Volume 8, Issue 11, November 1996
Index of content:

A new net‐like structure formed by a metal/oil electrorheological fluid
View Description Hide DescriptionA new kind of net‐like structure formed by the metal spheres suspended in a metal/oil electrorheological (ER) fluid is reported for the first time in this Letter. The experimental results show that this structure is totally different from that formed by dielectric particles. After comparing the two formation patterns, it is found that the dielectric particles in certain ER fluids align themselves into chains or columns in the direction of the external electric field. The metal particles in a metal/oil ER fluid, on the other hand, form a net‐like structure of chains and no column could be observed even when the ER fluid has been exposed to a high electric field. We attribute the net‐like structure of the metal ER fluid to the strong interaction between dipole fields induced on the metal particles under the external electric field. Finally, the dielectric properties of the different structures were measured and are discussed in this paper.

Rheology of dilute suspensions of charged fibers
View Description Hide DescriptionThe rheology of a dilute suspension of charged fibers with a large ratio of length L to diameter d is examined. The fibers may possess both a net charge and a charge dipole and it is assumed that the Hartmann number is small. The double layer thickness λ is large compared with the rod diameter and may be comparable with the fiber length. Although the shear rate is sufficiently small so that the deformation of the double layer is small, no restriction is placed on the rotary Péclet number of the rods. The velocity disturbance caused by the rods is neglected when calculating the double layerdeformation. This approximation is accurate when λ/L=O(1) and L/d is very large, but leads to an overestimate of the ion cloud distortion for small values of λ/L or moderate values of L/d. The counterion cloud affects the stress both directly through a primary electroviscous stress and indirectly by exerting an electric torque that changes the fiber orientation distribution. The additional stress caused by electrostatics shear thins for a fiber with a net charge. However, when the fiber has a charge dipole, the electrical stress may increase with increasing shear rate at sufficiently high Péclet numbers. At very high Péclet numbers, the electrical torque can lead to a fixed orientation of the fibers near the flow direction of the simple shear flow.

Phase diagrams for sonoluminescing bubbles
View Description Hide DescriptionSound driven gas bubbles in water can emit light pulses. This phenomenon is called sonoluminescence(SL). Two different phases of single bubble SL have been proposed: diffusively stable and diffusively unstable SL. We present phase diagrams in the gas concentration versus forcing pressure state space and also in the ambient radius versus gas concentration and versus forcing pressure state spaces. These phase diagrams are based on the thresholds for energy focusing in the bubble and two kinds of instabilities, namely (i) shape instabilities and (ii) diffusive instabilities. Stable SL only occurs in a tiny parameter window of large forcing pressure amplitude P _{ a }∼1.2–1.5 atm and low gas concentration of less than 0.4% of the saturation. The upper concentration threshold becomes smaller with increased forcing. Our results quantitatively agree with experimental results of Putterman’s UCLA group on argon, but not on air. However, air bubbles and other gas mixtures can also successfully be treated in this approach if in addition (iii) chemical instabilities are considered. All statements are based on the Rayleigh–Plesset ODE approximation of the bubble dynamics, extended in an adiabatic approximation to include mass diffusion effects. This approximation is the only way to explore considerable portions of parameter space, as solving the full PDEs is numerically too expensive. Therefore, we checked the adiabatic approximation by comparison with the full numerical solution of the advection diffusionPDE and find good agreement.

Pinching threads, singularities and the number 0.0304...
View Description Hide DescriptionThe dynamics of capillary pinching of a fluid thread are described by similarity solutions of the Navier–Stokes equations. Eggers [Phys. Rev. Lett. 71, 3458 (1993)] recently proposed a single universal similarity solution for a viscous thread pinching with an inertial–viscous–capillary balance in an inviscid environment. In this paper it is shown that there is actually a countably infinite family of such similarity solutions which are each an asymptotic solution to the Navier–Stokes equations. The solutions all have axial scale t ^{′1/2} and radial scale t ^{′}, where t ^{′} is the time to pinching. The solution obtained by Eggers appears to be special in that it is selected by the dynamics for most initial conditions by virtue of being less susceptible to finite‐amplitude instabilities. The analogous problem of a thread pinching in the absence of inertia is also investigated and it is shown that there is a countably infinite family of similarity solutions with axial scale t ^{′β} and radial scale t ^{′}, where each solution has a different exponent β.

