Instability Of Free Surface Research Articles

Buckling instabilities in models of viscoelastic free surface flows

We study here some theoretical model problems, with the goal of obtaining a better understanding of viscoelastic free surface flows and their unique flow instabilities. The first analysis examines the stability of inward radial flow of an Oldroyd-B fluid in a washer-shaped domain, showing that the azimuthal compression in this flow leads to a free surface instability — a crinkling or buckling in the azimuthal direction. This instability is suppressed by surface tension at large wave numbers, and growth rates are strongly attenuated by solvent viscosity. A second analysis shows how thin stress boundary layers can develop in free surface flows, and the final analysis takes the stress localization idea literally, using a thin elastic membrane as a model of stress boundary layer. Under elongation at constant enclosed volume, initially axisymmetric membranes with fixed circular ends, e.g. truncated cones, become unstable with respect to nonaxisymmetric disturbances, again due to azimuthal compressive stresses. The resulting configurations appear similar to those observed in filament stretching experiments.

Effect of dynamic surface tension on the growth rate of the Tonks-Frenkel instability

By means of a numerical analysis of the dispersion equation for capillary motions of a liquid with a charged flat free surface subjected to relaxation of the surface tension, it is shown that the growth rate of the instability of the free surface of the liquid decreases as the characteristic relaxation time of the surface tension increases and the Tonks-Frenkel parameter decreases. The instability itself occurs in a limited range of wave numbers whose width is also determined by the value of the Tonks-Frenkel parameter.

Initial Free Surface Instabilities on a High-Speed Water Jet Simulating a Liquid-Metal Target

Experiments are conducted on the initial growth of free surface waves on a high-speed (3.5 to 20 m/s) water jet flow that simulates related aspects of the liquid-lithium target in the International Fusion Materials Irradiation Facility. The waves are measured by using laser beam refraction at the water surface. The boundary layer at the nozzle exit and the recovery of the free surface velocity along the jet are also measured. The experimental results confirm that the nozzle-exit boundary layer has a significant influence on the initial growth of waves. With a turbulent boundary layer at the exit, the jet is covered by three-dimensional irregular waves from its beginning. With a laminar boundary layer, however, two-dimensional regular waves grow on an initially smooth water surface. For the latter case, the dominant frequency of the two-dimensional waves agrees well with the linear stability theory of Brennen.

Heap corrugation and hexagon formation of powder under vertical vibrations.

We report free-surface instabilities in a deep bed of fine granular material of irregular shape under vertical vibrations. At low frequency of vibration, the conical heap due to convective flow becomes unstable above a critical amplitude of vibration and acquires an azimuthal dependence which makes the heap surface corrugated. At even higher amplitude, the heap is no longer stable and splits into small heaps on a hexagonal lattice. At high frequency, we observe standing waves (stripes) at the same frequency as the driving one. The main mechanism of these instabilities can be traced back to the presence of the surrounding gas, since they vanish under vacuum conditions.

Influence of viscosity relaxation on the growth rate of the Tonks-Frenkel instability

A numerical analysis of the dispersion equation for the capillary motion of a viscoelastic liquid is used to show that the growth rate of the instability of a charged free liquid surface increases substantially as the characteristic time for the relaxation of viscous stresses and the Tonks-Frenkel parameter increase. This instability is achieved in a bounded range of wave numbers whose width is also determined by the Tonks-Frenkel parameter.

Wave number dependence of the critical conditions for instability of a charged liquid film in a fluctuational force field

It is shown that the critical conditions for instability of the charged free surface of a liquid film with a fixed thickness d in the region where the influence of fluctuational forces is substantial (d<100 nm) depend strongly on the wave number and do not depend on the viscosity of the liquid.

Instability of a charged free surface of solutions of inactive substances

It is shown that the simultaneous buildup of instability of the free surface of a solution of an inactive substance in relation to its concentration and the Tonks-Frenkel instability, causes the branches of the dispersion equation describing each of these instabilities separately to close onto one another and form two new composite branches of unstable liquid motion.

Potential Effects of Translatory Waves on Estimation of Peak Flows

During the afternoon of August 19, 1971, an intense thunderstorm a few miles southwest of Wikieup, Arizona, produced one of the largest known flood peaks for a 49.2-square-km drainage basin. Initial computations of the peak discharge assumed stable flow conditions and a four-section slope area measurement indicated that discharge was 2,082 m3/s. Recent findings based on free-surface instability characteristics at the site suggest that gravitational forces exceeded boundary retarding forces, and flow in the wide sand channel was unstable. Computations for roll or translatory waves indicate that waves crashed into the highway bridge at velocities of as much as 12.5 m/s. The close agreement of free surface instability results, translatory wave computations, estimates of the steady flow on which the translatory waves traveled, and an eyewitness account of the translatory waves suggest the total peak discharge could have been 2,742 m3/s or 32% greater than the published discharge. The occurrence of translatory...

