Volume 15, Issue 5, May 2003
 LETTERS


Multiple stationary states for deformable drops in linear Stokes flows
View Description Hide DescriptionUsing a smalldeformation expansion and numerical simulations we study stationary shapes of viscous drops in twodimensional linear Stokes flows with nonzero vorticity. We show that highviscosity drops in flows with vorticity magnitude have two branches of stable stationary states. One branch corresponds to nearly spherical drops stabilized primarily by rotation, and the other to elongated drops stabilized primarily by capillary forces. For droptocontinuousphase viscosity ratios beyond a critical value the rotationally stabilized solution exists in the absence of capillary stresses, because the rate of drop deformation (but not rotation) decreases with drop viscosity. We show that and the capillary stresses required for drop stability vanish at with exponent 1/2, as required by flowreversal symmetry.

The atomic detail of a wetting/dewetting flow
View Description Hide DescriptionAtomistic simulation is used to study flow in the vicinity of the advancing (wetting) and receding (dewetting) solid–liquid–vapor contact lines of a twodimensional (in the mean) liquid drop in thermodynamic equilibrium with its own vapor and moving steadily on an atomically smooth solid surface under the influence of an applied body force. Wetting and dewetting are found to be asymmetric, counter to some predictions based on linear theory. There is a rolling flow of the liquid in the drop and a dividing streamline extends from the wetting common line into the displaced vapor as observed macroscopically. At the dewetting common line there is substantial evaporation, which alters the flow field behind the drop.Evaporation is also observed above the advancing contact line, but there is a net mass flux into the drop right at the contact line. There is evidence of slip flow just in advance of the wetting contact line, but not at the dewetting line. Results are discussed in the context of phasefield models.
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 SPECIAL SECTION


Control of turbulent boundary layers
View Description Hide DescriptionThe objective of this paper is to give an overview of recent progress on boundary layer control made by the author’s research group at University of California, Los Angeles. A primary theme is to highlight the importance of a certain linear mechanism and its contribution to skinfriction drag in turbulent boundary layers—and the implication that significant drag reduction can be achieved by altering this linear mechanism. Examples that first led to this realization are presented, followed by applications of linear optimal control theory to boundarylayer control. Results from these applications, in which the linear mechanism in turbulent channel flow was targeted, indirectly confirm the importance of linear mechanisms in turbulent—and hence, nonlinear—flows. Although this new approach has thus far been based solely on numerical experiments which are yet to be verified in the laboratory, they show great promise and represent a fundamentally new approach for flow control. The success and limitations of various controllers and their implications are also discussed.
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 ARTICLES


Wall migration and shearinduced diffusion of fluid droplets in emulsions
View Description Hide DescriptionThe spatial distribution of drops in multiphase Stokes flow is derived theoretically as a function of two dimensionless parameters, accounting for wall migration, buoyancy, and shearinduced diffusion. The wall migration effect, which drives drops away from the walls and toward the center of the gap, is often significant even when droplets are 100 times smaller than the gap. By comparison with the experimental drop concentration profile, the shearinduced downgradient diffusivity is measured and found to be approximately four to five times larger than the prediction for dropselfdiffusivity. These are the first such measurements of the diffusivity of drops with clean interfaces and contrast markedly with previous measurements on surfactantladen drops. Nonuniform concentration along the vorticity axis is also investigated briefly.

Flow over a surface with parallel grooves
View Description Hide DescriptionStokes shear flow over a surface with evenly spaced, finitedepth rectangular grooves is solved analytically by eigenfunction expansions and matching. Macroscopically the rough surface is equivalent to a smooth surface with partial slip. The slip coefficients are determined for shear flow both along and transverse to the grooves. The partial slip condition is then applied to the flow through a channel with nonaligned grooves on the walls.