One‐dimensional models for slender axisymmetric viscous liquid bridges
View Description Hide DescriptionA set of one‐dimensional models, previously derived for liquid jets, is generalized to viscous liquid bridges by applying suitably modified boundary conditions at the anchoring disks. A linear analysis for small‐amplitude perturbations around the cylindrical static solution is performed. The oscillation frequencies and growth factors so obtained are compared to the already known linear three‐dimensional results for a wide range in both the slenderness and viscosity. The relative error of each model is studied in terms of the typical axial length. Good agreement is found for slender enough bridges. The existence of boundary layers for weakly dissipative liquid bridges in the context of one‐dimensional models is also discussed.

Two‐dimensional velocity profiles and laminar boundary layers in flowing soap films
View Description Hide DescriptionIn this study we examine laminar velocity profiles of freely suspended flowing soap films. We introduce a new device which supports large uniform films for indefinite periods of time. The geometry of the flow is two‐dimensional (2D), yet the measuredvelocity profiles depart from ideal 2D behavior. The main reason for this departure is that the soap film experiences an air drag force across its entire surface. Describing the air with Prandtl boundary layer theory, we predict the observed flow patterns with good accuracy. The downstream development of the profiles is self similar. Our models set an apparent upper limit on the film 2D viscosity of 5⋅10^{−6} surface poise for dilute soap concentrations. This measurement implies that the surfactant layers on the film may not contribute measurably to the 2D viscosity. For higher soap and glycerol concentrations the opposite appears to be true.

Linear stability analysis of salt fingers with surface evaporation or warming
View Description Hide DescriptionOceanic observations [Atmos. Ocean29, 340 (1991)] have revealed small‐scale thermohaline plumes near the surface of a calm sea under warming conditions. The stratification was favorable for the double‐diffusive salt finger instability, though a previously unreported up–down asymmetry was found in which narrow downward cells are balanced by a broader, weaker upwelling. The scales of the thermal structures are consistent with asymmetric hexagonal salt‐finger modes [J. Phys. Oceanogr. 24, 855 (1994)], but no selection mechanism for the asymmetry has previously been identified. This paper explores the influence of nonlinear profiles of temperature and salinity, as might arise due to surface evaporation or warming, on the linear stability problem in a salt‐fingering regime. Three models are considered. In the first, a sharp, nonlinear solute‐concentration gradient is applied at the upper boundary, as might arise by surface evaporation. A Bénard mode appears, driven by the destabilizing density gradient in the thin boundary layer and influencing motion only within the boundary‐layer thickness. In the second model, a weak salinity gradient is introduced below the boundary layer; double‐diffusive bulk modes influence the motion across the entire fluid. Nonlinear interaction of the boundary layer and bulk modes provides a mechanism for maintaining salt fingers with up–down asymmetry. The third model contains a large temperature gradient at the surface, as might arise from warming by solar radiation, overlying a quasi‐isothermal region above a region of moderate gradient. The largest‐growth modes are found to be salt fingers that extend throughout the middle region and disappear in the top and bottom regions. This vertical structure is close to that of the asymmetric salt fingers described in Osborn [Atmos. Ocean29, 340 (1991)]. The differing length scales of the regions impress an up–down asymmetry on plumes; this is expected to yield a hexagonal pattern at the onset.

Granular dynamics of inelastic spheres in Couette flow
View Description Hide DescriptionA numerical program has been developed to simulate an assembly of inelastic, frictional hard spheres inside a control volume undergoing a steady‐state rapid Couette flow induced by the top and bottom bumpy walls. The bumpy walls are made of hemispheric particles fixed onto flat plates. The flow particles can collide with the wall particles and the exposed flat areas of the walls. The macroscopic flowproperties are found to depend on a number of material and geometric properties of the granules, the bumpy walls, and the control volume. These properties include the overall solids fraction of the system, the height of the shear gap, the wall‐particle concentration, the wall‐particle distribution, the diameter ratio of the wall particle to the flow particle, the coefficients of restitution, the friction coefficients, and the sticking tangential restitution coefficients between the flow particles, the wall particles, and the flat walls. A parametric study is undertaken to examine the effect of some of the interesting factors identified above. A new definition for the slip velocity yields positive values consistently, and it represents a significant improvement over the previous ones. By exposing the flat areas of the bumpy walls for collisions, the transfer of energy and momentum from the driving surfaces to the flow medium can be enhanced. Depending on the wall‐particle distribution, there exist optimal wall‐particle concentrations at which the stresses may be maximized or the slip velocities may be minimized. For hemispheric wall particles arranged in an equilateral triangular lattice, the optimal wall‐particle area fraction for maximizing the stresses is about 0.44 while the one for minimizing the slip velocity is about 0.36. The simulation results also show that there exists for gravity‐free Couette flow of inelastic, frictional spheres a critical solids fraction of about 0.5 beyond which the stresses are found to decrease with increasing solids concentration. In general, there is reasonable agreement between the simulation results for stresses and the experimental measurements.

