluids 25(10), 102–107 (2013)] has shown that a radially expanding liquidsheet is unstable to sinuous wave disturbances due to the thinning of the liquidsheet while ignoring the presence of a surrounding gas phase. In this work, we compare the predictions of the aforementioned theory with the measurements of Crapper et al. [“Large amplitude KelvinHelmholtz waves on thin liquid sheets,” Proc. R. Soc. London, Ser. A 342(1629), 209–224 (1975)] who measured the amplitude and spatial growth rates of sinuous waves induced in radially expanding liquidsheets produced by fan spray nozzles. The predicted growth rates are remarkably close to the measurements over a range of forcing frequencies and amplitudes even though the experiments were performed in the presence of a surrounding gas phase. This is in contrast to large discrepancies observed by Crapper et al. when the same measurements were compared with the predictions of a spatial stability analysis for a moving liquidsheet that accounts for the inertia of the surrounding gas phase but ignores the thickness variation of the sheet.

Effect of superheat and electric field on saturated film boiling
View Description Hide DescriptionThe objective of this investigation is to study the influence of superheat temperature and applied uniform electric field across the liquidvapor interface during film boiling using a coupled level set and volume of fluid algorithm. The hydrodynamics of bubble growth, detachment, and its morphological variation with electrohydrodynamic forces are studied considering the medium to be incompressible, viscous, and perfectly dielectric at near critical pressure. The transition in interfacial instability behavior occurs with increase in superheat, the bubble release being periodic both in space and time. Discrete bubble growth occurs at a smaller superheat whereas vapor columns form at the higher superheat values. Destabilization of interfacial motion due to applied electric field results in decrease in bubble separation distance and increase in bubble release rate culminating in enhanced heat transfer rate. A comparison of maximum bubble height owing to application of different intensities of electric field is performed at a smaller superheat. The change in dynamics of bubble growth due to increasing superheat at a high intensity of electric field is studied. The effect of increasing intensity of electric field on the heat transfer rate at different superheats is determined. The boiling characteristic is found to be influenced significantly only above a minimum critical intensity of the electric field.

Simulation of bubble expansion and collapse in the vicinity of a free surface
View Description Hide DescriptionThe present paper focuses on the numerical simulation of the interaction of lasergenerated bubbles with a free surface, including comparison of the results with instances from highspeed videos of the experiment. The Volume Of Fluid method was employed for tracking liquid and gas phases while compressibility effects were introduced with appropriate equations of state for each phase. Initial conditions of the bubble pressure were estimated through the traditional Rayleigh Plesset equation. The simulated bubble expands in a nonspherically symmetric way due to the interference of the free surface, obtaining an oval shape at the maximum size. During collapse, a jet with mushroom cap is formed at the axis of symmetry with the same direction as the gravity vector, which splits the initial bubble to an agglomeration of toroidal structures. Overall, the simulation results are in agreement with the experimental images, both quantitatively and qualitatively, while pressure waves are predicted both during the expansion and the collapse of the bubble. Minor discrepancies in the jet velocity and collapse rate are found and are attributed to the thermodynamic closure of the gas inside the bubble.
 Viscous and NonNewtonian Flows

Basal entrainment by Newtonian gravitydriven flows
View Description Hide DescriptionGravitydriven flows can erode the bed along which they descend and increase their mass by a factor of 10 or more. This process is called “basal entrainment.” Although documented by field observations and laboratory experiments, it remains poorly understood. This paper examines what happens when a viscous gravitydriven flow generated by releasing a fixed volume of incompressible Newtonian fluid encounters a stationary layer (composed of fluid with the same density and viscosity). Models based on depthaveraged mass and momentum balance equations deal with bedflow interfaces as shock waves. In contrast, we use an approach involving the longwave approximation of the NavierStokes equations (lubrication theory), and in this context, bedflow interfaces are acceleration waves that move quickly across thin stationary layers. The incoming flow digs down into the bed, pushing up downstream material, thus advancing the flow front. Extending the method used by Huppert [“The propagation of twodimensional and axisymmetric viscous gravity currents over a rigid horizontal surface,” J. Fluid Mech. 121, 43–58 (1982)] for modeling viscous dambreak waves, we end up with a nonlinear diffusion equation for the flow depth, which is solved numerically. Theory is compared with experimental results. Excellent agreement is found in the limit of low Reynolds numbers (i.e., for flowReynolds numbers lower than 20) for the front position over time and flow depth profile.

