Volume 18, Issue 6, June 2006
 ARTICLES

 Interfacial Flows

Evolution of a compound droplet attached to a coreshell nozzle under the action of a strong electric field
View Description Hide DescriptionThe shape evolution of small compound droplets at the exit of a coreshell system in the presence of a sufficiently strong electric field is studied both experimentally and theoretically. It is shown that the jetting effect at the tip of the shell nozzle does not necessarily cause entrainment of the core fluid, in which case the coelectrospinning process fails to produce coreshell nanofibers. The remedy lies in extending the core nozzle outside its shell counterpart by about half the radius of the latter. The results also show that the free charges migrate very rapidly from both fluids and their interface to the free surface of the shell. This reflects the fact that most of the prejetting evolution of the droplet can be effectively described in terms of the perfect conductor model, even though the fluids can be characterized as leaky dielectrics. The stress level at the coreshell interface is of the order of , the relevant value in assessing the viability of viruses, bacteria, DNA molecules, drugs, enzymes, chromophores, and proteins to be encapsulated in nanofibers via coelectrospinning.

Influence of variable Froude number on waves generated by ships in shallow water
View Description Hide DescriptionPassage through the transcritical speed region of a moving disturbance in a shallow channel, is examined using numerical simulations based on a set of forced Boussinesq equations. The transition is accomplished either by accelerating the wave generating disturbance in a region of constant depth or by moving the disturbance with constant speed over a sloping bottom topography. A series of test cases are examined where the transcritical region is traversed both from subcritical to supercritical speed and vice versa. Results show that the generation of upstream solitary waves depends on the time required for the transition, with large waves being generated for long transition times. It is also apparent that the shape of the wave pattern, and the maximum amplitude of the waves, differ significantly depending on whether the Froude number increase or decrease during the transition of the transcritical region. However, the wave pattern is not determined simply in terms of the Froude number. The strength of the forcing term as well as the underlying process which cause the Froude number to vary, i.e., acceleration and depth variation, influence the wave pattern in different ways. The Froude number is none the less a useful indicator for the problem, as all cases with similar Froude number variations share some common characteristic features.

Hole dynamics in polymer Langmuir films
View Description Hide DescriptionThis article develops a model for the closing of a gaseous hole in a liquid domain within a twodimensional fluid layer coupled to a Stokesian subfluid substrate, and compares this model to experiments following hole dynamics in a polymerLangmuirmonolayer. Closure of such a hole in a fluid layer is driven by the line tension at the hole boundary and the difference in surface pressure within the hole and far outside it. The observed rate of hole closing is close to that predicted by our model using estimates of the line tension obtained by other means, assuming that the surface pressure in the gas is negligible. This result both supports the model and suggests an independent means of determining the line tension. Unlike most previous hydrodynamics models of Langmuirfilms, the closing of a hole necessarily involves vertical motion of the underlying incompressible fluid. Fluid is dragged along with the liquidmonolayer towards the center of the hole, and must plunge away from the surface. An explicit expression is found for this vertical fluid flow in the bulk substrate.
 Viscous and NonNewtonian Flows

The swimming of animalcules
View Description Hide DescriptionAnimalcules can swim in a viscous fluid at low Reynolds number and low Stokes number by moving their body parts in a periodic coherent fashion. The swimming motion is analyzed in a simple model of beads subject to periodic onebody forces. In the model the animalcule is held together by reactive twobody forces. The nonlinear equations of Stokesian dynamics are formulated on the basis of the Oseen tensor. Under suitable conditions the solution of the equations of motion has a limit cycle character. The limit cycle is analyzed for small amplitude motion in the framework of a bilinear theory. The linearized equations of motion are solved analytically for longitudinal and transverse modes of motion for a linear trimer, and expressions are derived for the swimming velocity and the mean dissipation to second order in the force amplitude. The results of the bilinear theory are compared to numerical solution of the nonlinear equations of motion. A similar comparison is made for chains of twelve beads.