Marangoni instability at a contaminated liquid–vapor interface of a burning thin film
View Description Hide DescriptionWe consider the evaporation and subsequent burning of thin films of liquid fuels on which a nonsoluble surface active agent (surfactant) is present. This work complements a previous study where we have considered the same problem but in the absence of surfactant.Surfactant may result from impurities of the liquid fuel or from backward diffusion of unoxidized combustion intermediaries and heavy soot precursors. When burning occurs in a quiescent ambient, the mathematical problem can be systematically reduced to a pair of nonlinear evolution equations for the film’s thickness and surfactant’s concentration. These equations contain, in particular, the temperature and mass flux at the liquid–vaporinterface as additional parameters, determined from full consideration of the gasphase processes. We show that in the absence of combustion or, when the heat released by the chemical reactions is relatively small, thermocapillary effects tend to destabilize a nominally planar interface. The presence of surfactant brings about a slower growth and can possibly stabilize the film. Combustion generally acts to reverse these trends: When the heat release is large, thermocapillary effects stabilize the liquid–vaporinterface while the presence of surfactant leads to destabilization.

A methodology for optimal laminar flow control: Application to the damping of Tollmien–Schlichting waves in a boundary layer
View Description Hide DescriptionA methodology for determining the optimal steady suction distribution for the delay of transition in a boundary layer is presented. The flow state is obtained from the coupled system of boundary layerequations and parabolized stabilityequations (PSE), to account for the spatially developing nature of the flow. The wall suction is defined by an optimal control procedure based on the iterative solution of the equations for the state and the dual state; the latter is available from the adjoint boundary layerequations and the adjoint PSE. The technique is applied to the control of twodimensional Tollmien–Schlichting (TS) waves. Results show that the onset of the instability can be significantly postponed and/or the growth rate considerably reduced by applying an appropriate suction through the whole wall length, in a wide frequency band. Control over panels of finite length completes the study and brings useful, preliminary information on the practicality of the approach in view of implementation. Finally, a simplified methodology which does not rely on the PSE is discussed, based on the minimization of the shape factor. Satisfactory results are achieved with this simpler approach which might, thus, constitute a method of choice when results are needed rapidly, i.e., during online control of TS waves.

Drop breakup in the flow through fixed fiber beds: An experimental and computational investigation
View Description Hide DescriptionDilute fixed fiber beds provide a model system for studying drop dynamics in disordered flows. Fluctuations about the mean uniform velocity are generated by fiber elements within the media, and the disturbance velocities far from any single fiber (at distances on the order of the pore size) have been predicted to be strong in terms of drop deformation and breakup by Mosler and Shaqfeh [Phys. Fluids 9, 5 (1997)]. In this work, we focus on the importance of nearfield interactions, or the flow close to individual fibers. We present experimental observations of drop deformation and breakup during flow through a dilute bed of randomly placed fibers. We found breakup to result from only close interactions with fibers and describe two nearfield breakup mechanisms which we term “graze” and “hairpin” processes. In addition, we present the breakup probability through the experimental fiber bed as a function of the appropriate Capillary number Ca. To better understand the nearfield interactions, we used the boundary integral method to determine drop shape evolution in the flow around an infinite fiber within a porous medium, and our simulations capture the breakup mechanisms observed during experiments. To compare with experimental breakup probabilities, we have defined a critical offset for breakup during flow past a fiber and assuming straight centerofmass trajectories, calculated breakup probabilities based on this simple model. These predictions compare well with the experimental measurements for

Disintegration of planar liquid film impacted by twodimensional gas jets
View Description Hide DescriptionThe distortion and breakup of a thin planar liquid film impacted by two gas jets while discharging from a twinfluid atomizer is studied numerically. The gas momentum vector has components normal and parallel to the liquid stream. Viscosity and compressibility are neglected in both the liquid phase and the gas phase. The reduceddimension (lubrication) approximation is employed to describe the nonlinear distortion and breakup of the thin film. The gasphase dynamics are modelled by using a boundaryelementmethod formulation. For the considered parameter range and for a given energy expenditure, direct modulation of liquidphase velocities at the nozzle exit is found to be more effective in causing film rupture than indirect modulation via adjacent impacting gas jets. In the former case, dilational film modulation results in shorter breakup lengths than sinuous modulation. On the other hand, for gasjet modulated films, sinuous mode forcing is more effective than dilational forcing for the same energy input. Coflowing gas streams significantly alter wavelengths and amplitudes of film disturbances generated by direct film modulation. Large ratios of gasjet momentum to liquidfilm momentum result in “immediate” film rupture in response to the dynamics of the impacting gas jets, whereas for lower ratios films disintegration occurs further downstream after continuous growth of the initial disturbances. Film distortion is characterized by the formation of fluid blobs or long bandlike films depending on Weber number values and density ratio.