Dipcoating of yield stress fluids
View Description Hide DescriptionWe review and discuss the characteristics of dipcoating of yield stress fluids on the basis of theoretical considerations, numerical simulations of the flow in the bath, and experimental data with different materials. We show that in general, due to the yield stress,viscous dissipations are sufficiently large for capillary effects to be negligible in the process. Dipcoating with yield stress fluids is thus essentially governed by an equilibrium between viscous and gravity effects. In contrast with simple liquids, the coated thickness is uniform and remains fixed to the plate. At low velocities, it appears to tend to a value significantly smaller than the Derjaguin and Levi prediction [B. V. Derjaguin and S. M. Levi, Film Coating Theory (The Focal Press, London, 1964)], i.e., critical thickness of stoppage of a free surface flow along a vertical plate. We show that this comes from the fact that in the bath only a relatively small layer of fluid is in its liquid regime along the moving plate, while the rest of the material is in a solid regime. From numerical simulations, we describe the general trends of this liquid layer, and in particular, its thickness as a function of the rheological characteristics and plate velocity. We finally propose a model for the dipcoating of yield stress fluid, assuming that the solid volume of fluid finally fixed to the plate results from the mass flux of the liquid layer in the bath minus a mass flux due to some downward flow under gravity in the transition zone. A good agreement between this model and experimental data is found for a fluid with a yield stress larger than 20 Pa.

Onedimensional nonlinear instability study of a slightly viscoelastic, perfectly conducting liquid jet under a radial electric field
View Description Hide DescriptionA onedimensional electrified viscoelastic model is built to study the nonlinear behavior of a slightly viscoelastic, perfectly conducting liquid jet under a radial electric field. The equations are solved numerically using an implicit finite difference scheme together with a boundary element method. The electrified viscoelastic jet is found to evolve into a beadsonstring structure in the presence of the radial electric field. Although the radial electric field greatly enhances the linear instability of the jet, its influence on the decay of the filament thickness is limited during the nonlinear evolution of the jet. On the other hand, the radial electric field induces axial nonuniformity of the first normal stress difference within the filament. The first normal stress difference in the center region of the filament may be greatly decreased by the radial electric field. The regions with/without satellite droplets are illuminated on the χ (the electrical Bond number)k (the dimensionless wave number) plane. Satellite droplets may be formed for larger wave numbers at larger radial electric fields.

Stretch and hold: The dynamics of a filament governed by a viscoelastic constitutive model with thixotropic yield stress behavior
View Description Hide DescriptionThe transient behavior of filament stretching is studied for a viscoelastic constitutive model that combines a partially extending strand convection model with a Newtonian solvent. The vertical filament is fixed at the bottom and the top is pulled up and held. Gravity and surface tension are also included in the model though they are not the primary mechanisms in this study. An axisymmetric circular slender jet approximation is applied. An asymptotic analysis for the initial stages of evolution is performed for large relaxation time, so that an interplay of fast and slow time scales emerges, and gives a criterion for whether the fluid yields immediately or whether slow dynamics ensues, depending on elastic stresses, gravity, and capillary stress. The analysis guides the choice of parameters to exemplify thixotropy and yield stress behavior through numerical simulations of the full governing equations from start to finish of the filament evolution. Elastic effects promote a spring back of the filament toward its initial shape, while pulling at the top stretches the filament locally to promote yielding, with the lower portion of the filament remaining unyielded. In addition, a parameter regime that models extensional experiments in the literature for yield stress fluids sheds light on the differences in filament shapes.

Flipping and scooping of curved 2D rigid fibers in simple shear: The Jeffery equations
View Description Hide DescriptionThe dynamical system governing the motion of a curved rigid twodimensional circulararc fiber in simple shear is derived in analytical form. This is achieved by finding the solution for the associated lowReynoldsnumber flow around such a fiber using the methods of complex analysis. Solutions of the dynamical system display the “flipping” and “scooping” recently observed in computational studies of threedimensional fibers using linked rigid rod and beadshell models [J. Wang et al., “Flipping, scooping, and spinning: Drift of rigid curved nonchiral fibers in simple shear flows,” Phys. Fluids 24, 123304 (2012)]. To complete the Jefferytype equations for a curved fiber in a linear flow field we also derive its evolution equations in an extensional flow. It is expected that the equations derived here also govern the motion of slender, curved, threedimensional rigid fibers when they evolve purely in the plane of shear or strain.