Simulating flow of DNA suspension using dissipative particle dynamics
View Description Hide DescriptionWe simulate DNAsuspensionmicrochannel flows using the dissipative particle dynamics (DPD) method. Two developments make this simulation more realistic. One is to improve the dynamic characteristics of a DPD system by modifying the weighting function of the dissipative force and increasing its cutoff radius, so that the Schmidt number can be increased to a practical level. Another is to set up a wormlike chain model in the DPD framework, according to the measured extension properties of a DNA molecule in uniform flows. This chain model is then used to study flows of a DNAsuspension through microchannels. Interesting results on the conformation evolution of DNA molecules passing through the microchannels, including periodic contractiondiffusion microchannels, are reported.

Twodimensional simulations of flow near a cavity and a flexible solid boundary
View Description Hide DescriptionTwodimensional fluid flow near a cavity and a flexible solid boundary is examined in this work. Stokes’ equations are used to describe the fluid flow, while the flexible solid boundary is modeled as a uniformly tensioned membrane. Equations for elliptic mesh generation are solved iteratively along with Stokes’ equations, and the equation describing the membrane is used to update its position during the iterations. Two different configurations are considered. In the first, flow passes through the gap between a moving flexible wall and a rigid cavity. This configuration is studied in order to verify the validity of a lubrication model for this flow which was developed in previous work [X. Yin and S. Kumar, Phys. Fluids17, 063101 (2005)]. In the second, flow driven by an externally applied pressure gradient passes through the gap between a stationary rigid wall and a cavity with a flexible bottom wall that can be deformed by an external pressure. This configuration is studied in order to explore the effect of boundary deformation on the flow pattern in the cavity. The results for the first configuration indicate that the lubrication model yields good predictions of the pressure profile, position of the flexible wall, and flow rate. The comparison also confirms that the lubrication model can only predict the existence of one primary eddy in the cavity, but not multiple primary eddies or corner eddies. The results for the second configuration indicate that the flow pattern in the cavity is dramatically altered as the external pressure changes. Replacing the bottom of a cavity with a flexible wall and applying a timeperiodic pressure to it may thus be a potentially useful way to improve mixing and heat/mass transport in the cavity.
 Particulate, Multiphase, and Granular Flows

A pseudospectral method to evaluate the fluid velocity produced by an array of translating slender fibers
View Description Hide DescriptionA simulation method for the flow in a fiber suspension is developed based on slenderbody theory and a pseudospectral solution of the NavierStokes equations. The method is applicable when the Reynolds number based on the fiber radius is asymptotically small, but it takes account of the effects of fluid inertia on the scale of the fiber halflength . Here and are the fluid density and viscosity, respectively, and is a characteristic relative velocity between the fiber and the fluid. The method is applied to computing the force and torque due to the translational motion of a cubic array of fibers relative to the fluid as functions of . A comparison of the simulation results with an analytical solution to Oseen’s approximation to the equations of motion verifies the validity of the simulation method.

Properties of the particle velocity field in gassolid turbulent channel flow
View Description Hide DescriptionSpatial characteristics of the particle velocity field are investigated using numerical simulations of gassolid turbulent channel flow. The carrier phase is resolved using large eddy simulation (LES) of the incompressible NavierStokes equations. The dispersed phase is computed using Lagrangian tracking in which particle motion is governed by the drag force. Predictions of dispersed phase transport are obtained for three particle response times in simulations with and without interparticle collisions.Spatial correlations of the particle velocity field are measured in planes parallel to the wall and exhibit a discontinuity at the origin. The discontinuity in the spatial correlations is consistent with recent work by Fevrier et al. [J. Fluid Mech., 533, 1 (2005)] that shows the velocity of a particle is comprised of a contribution from a continuous field, shared by all the particles, and a random velocity component that is not spatially correlated. Analysis of the simulation database shows that the random component of the particle velocity increases with increasing particle response time. The influence of interparticle collisions leads to a changes in the partitioning of the particle velocity, with a greater fraction residing in the uncorrelated component compared to the correlated part.
 Laminar Flows

Accumulation of heavy particles in vortex flow on a disk
View Description Hide DescriptionThe motion of heavy particles in potential vortexflows on the unit disk is investigated theoretically and numerically. Configurations with one vortex and with two vortices are considered. In both cases, each vortex follows a regular path on the disk. In the onevortex case, it is shown that small, heavy particles may accumulate in elliptic regions of the flow, counterrotating with respect to the vortex. When the particle Stokes number exceeds a threshold depending on the vortex configuration, all particles are expelled from the circular domain. A stability criterion for particle accumulation is derived analytically and verified by numerical results. In the twovortex case, heavy particles are shown to accumulate in elliptic islands of regular motion. Again, this result is explained by a stability analysis. The results may be useful in the design of gasparticle separators containing a helical vortex filament.