Hydrodynamic stability of Taylor–Dean flow between rotating porous cylinders with radial flow
View Description Hide DescriptionA linear stability analysis has been implemented for the Taylor–Dean flow between porous concentric rotating cylinders when radial flow is present. The stability equations with respect to both axisymmetric and nonaxisymmetric disturbances are derived and solved by a direct numerical procedure. Both types of radial flows, inward and outward flows, are considered. A parametric study covering wide ranges of α, the radial Reynolds number based on the radial velocity at the inner cylinder and inner radius, and β, a parameter characterizing the ratio of average pumping velocity due to azimuthal Poiseuille flow and rotation velocity due to inner cylinder rotation, is conducted for the situation of practical interest where the outer cylinder is stationary and the inner cylinder is rotating. The area where the onset mode is nonaxisymmetric is shown in the plane (β,α). A critical curve is discovered that the most stable state always occurs at the point on this curve for an assigned value of α. Moreover, a discontinuity of the critical axial wavenumber happens when the parameters α or β cross this curve. The critical mode transition of the onset of instability is demonstrated in detail and results for the variations of the critical Taylor number and axial wavenumber are presented. It is found that the superimposed radial flow may produce a stabilizing or destabilizing effect depending heavily on the value of β related to the basic state.

An experimental study on resonance of oscillating air/vapor bubbles in water using a twofrequency acoustic apparatus
View Description Hide DescriptionA twofrequency acoustic apparatus is employed to study the growth behavior of vaporsaturated bubbles driven in a volumetric mode. A unique feature of the apparatus is its capability of trapping a bubble by an ultrasonic standing wave while independently driving it into oscillations by a second lowerfrequency acoustic wave. It is observed that the growing vapor bubbles exhibit a periodic shape transition between the volumetric and shape modes due to resonant coupling. In order to explain this observation, we performed an experimental investigation on resonant coupling of air bubbles and obtained the following results: First, the induced shape oscillations are actually a mixed mode that contains the volume component, thus, vapor bubbles can grow while they exhibit shape oscillations. Second, the acoustically levitated bubbles are deformed and therefore, degeneracy in resonant frequency is partially removed. As a result, the vapor bubbles exhibit the shape oscillations in both the axisymmetric mode and asymmetric (threedimensional) modes. Nonlinear effects in addition to the frequency shift and split due to deformation creates overlapping of the coupling ranges for different modes, which leads to the continuous shape oscillations above a certain bubble radius as the bubble grows.

Orientation of carbon nanotubes in a sheared polymer melt
View Description Hide DescriptionOptical measurements of the shear response of semidilute dispersions of polymerdispersed multiwalled carbon nanotubes are presented. For a weakly elasticpolymer melt, the data suggest that the semiflexible tubes orient along the direction of flow at low shear stress, with a transition to vorticity alignment above a critical shear stress, corresponding to a critical Deborah number of approximately 0.15. In contrast, data for a highly elasticpolymer solution suggest that the tubes orient with the flow field at high shear rates, in the limit of large Deborah number. The measurements are in qualitative agreement with previous experimental and theoretical studies of fiber orientation in elastic fluids under simple shear flow.

Streak breakdown instability in pipe Poiseuille flow
View Description Hide DescriptionThis work is devoted to the study of the stability of Hagen–Poiseuille flow or pipe flow. The analysis is focused on the streak breakdown process by which twodimensional streamwiseindependent finite amplitude perturbations transiently modulate the basic flow leading to a profile that contains saddle points and is linearly unstable with respect to very small streamwisedependent perturbations. This mechanism is one possible route of transition to turbulence in subcritical shear flows. The exploration is carried out for initial disturbances of different finite amplitudes and axial and azimuthal periodicity. This study covers a wide range of Reynolds numbers and the double threshold curve obtained for transition is consistent with experimental observations.