Analytical and numerical analysis of bifurcations in thermal convection of viscoelastic fluids saturating a porous square box
View Description Hide DescriptionWe report theoretical and numerical results on bifurcations in thermal instability for a viscoelastic fluid saturating a porous square cavity heated from below. The modified Darcy law based on the OldroydB model was used for modeling the momentum equation. In addition to Rayleigh number ℜ, two more dimensionless parameters are introduced, namely, the relaxation time λ 1 and the retardation time λ 2. Temporal stability analysis showed that the first bifurcation from the conductive state may be either oscillatory for sufficiently elastic fluids or stationary for weakly elastic fluids. The dynamics associated with the nonlinear interaction between the two kinds of instabilities is first analyzed in the framework of a weakly nonlinear theory. For sufficiently elastic fluids, analytical expressions of the nonlinear threshold above which a second hysteretic bifurcation from oscillatory to stationary convective pattern are derived and found to agree with twodimensional numerical simulations of the full equations. Computations performed with high Rayleigh number indicated that the system exhibits a third transition from steady singlecell convection to oscillatory multicellular flows. Moreover, we found that an intermittent oscillation regime may exist with steady state before the emergence of the secondary Hopf bifurcation. For weakly elastic fluids, we determined a second critical value above which a Hopf bifurcation from steady convective pattern to oscillatory convection occurs. The well known limit of for Newtonian fluids is recovered, while the fluid elasticity is found to delay the onset of the Hopf bifurcation. The major new findings were presented in the form of bifurcation diagrams as functions of viscoelastic parameters for ℜ up to 420.

Selfdiffusiophoretic colloidal propulsion near a solid boundary
View Description Hide DescriptionSelfpropelled, chemically powered colloidal locomotors are swimmers designed to transverse small scale landscapes in a range of applications involving micropumping, sensing, and cargo transport. Although applications can require precise navigation and onboard steering mechanisms, here we examine by calculation how locomotors through their hydrodynamic interaction can navigate along a boundary. We adopt an engine model consisting of a spherical Janus colloid coated with a symmetrical catalyst cap, which converts fuel into a product solute. The solute is repelled from the colloid through a repulsive interaction, which occurs over a distance much smaller than the swimmer radius. Within this thin interaction layer, a concentration difference develops along the surface, which generates a pressure gradient as pressure balances the interaction force of the solute with the surface. The pressure gradient drives a slip flow towards the high concentration, which propels the particle oppositely, away from product accumulation (selfdiffusiophoresis). To study boundary guidance, the motion near an infinite noslip planar wall that does not adsorb solute is obtained by analytical solution of the solute conservation and the Stokes equations using bispherical coordinates. Several regimes of boundary interaction unfold: When the colloid is oriented with its cap axisymmetrically facing the wall, it is repelled by the accumulation of solute in the gap between the swimmer and the wall. With the cap opposite to the wall, the swimmer moves towards the wall by the repulsion from the solute accumulating on the cap side, but very large caps accumulate solute in the gap, and the motor stops. For oblique approach with the cap opposite to the wall and small cap sizes, the swimmer is driven to the wall by accumulation on the cap side, but rotates as it approaches the wall, and eventually scatters as the cap reorients and faces the wall. For a swimmer approaching obliquely with a larger cap (again facing away from the wall), boundary navigation results as the accumulation of product in the gap suppresses rotation and provides a normal force, which directs the swimmer to skim along the surface at a fixed distance and orientation or to become stationary. We also demonstrate how gravity can force transitions between skimming and stationary states.
 Particulate, Multiphase, and Granular Flows

Characterizing dynamic hysteresis and fractal statistics of chaotic twophase flow and application to fuel cells
View Description Hide DescriptionIn this study, we analyze the stability of twophase flow regimes and their transitions using chaotic and fractal statistics, and we report new measurements of dynamic twophase pressure drop hysteresis that is related to flow regime stability and channel water content. Twophase flow dynamics are relevant to a variety of realworld systems, and quantifying transient twophase flow phenomena is important for efficient design. We recorded twophase (air and water) pressure drops and flow images in a microchannel under both steady and transient conditions. Using Lyapunov exponents and Hurst exponents to characterize the steadystate pressure fluctuations, we develop a new, measurable regime identification criteria based on the dynamic stability of the twophase pressure signal. We also applied a new experimental technique by continuously cycling the air flow rate to study dynamic hysteresis in twophase pressure drops, which is separate from steadystate hysteresis and can be used to understand twophase flow development time scales. Using recorded images of the twophase flow, we show that the capacitive dynamic hysteresis is related to channel water content and flow regime stability. The mixedwettability microchannel and inchannel water introduction used in this study simulate a polymer electrolyte fuel cell cathode air flow channel.

