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.

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.

Distorted gas bubbles at large Reynolds number

1974 ◽  
Vol 62 (1) ◽  
pp. 163-183 ◽  
Author(s):  
M. El Sawi
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Liquid Metals ◽  
Gas Bubbles ◽  
Joint Effect ◽  
Large Reynolds Number ◽  
Recent Experimental Data ◽  
Approximate Theory ◽  
Axis Ratio ◽  
Comparison Of The Results

The distortion of a gas bubble rising steadily in an inviscid incompressible liquid of infinite extent under the action of surface tension forces is investigated theoretically using an appropriate extension of the tensor virial theorem. A convenient parameter for distinguishing the bubble shape is the Weber numberW. The virial method leads to an expression relatingWand the axis ratio χ, of the transverse and longitudinal axes of the bubble. To first order inW, this relation agrees with the linear theory established by Moore (1959). Also, comparison of the results with his (1965) approximate theory reveals similar features and excellent agreement up to χ = 2. In particular, it confirms his prediction of the existence of a maximum Weber number. Although the present work does not consider the stability of these bubbles, it is interesting to note that the maximum value of 3.271 attained byWdiffers only by about 2.8% from the critical Weber number obtained by Hartunian & Sears (1957) for the onset of instability.An approximate method for the study of slightly distorted spheroidal gas bubbles is also formulated and the resulting boundary-value problem solved numerically. The theory is then extended to include gravity. The joint effect of surface tension as well as gravitational forces has not been included in earlier theories. The shapes of the bubbles are traced and compared with the unperturbed spheroids. Comparisons for the velocity of bubble rise are made between the present predictions and some experimental results. In particular the results are compared with recent experimental data for the motion of gas bubbles in liquid metals.

scholarly journals Stability of an electrified liquid jet approaching to critical point

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402093637
Author(s):  
Zixuan Fang ◽  
Ping Wang
Keyword(s):  
Surface Tension ◽  
Critical Point ◽  
Weber Number ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Wave Number ◽  
Electrical Field ◽  
Electric Stress ◽  
Electrical Field Intensity ◽  
The Stability

This article reports the linear stability analysis of a thermodynamic-transcritical jet sprayed to a radial electrical field. An asymptotic approach was used to obtain the stability solution of a supercritical jet subjected to electrical field. In order to obtain the solutions for the electrified supercritical jet, the surface tension was decreased and consequently led the increase in Weber number in the linear governing equation of subcritical charged jet. To investigate the role of surface tension and electric stress playing in the destabilizing process when approaching the critical point, the energy budget is performed by tracing the energy sources. It was found that, when the Weber number is increased to a sufficiently large value, the solution will become an asymptotic value, which can be considered as a solution under the supercritical conditions. The electric stress can increase both the maximum growth rate and the dominant wave number of electrified supercritical jet, that is, higher electrical field intensity would enhance the instability of the electrified supercritical jet and decrease the wavelength of the disturbances.

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 wind force needed to dislodge a drop adhered to a surface

1988 ◽  
Vol 196 ◽  
pp. 205-222 ◽  
Author(s):  
Paul A. Durbin
Keyword(s):  
Differential Equation ◽  
Surface Tension ◽  
Contact Angle ◽  
Weber Number ◽  
Dynamic Pressure ◽  
Contact Angle Hysteresis ◽  
Wind Force ◽  
Drop Shape ◽  
Integro Differential Equation ◽  
Critical Weber Number

The dislodging by dynamic pressure forces of a drop adhered by surface tension to a plane is analysed. An integro-differential equation describing the drop shape is solved numerically and the critical Weber number as a function of contact angle hysteresis is found.

scholarly journals A pH-Responsive Foam Formulated with PAA/Gemini 12-2-12 Complexes

2021 ◽  
Vol 5 (3) ◽  
pp. 37
Author(s):  
Hernán Martinelli ◽  
Claudia Domínguez ◽  
Marcos Fernández Leyes ◽  
Sergio Moya ◽  
Hernán Ritacco
Keyword(s):  
Surface Tension ◽  
Dynamic Surface Tension ◽  
Foam Formation ◽  
Ph Responsive ◽  
Dynamic Surface ◽  
X Ray ◽  
Equilibrium Surface Tension ◽  
Potential Applications ◽  
The Stability ◽  
Air Interfaces

In the search for responsive complexes with potential applications in the formulation of smart dispersed systems such as foams, we hypothesized that a pH-responsive system could be formulated with polyacrylic acid (PAA) mixed with a cationic surfactant, Gemini 12-2-12 (G12). We studied PAA-G12 complexes at liquid–air interfaces by equilibrium and dynamic surface tension, surface rheology, and X-ray reflectometry (XRR). We found that complexes adsorb at the interfaces synergistically, lowering the equilibrium surface tension at surfactant concentrations well below the critical micelle concentration (cmc) of the surfactant. We studied the stability of foams formulated with the complexes as a function of pH. The foams respond reversibly to pH changes: at pH 3.5, they are very stable; at pH > 6, the complexes do not form foams at all. The data presented here demonstrate that foam formation and its pH responsiveness are due to interfacial dynamics.