Reynolds number effects on the flow structure behind two sidebyside cylinders
View Description Hide DescriptionThe wake structure of two sidebyside cylinders was experimentally investigated using the laserinduced fluorescenceflow visualization, particle imagevelocimetry and hotwire techniques. The investigation was focused on the asymmetrical flow regime, i.e., where T is the centertocenter cylinder spacing and d is the cylinder diameter. Experiments were conducted in both the water tunnel and the wind tunnel at a Reynolds number (Re) range of 150–14 300. It has been found that, as Re increases, the flow structure behind the cylinders may change from one single vortex street to two streets with one narrow and one wide for the same The onestreet flow structure is dominated by one frequency where is the dominant frequency and is the freestream velocity. On the other hand, two frequencies, and 0.09, characterized the twostreet flow structure. These are associated with the narrow and wide street, respectively. It is further observed that the critical Re, at which the transition from single to two streets occurs, increases as decreases. The present finding clarifies previous scattered reports for the detection of one dominant frequency by some but two by others.

Full velocityscalar probability density function computation of heated channel flow with wall function approach
View Description Hide DescriptionA joint velocityscalar probability density function (PDF) method is presented to model and simulate turbulent flows with passive inert scalars (here temperature). The full PDF approach is applied for wallbounded flows. In the present work, the boundary conditions are imposed in the logarithmic region and the modeling is therefore performed in the wallfunction spirit. The PDF equation is solved by a Monte Carlo method and the whole approach appears as a Lagrangian simulation using stochastic particles. The purpose of the work is to analyze the behavior of classical PDF models in the nearwall region and to develop new particle boundary conditions for the velocity and scalars attached to each particle. First of all, the logarithmic region is described as an equilibrium zone and resulting analytical formulas for secondorder temperature–velocity statistics are derived. Boundary conditions for scalars are then developed and formulated in terms of instantaneous particle variables. These results are useful to discuss consistency issues between the formulation of scalar mixing models and the statement of boundary conditions. Finally, heated channel flow is simulated with a standalone PDF code for two different heatflux conditions and results are compared with available direct numerical simulation and experimental data.

An experimental investigation of the nearfield flow development in coaxial jets
View Description Hide DescriptionThe nearfield region of a coaxial jet having inner to outer diameter ratio is investigated experimentally for four ratios of annular to central jet velocities of η=0.18, 0.48, 0.8, and 1.11. Measurements were acquired nonintrusively using molecular tagging velocimetry at downstream distances up to six inner jet diameters. High spatialresolution profiles of mean axial velocity, axial turbulent intensity, skewness, kurtosis, radial gradients of mean velocity, and velocity gradient fluctuations are presented and discussed. In the nearexit region of the inner mixing layer, evidence suggests the existence of two trains of vortices shed from the inner jet wall for velocity ratios η>0.18. The results also indicate that for the flow configuration examined the length of the annular potential core is a function of the velocity ratio. Turbulence characteristics of the flow appear to be influenced by both the velocity ratio and absolute velocity of the annular jet. Integral length and Taylor microscales in the inner shear layer are shown to grow monotonically with downstream distance, with their ratio reaching a constant value. It is concluded that the turbulence structure in the inner mixing layer is highly anisotropic and that the levels of anisotropy are a relatively strong function of the velocity ratio.

Polymer dynamics in a model of the turbulent buffer layer
View Description Hide DescriptionA Brownian dynamics study of bead–spring–chain polymerdynamics is undertaken in a modelflow that captures key features of the buffer region of nearwall turbulence—wavy streamwise vortices superimposed on a mean shear. In this flow and in any Lagrangian chaotic flow, a Hookean dumbbell polymer will stretch indefinitely if and only if the Weissenberg number based on the largest Lyapunov exponent for the velocity field is In the flow investigated here, this criterion is found to be good predictor of when the stretch of finitely extensible chains approaches its maximum value. The chains become highly stretched in the streamwise streaks and relax as they move into and around the vortex cores, leading to large differences in stress in different regions of the flow. Hydrodynamic and excluded volume interactions between polymer segments have no qualitative effects once results are normalized for the change in relaxation time due to their inclusion. The results from the bead–spring–chain models are used to assess the utility of the simpler FENEP model. Although the FENEP model does not capture the hysteresis in stress that is seen with the bead–spring–chain models, it otherwise qualitatively captures the behavior of the bead–spring chains. Most importantly, large polymer stress in the flow is seen at the same spatial positions for both the FENEP and the more detailed models.

