Stability of a viscous liquid curtain

1981 ◽  
Vol 104 ◽  
pp. 111-118 ◽  
Author(s):  
S. P. Lin
Keyword(s):  
Group Velocity ◽  
Viscous Liquid ◽  
Weber Number ◽  
Linear Analysis ◽  
Dual Roles ◽  
Amplification Rate ◽  
Damping Rate ◽  
Upstream Direction ◽  
Critical Weber Number ◽  
The Stability

The stability of a viscous liquid curtain falling down steadily under the influence of gravity is investigated. Both spatially and temporally changing disturbances are considered in the linear analysis. Only the spatially growing sinuous disturbances whose group velocity points toward upstream are unstable. The group velocity is in the upstream direction only when the Weber number of the curtain flow exceeds ½. The predicted critical Weber number agrees completely with that found experimentally by Brown (1961). The viscosity is shown to have the dual roles of increasing the amplification rate as well as the damping rate of the disturbances.

On the instability of small gas bubbles moving uniformly in various liquids

1957 ◽  
Vol 3 (1) ◽  
pp. 27-47 ◽  
Author(s):  
R. A. Hartunian ◽  
W. R. Sears
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Gas Bubbles ◽  
Hydrodynamic Pressure ◽  
Terminal Velocity ◽  
Approximate Methods ◽  
Stability Calculation ◽  
Fluid Medium ◽  
Critical Weber Number ◽  
The Stability

The instability of small gas bubbles moving uniformly in various liquids is investigated experimentally and theoretically.The experiments consist of the measurement of the size and terminal velocity of bubbles at the threshold of instability in various liquids, together with the physical properties of the liquids. The results of the experiments indicate the existence of a universal stability curve. The nature of this curve strongly suggests that there are two separate criteria for predicting the onset of instability, namely, a critical Reynolds number (202) and a critical Weber number (1.26). The former criterion appears to be valid for bubbles moving uniformly in liquids containing impurities and in the somewhat more viscous liquids, whereas the latter criterion is for bubbles moving in pure, relatively inviscid liquids.The theoretical analysis is directed towards an investigation of the possibility of the interaction of surface tension and hydrodynamic pressure leading to unstable motions of the bubble, i.e. the existence of a critical Weber number. Accordingly, the theoretical model assumes the form of a general perturbation in the shape of a deformable sphere moving with uniform velocity in an inviscid, incompressible fluid medium of infinite extent. The calculations lead to divergent solutions above a certain Weber number, indicating, at least qualitatively, that the interaction of surface tension and hydrodynamic pressure can result in instabilities of the bubble motion.A subsequent investigation of the time-independent equations, however, shows the presence of large deformations in shape of the bubble prior to the onset of unstable motion, which is not compatible with the approximation of perturbing an essentially spherical bubble. This deformation and its possible effects on the stability calculation are therefore determined by approximate methods. From this it is concluded that the deformation of the bubble serves to introduce quantitative, but not qualitative, changes in the stability calculation.

Absolute and convective instability of a viscous liquid curtain in a viscous gas

1997 ◽  
Vol 332 ◽  
pp. 105-120 ◽  
Author(s):  
C. H. Teng ◽  
S. P. Lin ◽  
J. N. Chen
Keyword(s):  
Surface Tension ◽  
Viscous Liquid ◽  
Weber Number ◽  
Convective Instability ◽  
Liquid Sheet ◽  
Linear Instability ◽  
Liquid Density ◽  
Amplification Rate ◽  
Centreline Velocity ◽  
Instability Regime

The linear instability of a viscous liquid flowing in a vertical sheet sandwiched between two viscous gases bounded externally by two vertical walls is investigated. The critical Weber number below which the flow is absolutely unstable and above which the flow is convectively unstable is found to be approximately equal to one and is weakly dependent on the rest of the parameters. The Weber number is defined asWe≡ρ1U20d/SwhereSis the surface tension,ρ1is the liquid density,U0is the centreline velocity of the liquid sheet, anddis the half-thickness of the uniform liquid sheet. The sinuous mode is found to have a greater amplification rate than the varicose mode in the convective instability regime. While absolute instability is caused by the surface tension, convective instability is caused by the amplification of disturbances near the liquid-gas interface. The surface tension, and viscosities of liquids and gases all suppress the amplification of the convectively unstable disturbances. An increase in the gravitational force or the gas density results in an enhancement of the amplification rate.

Penetration Dynamics of Solid Particles into Liquids High-Speed Experimental Results and Modelling

2005 ◽  
Vol 473-474 ◽  
pp. 429-434 ◽  
Author(s):  
Olga Verezub ◽  
György Kaptay ◽  
Tomiharu Matsushita ◽  
Kusuhiro Mukai
Keyword(s):  
Contact Angle ◽  
Particle Size ◽  
Aqueous Solutions ◽  
Particle Velocity ◽  
Weber Number ◽  
High Speed ◽  
Solid Particles ◽  
Bulk Liquid ◽  
Distilled Water ◽  
Critical Weber Number

Penetration of model solid particles (polymer, teflon, nylon, alumina) into transparent model liquids (distilled water and aqueous solutions of KI) were recorded by a high speed (500 frames per second) camera, while the particles were dropped from different heights vertically on the still surface of the liquids. In all cases a cavity has been found to form behind the solid particle, penetrating into the liquid. For each particle/liquid combination the critical dropping height has been measured, above which the particle was able to penetrate into the bulk liquid. Based on this, the critical impact particle velocity, and also the critical Weber number of penetration have been established. The critical Weber number of penetration was modelled as a function of the contact angle, particle size and the ratio of the density of solid particles to the density of the liquid.