Computer simulation of hopper flow
View Description Hide DescriptionThis paper describes two‐dimensional computer simulations of granular flow in plane hoppers. The simulations can reproduce an experimentally observed asymmetric unsteadiness for monodispersed particle sizes, but also could eliminate it by adding a small amount of polydispersity. This appears to be a result of the strong packings that may be formed by monodispersed particles and is thus a noncontinuum effect. The internal stress state was also sampled, which among other things, allows an evaluation of common assumptions made in granular materialmodels. These showed that the internal friction coefficient is far from a constant, which is in contradiction to common models based on plasticity theory which assume that the material is always at the point of imminent yield. Furthermore, it is demonstrated that rapid granular flow theory, another common modeling technique, is inapplicable to this problem even near the exit where the flow is moving its fastest.

Nonlinear dynamics of modulated flow between a porous injector and an impermeable substrate
View Description Hide DescriptionThe stable, time‐periodic flow between a porous injector disk and an impermeable substrate disk is explored for the case where fluid is injected into the gap region with a spatially uniform time‐periodic velocity V(τ)=V _{0}(1+α cos(στ)), where V _{0} is the mean injection velocity, α is the flow modulation amplitude, and σ is the flow modulation frequency. Fourier series expansions in time (τ) are combined with regular perturbation expansions of the Fourier coefficients in powers of α to describe the linear and nonlinear frequency dispersion in the system when 0<α<1. Generalized analytical expressions are obtained for the quasisteady response, and the method of matched asymptotic expansions is used to analyze the high frequency linear response of the system.Finite difference methods are used to calculate the frequency dispersion of the system for a wide range of modulation frequencies (σ) and Reynolds numbers. Oscillating harmonics are shown to interact destructively (via nonlinear inertial terms), resulting in the nullification of certain Fourier modes in the flow field. The Reynolds number and frequency dependence of harmonic nullification events are explored and their implications for creating multilayered alloys are briefly discussed.

Oscillatory Marangoni convection in cylindrical liquid bridges
View Description Hide DescriptionOscillatoryMarangoni convection in silicon–oil liquid bridges, sustained by two circular coaxial disks with prescribed time‐dependent temperature profiles and bounded by cylindrical free surfaces, is investigated by direct three‐dimensional (3‐D) and time‐dependent simulation of the model equations, using finite difference methods explicit in time and a staggered spatial mesh in cylindrical coordinates. It is shown that, for low enough values of the dimensionless rate of ramping, the time‐dependent nature of the boundary conditions becomes unimportant and the computed critical Marangoni numbers approach the values obtained with steady stability analyses. For typical microgravity experiments, involving unsteady boundary conditions, the computed critical Marangoni numbers and the oscillation frequencies agree with available experimental data of sounding rockets and Spacelab experiments. The 3‐D thermo‐fluid‐dynamic oscillatory regime structures are depicted, discussed, and compared with previous experimental and theoretical analyses, providing physical explanations of the onset of instability and coherent pictures of the flow organization when oscillatory conditions are established. Immediately after the onset of instability, the oscillatoryflow can be described by a standing wave and a pulsating temperature distribution. When the oscillatory disturbances become large, the azimuthal velocity causes the rotation of ‘‘temperature spots’’ along the free surface of the liquid bridge so that the time‐dependent temperature and velocity fields can be properly described by the dynamic model of an azimuthally traveling wave.

On the instability of pipe Poiseuille flow
View Description Hide DescriptionStability of the flow of incompressible viscous fluid in a circular pipe is studied numerically. A perturbation consisting of finite‐amplitude two‐dimensional and infinitesimal three‐dimensional parts is imposed on the basic flow. The temporal evolution of the perturbation is analyzed by direct numerical calculation of the Navier–Stokes equations. The two‐dimensional disturbances are independent of the streamwise coordinate and initially take the form of streamwise rolls. It is shown that the nonlinear development of two‐dimensional perturbations results in substantial spanwise modulation of the streamwise velocity component manifesting itself as a formation of streaks and the occurrence of inflection points. The modulated mean flow is found to be highly unstable to the three‐dimensional perturbations which are localized spatially near these points. An instability mechanism that includes the modulation of the flow by growing two‐dimensional disturbances and the inflectional instability of the modulated flow to three‐dimensional perturbations is proposed.