Finite-wavelength instability in a horizontal liquid layer on an oscillating plane

The linear stability of a thin liquid layer bounded from above by a free surface and from below by an oscillating plate is investigated for disturbances of arbitrary wavenumbers, a range of imposed frequencies and selective physical parameters. The imposed motion of the lower wall occurs in its own plane and is unidirectional and time-periodic. Long-wave instabilities occur only over certain bandwidths of the imposed frequency, as determined by a long-wavelength expansion. A fully numerical method based on Floquet theory is used to investigate solutions with arbitrary wavenumbers, and a new free-surface instability is found that has a finite preferred wavelength. This instability occurs continuously once the imposed frequency exceeds a certain threshold. The neutral curves of this new finite-wavelength instability appear significantly more complex than those for long waves. In a certain parameter regime, folds occur in the finite-wavelength stability limit, giving rise to isolated unstable regions. Only synchronous solutions are found, i.e. subharmonic solutions have not been detected. In Appendix A, we provide an argument for the non-existence of subharmonic solutions.

Free-surface flows with near-critical flow conditions

Open channel flow situations with near-critical flow conditions are often characterized by the development of free-surface instabilities (i.e., undulations). The paper develops a review of several near-critical flow situations. Experimental results are compared with ideal-fluid flow calculations. The analysis is completed by a series of new experiments. The results indicate that, for Froude numbers slightly above unity, the free-surface characteristics are very similar. However, with increasing Froude numbers, distinctive flow patterns develop. Key words: open channel flow, critical flow conditions, free-surface undulations, flow instability, undular surge, undular broad-crested weir flow, culvert flow.

On the Capillarity of Smectic-A Free Surfaces in Drops and Free Standing Films

Smectic-A free surfaces are discussed in the spirit of capillarity. It is shown that for most practical cases the bulk cannot be treated as a semi infinite nledium: the natural length over which a perturbation relaxes along a free surface is just that creating bulk distortions that propagate over the smectic thickness. Hence, the bulk distortions do not simply renormalize the surface tension as in a semi-infinite medium. The relaxation of the layers' distortion within the bulk is fairly linear in nlost cases: this allows to develop a functional analysis involving only the free surfaces, instead of all the layers. In drops with thickness h, the surface is found to relax exponentially with two capillary lengths ~J (~h)~/~, where ~~ = RIB is the ratio of the curvature over the dilation elastic constant. This allows to match boundary conditions both on the height and the tangent of the surface extremities. Films have two independent triodes: I) an average mode describing the film medium layer. It involves a pure curvature-capillary length ~1 = (Kh/r)~/~, where r is the smectic surface tension, and it) a differential mode of behavior similar to the drop one. The effects of added surfactants and applied external fields are discussed together with the possibility of free surface instabilities.

Asymptotic measurements of free surface instabilities in laser-induced shock waves

An experimental technique based on optical scattering to detect melting in release of strongly shocked materials is presented. This method is used to study the asymptotic behavior of the free surface of shock-loaded materials. After reflection of a shock wave from a metallic sample free surface, occurrence of a solid to liquid transition will induce a dynamic behavior such as mass ejection and development of instabilities. A study of the mass ejection due to laser-induced shock waves in aluminium, copper, and tin targets is presented. Shock waves of order of hundreds of kilobars to more than one megabar are produced by a Nd:YAG laser system with a wavelength of 1.06 μm, pulse width of 7 ns FWHM focused to spot of 200 μm. The velocities, size, and topological structure of the ejected particles are measured. The radii of the ejecta are in the range 0.5–7 μm.

Effect of Cross-Sectional Shape on Free-Surface Instability

Effect of Cross-Sectional Shape on Free-Surface Instability

新型フォーマ・スピードフォーマＭＢ 新しい脱水概念に基づく次世代のフォーマー

One of the most significant advance in fine paper forming has been the shift from fourdriniers to hybrid formers, which enable curl and formation to be much better controlled than on fourdriniers. But both fourdrinier and hybrid formers suffer from free surface instabilities which increase with speed. Paper quality and runnability often start to suffer at speeds lower than their limitations.On the other hand, Gap formers have been used for news and specialty fine paper grades because of higher speed potential and better control of curl than hybrid formers. However, gap formers have limitations of paper grades owing to limited drainage capacity.This paper will introduce “Speed-Former MB”, which has been developed as the latest roll and blade gap former concept to obtain the best solution for much improved fine paper forming.