Spin coating of thin liquid films on an axisymmetrically heated disk
View Description Hide DescriptionSpin coating of nonvolatile thin liquid films on an axisymmetrically heated disk is studied numerically under lubrication and zero Biot number assumptions. Important effects such as viscosity, centrifugal force, external air shearing, surface tension, disjoining pressure, thermocapillarity (temperature dependent surface tension), and thermoviscosity (temperature dependent viscosity) are included in the simulation. Both thermocapillarity and thermoviscosity effects are shown to be able to significantly enhance the film depletion rate when the disk center is at a higher temperature than the disk outer edge. The enhancing effect of thermoviscosity on the film depletion is not sensitive to the film thickness change and is larger than that of the external air shearing even at a moderate radial temperature difference applied to the disk. The thermocapillarity effect on the film depletion is negligible at the earlier stage of spin coating when the film thickness is relatively large, but its significance increases and eventually becomes dominant when the film thickness is further reduced. When the applied disk temperature profile has a steep change, a double shock structure for the liquid film is generated. Measurement of the anchored shock profile may provide an alternative mechanism to determine the viscosity change with temperature of wall bounded thin liquid films.
 Instability and Transition

Double Hopf bifurcation in corotating spiral Poiseuille flow
View Description Hide DescriptionNonlinear dynamics of the spiral Poiseuille problem for moderate axial through flow is investigated numerically within the corotating regime for medium gap geometry. The neighborhood of a double Hopf bifurcation point of the linear stability boundary, where spiral waves of opposite axial phase propagation compete, is explored by accurately solving timedependent NavierStokes equations with a solenoidal spectral method. The mode interaction generates a quasiperiodic stable regime of interpenetrating spirals, which coexists with stable limit cycles associated with the aforementioned spiral waves of opposite helicoidal orientation. The spatiotemporal properties of the computed solutions are explained and discussed in terms of equivariant bifurcation and normal form theories. Similar flows have also been observed experimentally in the past within the corotating region.

Numerical study of swirling flow in a cylinder with rotating top and bottom
View Description Hide DescriptionA numerical investigation of oscillatory instability is presented for axisymmetric swirling flow in a closed cylinder with rotating top and bottom. The critical Reynolds number and frequency of the oscillations are evaluated as function of the ratio of angular velocities of the bottom and the top . Earlier linear stability analysis (LSA) using the Galerkin spectral method by Gelfgat et al. [Phys. Fluids, 8, 2614 (1996)] revealed that the curve of the critical Reynolds number behaves like an “S” around in the corotation branch and around in the counterrotation branch. Additional finite volume computations, however, did not show a clear S behavior. In order to check the existence of the S shape, computations are performed using an axisymmetric finite volume NavierStokes code at aspect ratios 1.5 and 2.0. Comparisons with LSA at show that the S shape does exist. The S shape of the stability diagram predicted by LSA is thus confirmed by a finitevolume based NavierStokes solver. The additional computations at aspect ratio show that the curve of critical Reynolds number has a wider S shape in the corotating branch for about 0.7 whereas a sharp “beak” appears in the counterrotating branch for approximately .