scholarly journals Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

2021 ◽  
Vol 9 (11) ◽  
pp. 1253
Author(s):  
Yuriy N. Savchenko ◽  
Georgiy Y. Savchenko ◽  
Yuriy A. Semenov
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Solution Process ◽  
Cavity Flow ◽  
Surface Tension Effect ◽  
Force Coefficient ◽  
Hodograph Method ◽  
Wide Range ◽  
Critical Weber Number ◽  
Cavity Boundary

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

Effect of Velocity Profile on the Stability of Liquid Sheet

2014 ◽  
Vol 694 ◽  
pp. 288-291
Author(s):  
Run Ze Duan ◽  
Zhi Ying Chen ◽  
Li Jun Yang
Keyword(s):  
Growth Rate ◽  
Velocity Profile ◽  
Linear Analysis ◽  
Liquid Sheet ◽  
Wave Number ◽  
Flat Plates ◽  
Chebyshev Spectral Collocation ◽  
The Stability ◽  
The Relationship ◽  
Temporal Growth Rate

An electrified liquid sheet injected into a dielectric moving through a viscous gas bounded by two horizontal parallel flat plates of a transverse electric field is investigated with the linear analysis method. The liquid sheet velocity profile and the gas boundary layer thickness are taken into account. The relationship between temporal growth rate and the wave number was obtained using linear stability analysis and solved using the Chebyshev spectral collocation method. The effects of the velocity profile on the stability of the electrified liquid sheet were revealed for both sinuous mode and varicose mode. The results show that the growth rate of the electrified Newtonian liquid is greater than that of corresponding Newtonian one under the same condition, and the growth rate of the sinuous mode is greater than that of the varicose mode. Keywords: instability; planar liquid sheet; velocity profile;spectral method;linear analysis

scholarly journals Dual functions of Rack1 in regulating Hedgehog pathway

2020 ◽  
Vol 27 (11) ◽  
pp. 3082-3096 ◽  
Author(s):  
Yan Li ◽  
Xiaohan Sun ◽  
Dongqing Gao ◽  
Yan Ding ◽  
Jinxiao Liu ◽  
...  
Keyword(s):  
Mammalian Cells ◽  
Cellular Localization ◽  
Multiple Roles ◽  
Dual Roles ◽  
Cubitus Interruptus ◽  
Trimeric Complex ◽  
Physiological Processes ◽  
Underlying Mechanisms ◽  
The Stability ◽  
Fine Tune

Abstract Hedgehog (Hh) pathway plays multiple roles in many physiological processes and its dysregulation leads to congenital disorders and cancers. Hh regulates the cellular localization of Smoothened (Smo) and the stability of Cubitus interruptus (Ci) to fine-tune the signal outputs. However, the underlying mechanisms are still unclear. Here, we show that the scaffold protein Rack1 plays dual roles in Hh signaling. In the absence of Hh, Rack1 promotes Ci and Cos2 to form a Ci–Rack1–Cos2 complex, culminating in Slimb-mediated Ci proteolysis. In the presence of Hh, Rack1 dissociates from Ci–Rack1–Cos2 complex and forms a trimeric complex with Smo and Usp8, leading to Smo deubiquitination and cell surface accumulation. Furthermore, we find the regulation of Rack1 on Hh pathway is conserved from Drosophila to mammalian cells. Our findings demonstrate that Rack1 plays dual roles during Hh signal transduction and provide Rack1 as a potential drug target for Hh-related diseases.

Analysis of the Nonlinear Dynamics of a Railway Vehicle Wheelset

1973 ◽  
Vol 95 (1) ◽  
pp. 28-35 ◽  
Author(s):  
E. Harry Law ◽  
R. S. Brand
Keyword(s):  
Lateral Displacement ◽  
Equations Of Motion ◽  
Vertical Displacement ◽  
Linear Analysis ◽  
Design Parameters ◽  
Railway Vehicle ◽  
Nonlinear Variation ◽  
Constraint Equations ◽  
The Stability ◽  
Nonlinear Equations Of Motion

The nonlinear equations of motion for a railway vehicle wheelset having curved wheel profiles and wheel-flange/rail contact are presented. The dependence of axle roll and vertical displacement on lateral displacement and yaw is formulated by two holonomic constraint equations. The method of Krylov-Bogoliubov is used to derive expressions for the amplitudes of stationary oscillations. A perturbation analysis is then used to derive conditions for the stability characteristics of the stationary oscillations. The expressions for the amplitude and the stability conditions are shown to have a simple geometrical interpretation which facilitates the evaluation of the effects of design parameters on the motion. It is shown that flange clearance and the nonlinear variation of axle roll with lateral displacement significantly influence the motion of the wheelset. Stationary oscillations may occur at forward speeds both below and above the critical speed at which a linear analysis predicts the onset of instability.

The Stability of a Radial Wall Jet

1977 ◽  
Vol 28 (4) ◽  
pp. 247-258 ◽  
Author(s):  
Yutaka Tsuji ◽  
Yoshinobu Morikawa ◽  
Masaaki Sakou
Keyword(s):  
Linear Stability ◽  
Water Flow ◽  
Wall Jet ◽  
Two Dimensional ◽  
Radial Wall ◽  
Linear Region ◽  
Stability Calculation ◽  
Amplification Rate ◽  
Vortex Patterns ◽  
The Stability

SummaryMeasured stability characteristics in a radial wall jet were compared with calculated results for a two-dimensional wall jet. It was found that the stability of the radial wall jet is similar in many respects to that of the two-dimensional wall jet. An exception is that the local amplification rate of the disturbance velocity is much higher than in the two-dimensional case. It was also found that quarter-harmonics appear in the non-linear region, as well as half-harmonics, and that their amplitude distributions show profiles similar to that of the fundamental component. Further, vortex patterns were visualised in water flow, and results corresponding to measurements in air flow and to the linear stability calculation were obtained.

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