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.

Electrohydrodynamic stability: Taylor–Melcher theory for a liquid bridge suspended in a dielectric gas

2002 ◽  
Vol 452 ◽  
pp. 163-187 ◽  
Author(s):  
C. L. BURCHAM ◽  
D. A. SAVILLE
Keyword(s):  
Surface Tension ◽  
Dielectric Constant ◽  
Electric Fields ◽  
Liquid Bridge ◽  
Numerical Solutions ◽  
Specific Conductivity ◽  
Axisymmetric Deformation ◽  
Aspect Ratios ◽  
The Stability ◽  
Theory And Experiment

A liquid bridge is a column of liquid, pinned at each end. Here we analyse the stability of a bridge pinned between planar electrodes held at different potentials and surrounded by a non-conducting, dielectric gas. In the absence of electric fields, surface tension destabilizes bridges with aspect ratios (length/diameter) greater than π. Here we describe how electrical forces counteract surface tension, using a linearized model. When the liquid is treated as an Ohmic conductor, the specific conductivity level is irrelevant and only the dielectric properties of the bridge and the surrounding gas are involved. Fourier series and a biharmonic, biorthogonal set of Papkovich–Fadle functions are used to formulate an eigenvalue problem. Numerical solutions disclose that the most unstable axisymmetric deformation is antisymmetric with respect to the bridge’s midplane. It is shown that whilst a bridge whose length exceeds its circumference may be unstable, a sufficiently strong axial field provides stability if the dielectric constant of the bridge exceeds that of the surrounding fluid. Conversely, a field destabilizes a bridge whose dielectric constant is lower than that of its surroundings, even when its aspect ratio is less than π. Bridge behaviour is sensitive to the presence of conduction along the surface and much higher fields are required for stability when surface transport is present. The theoretical results are compared with experimental work (Burcham & Saville 2000) that demonstrated how a field stabilizes an otherwise unstable configuration. According to the experiments, the bridge undergoes two asymmetric transitions (cylinder-to-amphora and pinch-off) as the field is reduced. Agreement between theory and experiment for the field strength at the pinch-off transition is excellent, but less so for the change from cylinder to amphora. Using surface conductivity as an adjustable parameter brings theory and experiment into agreement.

THE STABILITY ANALYSIS OF HEAT TRANSFER IN SATURATED LIQUID FILM OF THE SPECIAL MATERIALS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1547-1550
Author(s):  
YOULIANG CHENG ◽  
XIN LI ◽  
ZHONGYAO FAN ◽  
BOFEN YING
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Surface Tension ◽  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Relationship ◽  
Saturated Liquid ◽  
Nonlinear Surface ◽  
Isothermal Wall ◽  
The Stability

Representing surface tension by nonlinear relationship on temperature, the boundary value problem of linear stability differential equation on small perturbation is derived. Under the condition of the isothermal wall the effects of nonlinear surface tension on stability of heat transfer in saturated liquid film of different liquid low boiling point gases are investigated as wall temperature is varied.

Influencing Factors of Chromium Ion Stability in Microbe Culture Media

2012 ◽  
Vol 610-613 ◽  
pp. 215-219
Author(s):  
Yun Xiao He ◽  
Xiao Ming Chen
Keyword(s):  
Ionic Liquid ◽  
Liquid Medium ◽  
Culture Media ◽  
Fluid Medium ◽  
Chromium Ion ◽  
Medium Components ◽  
Salt Ions ◽  
Ion Stability ◽  
The Stability ◽  
Ionic Liquid Medium

The stability factors for Cr6+ and Cr3+ in microbiological media, including temperature, preservation conditions and medium components were studied in this research project, through potassium permanganate oxidation and DPC (Diphenylcarbazide) spectrophotometry. It shows that the protein component mainly influences Cr6+ content changes at pre- and post- heat sterilization to the chromium ionic liquid medium, other than being impacted basically by inorganic salt ions. It also indicates that the method can be introduced into experiment researches for microbe dechromisation i.e. Chromium ion aqueous solution and fluid medium are sterilized separately, and then are made into the chrome ions liquid as per a certain concentration. The concentration of hexavalent chromium ions is affected by preservation time and temperature also. For this reason, chromium ionic liquid medium is kept at low temperature, and as quickly as possible for the test.

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