Nonlinear growth (and breakdown) of disturbances in developing Hagen Poiseuille flow
View Description Hide DescriptionThe effect of imposing disturbances on developing Hagen Poiseuille flow is investigated for large Reynolds numbers. A formal large Reynolds number analysis is used throughout, which leads to a parabolic approximation (to the NavierStokes equations). In this inlet region [which is long radius], assuming uniform/near uniform inlet flow conditions, the boundary layers develop on the walls of the pipe, that eventually merge. Boundary layers are known to be susceptible to threedimensional eigensolutions that grow algebraically in the streamwise direction. In this study, nonaxisymmetric disturbances are triggered through (i) the imposition of the aforementioned eigenstates at the pipe inlet and (ii) forcing the azimuthal velocity on the pipe wall. Fully nonlinear, steady disturbances are considered in detail; if the disturbance amplitude is sufficiently large, a solution “breakdown” is observed (associated with a rapid growth of the radial and azimuthal velocity components close to lines of symmetry). This appears to be linked to reversals in both the azimuthal and radial velocity components, suggesting a possible mechanism for flow transition. Some comparison is also made with the analogous effect on planar (Blasiustype) boundary layers. The analysis is wholly rational, with (in particular) the highly nonlinear and nonparallel flow effects being treated in an entirely consistent manner.

Secondary circulations in Holmboe waves
View Description Hide DescriptionA sequence of direct simulations is used to study mechanisms for the growth of secondary circulations and turbulence in stratified shear flows. Five cases are examined, of which four deliver Holmboe waves as the primary instability and the fifth generates KelvinHelmholtz billows. Secondary circulations range in strength from weak, laminar motions to turbulence that destroys the parent wave. Processes that drive disturbance growth include shear production via the Orr mechanism, sheared convection in overturned regions, and sloping convection in stably stratified wave crests. Results are compared with previous predictions based on normal mode stability analysis.

Lowgravity sideways doublediffusive instabilities: Small wave number asymptotics
View Description Hide DescriptionWhen a stable salinity gradient in a vertical slot undergoes lateral heating, instabilities can arise. The level of heating required for instability can be several orders of magnitude smaller than is required in the absence of a salinity gradient. Previously it has been found that the portion of the stability boundary corresponding to this most unstable region could be derived using small wave number asymptotics. Although the leading order asymptotics are unaffected by consideration of vibration or gjitter, it has been observed that the region of the stability boundary given by these asymptotics could be reduced or eliminated by increasing the level of vibration. Here we look at the higher order asymptotics and determine how vibration affects the stability boundary in the region of maximum instability.

Linear and nonlinear RayleighTaylor growth at strongly convergent spherical interfaces
View Description Hide DescriptionRecent attention has focused on the effect of spherical convergence on the nonlinear phase of RayleighTaylor growth. For instability growth on spherically converging interfaces, modifications to the predictions of the Layzer model for the secular growth of a single, nonlinear mode have been reported [D. S. Clark and M. Tabak, Phys. Rev. E72, 056308 (2005)]. However, this model is limited in assuming a selfsimilar background implosion history as well as only addressing growth from a perturbation of already nonlinearly large amplitude. Additionally, only the case of single mode growth was considered and not the multimode growth of interest in applications. Here, these deficiencies are remedied. First, the connection of the recent nonlinear results (including convergence) to the wellknown results for the linear regime of growth is demonstrated. Second, the applicability of the model to more general implosion histories (i.e., not selfsimilar) is shown. Finally, to address the case of multimode growth with convergence, the recent nonlinear single mode results are combined with the Haan model formulation for weakly nonlinear multimode growth. Remarkably, convergence in the nonlinear regime is found not to modify substantially the multimode predictions of Haan’s original model.

On the application of confined twinjet instability to micromixing enhancement
View Description Hide DescriptionThe confined twinjet hydrodynamic instability is exploited to enhance mixing of low Reynolds numberlaminar flows. The baseline flow is investigated numerically and experimentally for three configurations, differing by the jet spacing and wall confinement. Using hotwire anemometry and particle image velocimetry, the Reynolds and Strouhal numbers associated with flowbifurcations were detected and are in good agreement with current and previously published numerical simulations. Superimposing weak harmonic excitation on the baseline twinjets flow is shown to significantly enhance the naturally unstable modes, and to generate considerable perturbations at the jets merging area. The influence of excitation frequency and amplitude on the resulting unsteadiness is also studied. It is found that applying excitation with the same Strouhal number to subcritical Reynolds numberflow creates similar perturbation structures as for supercritical Reynolds numberflows. These findings demonstrate the potential of the confined twinjet geometry to be utilized to enhance mixing for a wide range of applications where turbulent mixing is absent.