Stability of flow in a channel with a suddenly expanded part
View Description Hide DescriptionThe stability of a two‐dimensional flow in a symmetric channel with a suddenly expanded part is investigated numerically and analyzed by using the method of the nonlinear stability theory. From results of the numerical simulation, it is shown that the flow is steady, symmetric and unique at very low Reynolds numbers, while the symmetric flow loses its stability at a critical Reynolds number resulting in an appearance of asymmetric flow. The transition from the steady symmetric flow to the steady asymmetric one is found to occur due to the symmetry breaking pitchfork bifurcation when the aspect ratio, the ratio of the length of the expanded part to its width, is large. It is also found that the bifurcated flow becomes symmetric again when the Reynolds number is increased and the resultant symmetric flow loses its stability becoming periodic in time as the Reynolds number is further increased. On the other hand, when the aspect ratio is small there occurs no pitchfork bifurcation and the direct transition from the steady symmetric flow to a periodic flow occurs due to a Hopf bifurcation. The critical aspect ratio is found to be about 2.3. The critical Reynolds numbers for these bifurcations are evaluated.

Spin‐up in a rectangular tank with a discontinuous topography
View Description Hide DescriptionThe spin‐up from rest to a state of solid‐body rotation in a tank with one or more stepwise changes in depth is studied experimentally. Since flow across the steps is counteracted by the rotation acquired by the fluid in the course of the spin‐up process, eventually the flow is forced into a cellular pattern determined by the position of the steps. However, if the initial flow field has little resemblance with the quasisteady pattern imposed by the topography, most of the energy of the flow may be dissipated before the organization into the preferred pattern is complete.

Combined thermocapillary‐buoyancy convection in a cavity: An experimental study
View Description Hide DescriptionConvection in a cavity with a free surface and heated from the side is studied by a combination of flow visualization and particle imagevelocimetry. In these experiments, buoyancy and thermocapillarity are of comparable importance in driving the convection. The Prandtl number of the working fluid, the cavity aspect ratio, and the ratio of Rayleigh to Marangoni numbers are all held fixed; the primary experimentally varied parameter is the imposed temperature difference, which varied from 0.3 to 20 °C, resulting in a range of Marangoni numbers between 6×10^{3} and 4.2×10^{5}. For low Marangoni numbers, the flow is steady and two dimensional, as expected. The global nature of the flow is in good agreement with available numerical simulations of combined thermocapillary‐buoyancy driven convection. At higher Marangoni number, Ma>1.5×10^{5}, we observe a transition to steady three‐dimensional convection. The nature of this transition is typical of an imperfect bifurcation, and the flow structure is investigated both qualitatively and quantitatively. It is concluded that for the parameter values studied the first unstable mode consists of steady three‐dimensional, approximately cubical, vortical structures that are periodic along the axis of the cavity. The three‐dimensional flows observed by visualizations are in remarkable agreement with the recent numerical computations of Mundrane and Zebib [Phys. Fluids A 5, 810 (1993)].

Experimental study of heat and momentum transfer in rotating channel flow
View Description Hide DescriptionThe enhancement of momentum and heat transfer caused by stationary streamwise vortices due to a Coriolisinstability in a rotating straight channel is examined. It is shown that the changes in skin friction and Nusselt number depend on changes in the spanwise averaged mean flow and temperature distributions. Hot wire anemometry was used to experimentally determine the streamwise velocity and temperature distributions in a cross stream plane 68 channel widths downstream of the inlet. A technique to accurately compensate the velocity readings for the varying temperature in the channel was developed. It is shown that the streamwise vortices give rise to disturbance profiles which are close to those obtained from linear theory for small rotation numbers and that in this region there is no enhancement of either the averaged momentum or heat transfer. However, even for a disturbance amplitude in the streamwise velocity of the order of 20%, the disturbances are close to linear (both the disturbance distribution and growth rate). In this weakly non‐linear region the changes in the mean flow and temperature distributions could be estimated by using the linear eigenfunctions of the disturbances where the amplitude was taken from the measurements. In the fully non‐linear (saturated) region the Nusselt number on both the stable and unstable side of the channel was almost twice that at no rotation, however, the skin friction was almost unaffected on the stable side. This shows that the Reynolds analogy between momentum and heat transfer is not valid in this flow situation.