On the new vortex shedding mode past a rotating circular cylinder
View Description Hide DescriptionTo examine in detail the behavior of a new vortex shedding mode found in a previous investigation [Phys. Fluids 14, 3160 (2002)], a twodimensional numerical study on the laminar incompressible flow past a rotating circular cylinder in the Reynolds number range and at rotational rates was carried out. The results obtained clearly confirm the existence of the second shedding mode for the entire Reynolds number range investigated. A complete bifurcation diagram was compiled defining both kind of shedding modes. The unsteady periodic flow in the second mode is characterized by a frequency much lower than that known for classical von Kármán vortex shedding of the first mode. The corresponding Strouhal number shows a strong dependence on the rotational velocity of the cylinder, while only a weak dependence is observed for the Reynolds number. Furthermore, the amplitudes of the fluctuating lift and drag coefficients are much larger than those characterizing classical vortex shedding behind nonrotating or slowly rotating cylinders. Additionally, negative values for the mean drag denoting thrust are found within the second shedding mode.

On interfacial gravitycapillary solitary waves of the Benjamin type and their stability
View Description Hide DescriptionSymmetric solitary waves on the interface between two fluid layers are discussed for the case when the upper fluid is bounded above and the lower fluid is infinitely deep. In this flow geometry, under the conditions that the fluid densities are nearly equal and interfacial tension is relatively large, Benjamin [J. Fluid Mech. 245, 401 (1992)] derived a weakly nonlinear longwave evolution equation which admits a new kind of elevation solitary wave that features decaying oscillatory tails. We present computations of solitary waves of this type and examine their stability to small perturbations on the basis of the full Euler equations using numerical methods. Computed solitarywave profiles are found to be in good agreement with solutions of the Benjamin equation even for Weber and Froude numbers well outside the formal range of validity of weakly nonlinear longwave analysis. Furthermore, our computations reveal that, unless the upper fluid is very light relative to the lower fluid, moderately steep interfacial solitary waves behave qualitatively as predicted by the Benjamin equation: elevation waves with a tall center crest, akin to those found by Benjamin, are stable and coexist with depression solitary waves (not reported by Benjamin) which are unstable. As expected, for low enough density ratio, these two solution branches exchange stabilities and computed profiles resemble those of freesurface gravitycapillary solitary waves on deep water.

The significance of vortex ring formation to the impulse and thrust of a starting jet
View Description Hide DescriptionThe recent work of Gharib, Rambod, and Shariff [J. Fluid Mech. 360, 121 (1998)] studied vortex rings formed by starting jets generated using a pistoncylinder mechanism. Their results showed that vortex rings generated from starting jets stop forming and pinch off from the generating jet for sufficiently large values of the piston stroke to diameter ratio suggesting a maximization principle may exist for propulsion utilizing starting jets. The importance of vortex ring formation and pinch off to propulsion, however, rests on the relative contribution of the leading vortex ring and the trailing jet (which appears after pinch off) to the impulse supplied to the flow. To resolve the relative importance of the vortex ring and trailing jet for propulsion, a pistoncylinder mechanism attached to a force balance is used to investigate the impulse and thrust generated by starting jets for ratios in the range 2–8. Two different velocity programs are used, providing two different values beyond which pinch off is observed, in order to determine the effect of vortex ring pinch off. Measurements of the impulse associated with vortex ring formation show it to be much larger than that expected from the jet velocity alone and proportionally larger than that associated with a trailing jet for large enough to observe pinch off. The latter result leads to a local maximum in the average thrust during a pulse near values associated with vortex rings whose circulation has been maximized. These results are shown to be related to the nozzle exit overpressure generated during vortex ring formation. The overpressure is in turn shown to be associated with the acceleration of ambient fluid by vortex ring formation in the form of added and entrained mass.