Influence of inertia and gravity on the stability of filament jet flow
View Description Hide DescriptionThe interplay between inertia and gravity is examined for a filament jet flow. The velocity is imposed at the tube exit and jet tip downstream. Both linear and nonlinear stability analyses are carried out. The loss of stability coincides with the onset of a Hopf bifurcation. While both inertia and gravity enhance the stability of steady flow, inertia plays a more dominant role regarding critical parameters. In contrast, the disturbance frequency is more sensitive to the effect of gravity. Above criticality, finiteamplitude disturbances are amplified, and sustained oscillation is achieved. It is found that the growth rate increases with velocity ratio, but decreases with inertia and gravity, which suggests that initial transients tend to take longer to die out for a fluid with stronger inertia and gravity. Transient postcritical calculations show that the nonlinearity can be effectively halted by inertia and gravity. The oscillation frequency (jet radius) decreases (increases) with velocity ratio. However, the jet oscillates more frequently but less fiercely with stronger inertia and gravity effects. The rupture of the jet is also examined, and is found to be delayed by inertia and gravity. Although the oscillation amplitude is found to be weakest at the jet tip, it is at this location that the jet tends to rupture first. Finally, comparison is carried out between theory and experiment, leading to good agreement.

Shearflow and thermocapillary interfacial instabilities in a twolayer viscous flow
View Description Hide DescriptionCombined effects of shearflow and thermocapillary instabilities in a twolayer Couette flow are asymptotically examined in the thinlayer limit. The basic features of the system instability are revealed by first analyzing the twodimensional stability problem. A scaling analysis is devised to identify dominant mechanisms in various parameter regimes. With an appropriate scaling, the leading order linear stability is reduced to a onedimensional evolution equation containing a nonlocal contribution from viscosity stratification. Viscosity stratification destabilizes (stabilizes) the system with a more (less) viscous film, but the effect can be compromised by thermocapillary stabilization (destabilization) as the film is cooled (heated). Thermocapillary effects dominate over viscosity stratification effects for shortwave perturbations albeit the latter could be stronger than the former for long waves. The competition between these two effects gives rise to the critical Reynolds number for the onset of stability/instability. A nontrivial interplay is found within a window in the weak interfacialtension regime. It demonstrates a possibility of the existence of two neutral states in the wavenumber space. The threedimensional problem is also examined. For the first time, a twodimensional film evolution equation with the inclusion of a nonlocal term is systematically derived for the corresponding stability. It can be shown analytically that threedimensional perturbations can be more unstable than twodimensional ones due to thermocapillarity in line with the nonexistence of Squires’ theorem. The threedimensional problem has the critical Reynolds number larger than the twodimensional problem, but an instability in the latter does not necessarily suggest an instability in the former. An extension of each problem to the weakly nonlinear regime is also discussed in the context of the KuramotoSivashinsky equation.
 Turbulent Flows

Large eddy simulations of transitional round jets: Influence of the Reynolds number on flow development and energy dissipation
View Description Hide DescriptionTransitional round jets at Mach number, with identical initial conditions except for the diameter, yielding Reynolds numbers over the range , are computed by large eddy simulation(LES) using explicit selective/highorder filtering. The effects of the Reynolds number on the jet flows are first presented. As the Reynolds number decreases, the jets develop more slowly upstream from the end of the potential core, but more rapidly downstream. At lower Reynolds numbers, the decay of the centerline velocity and the jet spreading are indeed faster, and the turbulence intensities are higher after the potential core, in agreement with data of the literature. The integral length scales are also significantly larger. The results suggest moreover that the jet selfsimilar region is reached at shorter axial distances at lower Reynolds numbers. The influence of the Reynolds number on the energydissipation mechanisms involved in the LES, namely molecular viscosity and explicit filtering, is secondly investigated. At high Reynolds number, energy dissipation is mainly ensured by the explicit filtering, through the smaller scales discretized. As the Reynolds number decreases, the contribution of molecular viscosity increases and becomes predominant. Molecular viscosity is also shown to affect a large range of turbulent scales with a dissipation peak observed around the Taylor length scale.