Experiments on the oscillatory behavior of buoyant plumes of helium and helium‐air mixtures
View Description Hide DescriptionExperiments on the oscillatory behavior of axisymmetric buoyant plumes of helium and helium‐air mixtures are reported for a range of nozzle diameters (3.6 cm<d<20 cm), source velocities, and plume densities. Measurements include pulsation frequencies as determined from total pressure fluctuations along the plume centerline in addition to the phase resolved laser Dopplervelocity measurements. These nonreacting buoyant plumes are found to exhibit periodic oscillations of plume boundaries which subsequently evolve into toroidal vortices within one‐half diameter above the nozzle exit. These oscillations and vortices are similar to those observed in pool fires, although their frequency scaling is somewhat different. The frequency relationship is well represented by the expression S=0.8Ri^{0.38} _{1}, where the Strouhal number is S=fd/V _{0} and the Richardson number is defined as Ri_{1}=[(ρ_{∞}−ρ_{ p })gd]/ρ_{∞} V ^{2} _{0}. Parameters f, V _{0}, ρ are frequency, source velocity, and density and subscripts p and ∞ refer to the plume fluid and ambient, respectively. Between Ri_{1}=100 and 500, a transition in the frequency scaling is observed as evidenced by more turbulent and vigorously mixing plumes beyond this transition. In this region, S=2.1Ri^{0.28} _{1}. This change in scaling can be explained by the effect of turbulent mixing on local plume density and the resulting modification of the convection speed of the toroidal vortices. These results provide a consistent basis for the mechanism of the observed instability which is quite different than other types of flow instabilities. Additionally, the phase resolved velocity field of a pulsating buoyant plume reveals a strong buoyant acceleration along the plume centerline followed by a deceleration in the region of the toroidal vortex formation. The strong upward acceleration is also accompanied by significant radial inflow toward the plume centerline determining the entrainment characteristics of these pulsating buoyant plumes.

Experimental study of rotating disk flow instability. II. Forced flow
View Description Hide DescriptionThe destabilization of the rotating disk flow subject to a forcing is experimentally investigated. An isolated roughness element of size of order δ (the constant boundary layer thickness) is placed under the linear threshold of the cross‐flow instability in order to create a hydrodynamic pattern of finite amplitude and localized in space. The experimental neutral stability curve is first established. The resulting double parabolic curve exhibits two minima: one of which is due to the amplification of fundamental modes, the other one is linked to the emergence of superharmonic modes. Dispersion curves determined by means of two‐point measurements appear to be shifted away from those measured in the natural case (without forcing). We show that this discrepancy is due to the presence of weak nonlinear effects which can be described by a Ginzburg–Landau amplitude equation. Lastly, we present an original method that enables to determine both components of the group velocity vector using the measureddispersion relations and wave packet propagation angle.

Suction effect on an impulsively started circular cylinder: Vortex structure and drag reduction
View Description Hide DescriptionDrag reduction on an impulsively started circular cylinder by surface suction has been investigated with a joint numerical and experimental study. Two suction slots entraining mass with various rates were located symmetrically in a range of angles downstream of the points of zero shear stress. The Reynolds number Re of this study was between 500 and 2000, while the suction coefficient Ṁ varied from 0 to 0.08. Analysis based on the force contributed by fluid elements with nonvanishing vorticity [Chang, Proc. R. Soc. London Ser. A 437, 517 (1992)] has provided a clear view of the physical mechanism causing the drag reduction. For the impulsive flow with surface suction, the initial drag reduction is due to the strengthening of the front boundary layer, while the slender vortices in the near wake due to suction then become the dominant factor in reduction of the drag force in later stages. Close agreements were found between the experimental and numerical results, including streakline flow visualization and surfacevorticitymeasurements on the top of the cylinder. In addition, a parametric study on the slot location, the suction angle, and the width of the suction slot has also been carried out in detail.

A boundary integral method applied to the 3D water coning problem
View Description Hide DescriptionOften in oil reservoirs a layer of water lies under the layer of oil. The suction pressure due to a distribution of oil wells will cause the oil‐water interface to rise up towards the wells. A three‐dimensional boundary integral formulation is presented for calculating the steady interface shape when the oil wells are represented by point sinks. Sophisticated integration techniques are implemented in an effort to obtain accurate results. In particular, the efficiency of various integration methods are compared for this problem, including QUADPACK routines, adaptive methods based on the IMT rule, the Kronrod rule, the method of degenerate quadrilaterals, and the Gauss‐Rational rule for infinite integrals. Numerical results for various general multi‐sink distributions are discussed, as are some further results for the axisymmetric single well problem.