Closure to “ Self‐Aerated Flows on Chutes and Spillways ” by H. Chanson (February, 1993, Vol. 119, No. 2)

The writer thanks the discusser (ANWAR 1994) for his interesting comments and information. The writer wishes to clarify three points : free-surface instabilities, calculations of the inception point of air entrainment and analogy between self-aerated flows and sediment-laden flows.

Study of roughness formation induced by homogeneous stress at the free surfaces of solids

Distributions of surface dislocations used to investigate the free surface instability of a solid under compressive, tensile or shear stress. Calculation of the energy variation due to sinusoidal fluctuation of the surface allows the determination of the wavelength and the amplitude of the more probable roughness which can appear by surface or bulk diffusion or by plastic deformation. The role of surface tension is also studied; its main effect is to break the symmetry between tensile and compressive stress for the instability threshold.

Stability of free surface sediment flow

Observations of unusual surface level oscillations on the sediment‐laden Yellow River of China, have led to the suggestion that the oscillations arise from a free surface instability peculiar to fluids having the constitutive relation of a Bingham plastic (i.e., possessing a finite yield stress). A model has been proposed in which free surface flows of Bingham plastics appear unstable at conditions for which the corresponding flow of clear water would be stable. We argue here that gravity driven Bingham plastics are, in fact, stable to free surface oscillations and that consequently the Yellow River oscillations most likely do not stem from a simple surface instability.

Convective and free surface instabilities provoked by heating below an interface

Discussion d'un phenomene appele battement du cœur optique qui est forme dans certaines conditions par les oscillations d'une lentille thermique produite lors qu'un faisceau laser a onde continue se propage sous une surface libre liquide. discussion du mecanisme conduisant aux phenomenes observes; etude detaillee de la transition laminaire turbulente

Nonlinear free-surface Rayleigh-Taylor instability.

The nonlinear evolution of a Rayleigh-Taylor (RT) unstable free surface is studied by three independent approaches. (i) The method of least-squares approximation (LSA) is critically examined and applied to the general RT initial-value problem. It extends previous results of perturbation theories to higher orders and describes the appearance of bubbles and spikes for both single- and multiple-wavelength surface perturbations. Computational limitations, however, are found for the steady-state bubble regime where the number of harmonics becomes exceedingly large. (ii) A mathematically consistent sinusoidal flow model is developed valid for certain nonuniform gravitational accelerations. Its general properties are discussed, including a spike singularity and a unique steady-state bubble shape. As a special case, Layzer's model is obtained and compared with the LSA calculations. (iii) Steady-state bubbles are described more generally in terms of source potentials. A one-parameter family of possible bubble shapes and corresponding gravitational potentials can be derived. It includes the steady-state sinusoidal flow model and yields improved analytic expressions for the constant-acceleration bubble parameters. From this model it is also concluded that flow singularities can limit the general applicability of Fourier analyses to free-boundary flows.

Experimental study of free-surface flow instability and bedforms in shallow flows

To test erosion and development of bed sculpture in unstable, pulsating shallow flow, three series of experiments were performed in a 10-m flume with flows of Reynolds Number ( Re) up to 10 3, Froude Number ( Fr) up to 3.0, and slope up to 2%. In the first series of experiments (59 runs), the bed was rigid (glass flume-bottom), in the second (50 runs) and third (10 runs) series, planar beds were made from well-sorted and poorly sorted sand, respectively. Development of flow surface instability above the rigid bed showed the following stages: smooth surface; small wavelets; well-developed waves; and rough flow. Development of bedform morphology in the second series of tests showed the following sequence: smooth bed; flow-aligned ridge and trough pattern; combined ridge and rhomboid pattern; and rhomboid configuration. In presence of flow instability, ridge patterns form in flows with mean values indicative of laminar-subcritical regime, combined ridge and rhomboid patterns in laminar-supercritical regime, and rhomboid patterns in flows with mean values indicative of transitional turbulent-supercritical regime. The third series of experiments demonstrated transverse segregation of the bed material across the ridges. The results, in line with stability theory, show that laminar and transitional flows already become unstable when Fr = 1 2 and suggest that pulsations may appear in sheet-floods and overland flow, intensifying erosion and transport of sediment. The precise mechanism of origin of the parent kinematic flow configurations instrumental in generation of the ridge and the rhomboid patterns is not yet clear. It may be related to the mechanism operating in transition and generation of turbulence in parallel flows, or flows with a superimposed fluctuation, but other types of hydrodynamic instability are also possible.