On the front shape of an inertial granular flow down a rough incline
View Description Hide DescriptionGranular material flowing on complex topographies are ubiquitous in industrial and geophysical situations. In this paper, we study the smallscale experiment of a granular layer flowing on a rough incline. The shape of the granular front is solved analytically by using depthaveraged mass and momentum equations with a fractional expression for the frictional rheology μ(I), which is a generalization of Gray and Ancey [“Segregation, recirculation and deposition of coarse particles near twodimensional avalanche fronts,” J. Fluid Mech. 629, 387 (2009)]. Unlike previous studies where a “plug flow dynamics” is assumed, a free shape factor α describing the vertical velocity profile is taken into account. The effect of inertia and shear rate on the front profile is evidenced through the introduction of the Froude number and the shape factor α. The analytical predictions are compared to experimental results published by Pouliquen [“On the shape of granular fronts down rough inclined planes,” Phys. Fluids 11, 1956 (1999)] and with our new experimental data obtained at higher Froude numbers. A good agreement between theory and experiments is found for α = 5/4, corresponding to a Bagnoldlike velocity profile. However, we observe a systematic deviation near the head of the front where the height vanishes: the theory predicts a continuous precursor layer, while a grainfree region is observed experimentally. This suggests that the vertical velocity profile is not uniform inside the front, but the shape factor α tends to 1 near the head of the front. This raises questions about the vertical velocity profile in granular flows and about the expression of the rheological function μ(I) and its calibration from experimental data.

Two touching spherical drops in a uniaxial compressional flow: The effect of interfacial slip
View Description Hide DescriptionThis study presents a semianalytical solution for the problem of two touching drops with slipping interfaces pushed against each other in a uniaxial compressional flow at low capillary and Reynolds numbers. The jump in the tangential velocity at the liquidliquid interface is modeled using the Navier slip condition. Analytical solutions of the contact force, the dropscale stresses, and the dropscale pressure are provided as functions of the slip coefficient , the viscosity ratio , and the drop size ratio . Since unequal drop sizes are considered, two problems are solved in the tangent sphere coordinate system to determine the steady state position: a pair of touching drops with its contact point at the origin of an axisymmetric straining flow, and two touching drops placed in a uniform flow parallel to the axis of symmetry of the drops. A general observation is that the effect of slip is manifested most strongly for drops whose viscosity is much greater than the suspending fluid . For highly viscous drops, the flow and stress fields transition from those corresponding to solid particles for ακ ≪ 1, to those for inviscid drops in the limit ακ ≫ 1. The analytical expressions provided here for the contact force and the stress distributions will serve to provide the restrictions that complete the definition of the lubrication flow problem in the thin film between the two colliding drops. While the contact force that drains fluid out of the thin film is relatively unaffected by slip, the tangential stress and pressure in the nearcontact region are mitigated significantly for ακ ≫ 1. The latter is expected to assist coalescence at high capillary numbers.

Volumeoffluid simulations of bubble dynamics in a vertical HeleShaw cell
View Description Hide DescriptionBubbles in confined geometries serve an important role for industrial operations involving bubbleliquid interactions. However, high Reynolds number bubble dynamics in confined flows are still not well understood due to experimental challenges. In the present paper, combined experimental and numerical methods are used to provide a comprehensive insight into these dynamics. The bubble behaviour in a vertical HeleShaw cell is investigated experimentally with a fully wetting liquid for a variety of gap thicknesses. A numerical model is developed using the volume of fluid method coupled with a continuum surface force model and a wall friction model. The developed model successfully simulates the dynamics of a bubble under the present experimental conditions and shows good agreement between experimental and simulation results. It is found that with an increased spacing between the cell walls, the bubble shape changes from oblate ellipsoid and sphericalcap to more complicated shapes, while the bubble path changes from only rectilinear to a combination of oscillating and rectilinear; the bubble drag coefficient decreases and this results in a higher bubble velocity caused by a lower pressure exerted on the bubble; the wake boundary and wake length evolve gradually accompanied by vortex formation and shedding.

Multidimensional rheologybased twophase model for sediment transport and applications to sheet flow and pipeline scour
View Description Hide DescriptionSediment transport is fundamentally a twophase phenomenon involving fluid and sediments; however, many existing numerical models are onephase approaches, which are unable to capture the complex fluidparticle and interparticle interactions. In the last decade, twophase models have gained traction; however, there are still many limitations in these models. For example, several existing twophase models are confined to onedimensional problems; in addition, the existing twodimensional models simulate only the region outside the sand bed. This paper develops a new threedimensional twophase model for simulating sediment transport in the sheet flow condition, incorporating recently published rheological characteristics of sediments. The enduringcontact, inertial, and fluid viscosity effects are considered in determining sediment pressure and stresses, enabling the model to be applicable to a wide range of particle Reynolds number. A k − ε turbulence model is adopted to compute the Reynolds stresses. In addition, a novel numerical scheme is proposed, thus avoiding numerical instability caused by high sediment concentration and allowing the sediment dynamics to be computed both within and outside the sand bed. The present model is applied to two classical problems, namely, sheet flow and scour under a pipeline with favorable results. For sheet flow, the computed velocity is consistent with measured data reported in the literature. For pipeline scour, the computed scour rate beneath the pipeline agrees with previous experimental observations. However, the present model is unable to capture vortex shedding; consequently, the sediment deposition behind the pipeline is overestimated. Sensitivity analyses reveal that model parameters associated with turbulence have strong influence on the computed results.