scholarly journals Instability of compressible drops and jets

2012 ◽  
Vol 700 ◽  
pp. 441-458 ◽  
Author(s):  
Umpei Miyamoto
Keyword(s):  
Surface Tension ◽  
Unstable Mode ◽  
Mode Analysis ◽  
Instability Criterion ◽  
Classic Problem ◽  
Perfect Fluids ◽  
Spatial Dimensions ◽  
Minimal Radius ◽  
The Stability ◽  
Self Gravity

AbstractWe revisit the classic problem of the stability of drops and jets held by surface tension, while regarding the compressibility of bulk fluids and spatial dimensions as free parameters. By mode analysis, it is shown that there exists a critical compressibility above which the drops (and discs) become unstable for a spherical perturbation. For a given value of compressibility (and of the surface tension and the density at equilibrium), this instability criterion provides a minimal radius below which the drop cannot be in stable equilibrium. According to the existence of the above unstable mode of the drop, which corresponds to a homogeneous perturbation of a cylindrical jet, the dispersion relation of Rayleigh–Plateau instability for cylinders drastically changes. In particular, we identify another critical compressibility above which the homogeneous unstable mode is predominant. The analysis is carried out for non-relativistic and relativistic perfect fluids, the self-gravity of which is ignored.

scholarly journals Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids in a horizontal magnetic field

2008 ◽  
Vol 12 (3) ◽  
pp. 103-110 ◽  
Author(s):  
Aiyub Khan ◽  
Neha Sharma ◽  
P.K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Growth Rate ◽  
Unstable Mode ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Streaming Velocity ◽  
The Stability ◽  
Conducting Fluids ◽  
Streaming Motion

The Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids has been investigated in the taking account of effects of surface tension, when the whole system is immersed in a uniform horizontal magnetic field. The streaming motion is assumed to be two-dimensional. The stability analysis has been carried out for two highly viscous fluid of uniform densities. The dispersion relation has been derived and solved numerically. It is found that the effect of viscosity, porosity and surface tension have stabilizing influence on the growth rate of the unstable mode, while streaming velocity has a destabilizing influence on the system.

Convection in a rotating spherical fluid shell with an inhomogeneous temperature boundary condition at infinite Prandtl number

1993 ◽  
Vol 250 ◽  
pp. 209-232 ◽  
Author(s):  
Keke Zhang ◽  
David Gubbins
Keyword(s):  
Numerical Solutions ◽  
Unstable Mode ◽  
Mode Analysis ◽  
Mathematical Framework ◽  
Fluid Systems ◽  
Critical Wavelength ◽  
Resonance Solution ◽  
Inhomogeneous Temperature ◽  
Spherical Fluid ◽  
The Stability

We examine thermal convection in a rotating spherical shell with a spatially non-uniformly heated outer surface, concentrating on three distinct heating modes: first, with wavelength and symmetry corresponding to the most unstable mode of the uniformly heated problem; secondly, with the critical wavelength but opposite equatorial symmetry; and thirdly, with wavelength much larger than that of the most unstable mode. Analysis is focused on boundary-locked convection, the associated spatial resonance phenomena, the stability properties of the resonance solution, and time-dependent secondary convection. A number of new forms of instability and convection are found: the most interesting is perhaps the saddle-node bifurcation, which is the first to be found for realistic fluid systems governed by partial differential equations. An analogous Landau amplitude equation is also analysed, providing an important mathematical framework for understanding the complicated numerical solutions.

The Effects of Collisions with Neutral Particles on the Instability of Two Superposed Composite Plasmas Streaming Through Porous Medium

1999 ◽  
Vol 54 (6-7) ◽  
pp. 411-416 ◽  
Author(s):  
Mohamed Fahmy El-Sayed
Keyword(s):  
Porous Medium ◽  
Unstable Mode ◽  
Instability Criterion ◽  
Stable Configuration ◽  
Neutral Particles ◽  
Fluid Velocities ◽  
Stability And Instability ◽  
The Stability ◽  
The Magnetic Field

Abstract The effects of collisions with neutral atoms on the hydromagnetic stability of the plane interface separating two streaming superposed composite plasmas of uniform densities in a porous medium are investigated. In the absence of fluid velocities, it is found, for a potentially stable configuration, that the system remains stable, while for a potentially unstable configuraion, the unstable system becomes stable under a certain condition of the wavenumber depending on the values of the fluid densities, Alfvén velocities, and the orientation of the magnetic field. The porosity of the porous medium does not have any significant effect on the stability criterion. In the presence of fluid velocities, it is found that, the instability criterion is independent of the permeability of the medium and the collision effects with neutral particles. The criterion determing the stability does not depend on the permeability of the medium but depends on the density of neutral particles. The porosity of the medium is found to have a significant effect on both the stability and instability criteria in this case. The role of the permeability of the medium, the collisional frequency, and the porosity of the porous medium on the growth rate of the unstable mode is examined analitically. Routh’s test of stability is applied to confirm the above results.

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.

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.

scholarly journals Thermosolutal Instability in Compressible Viscoelastic Dusty Fluid through Porous Medium

2013 ◽  
Vol 18 (1) ◽  
pp. 99-112 ◽  
Author(s):  
P. Kumar ◽  
H. Mohan
Keyword(s):  
Porous Medium ◽  
Viscoelastic Fluid ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Medium Permeability ◽  
The Stability ◽  
Solute Gradient

Thermosolutal instability in a compressible Walters B’ viscoelastic fluid with suspended particles through a porous medium is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the Walters B’ viscoelastic fluid behaves like a Newtonian fluid and it is found that suspended particles and medium permeability have a destabilizing effect whereas the stable solute gradient and compressibility have a stabilizing effect on the system. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and viscoelasticity are found to introduce oscillatory modes in the system which are non-existent in their absence.

scholarly journals Effect of Vadasz Number on Magnetoconvection in a Darcy Porous Layer with Concentration Based Internal Heating

2019 ◽  
pp. 1-13
Author(s):  
C. Israel-Cookey ◽  
L. Ebiwareme ◽  
E. Amos
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Internal Heat ◽  
Lewis Number ◽  
Mode Analysis ◽  
Internal Heating ◽  
Vadasz Number ◽  
The Stability ◽  
Solutal Rayleigh Number

In this research article, the effect of Vadasz number on magnetoconvection in a Darcy Porous Layer with concentration based internal heating is studied. The flow is governed by the Oberbeck-Boussineq model for Newtonian fluid. The stability analysis method based on the perturbation of infinitesimal amplitude is carried out using the normal mode analysis. The onset criterion for both the stationary and oscillatory convection on the stability of system is obtained. The analysis examines the effects of pertinent parameters on the stability of the system: magnetic field parameter, solutal Rayleigh number, Lewis number and Vadasz number. The result show that, internal heat parameter,  and Lewis number, , hastens the onset of instability in the system, whereas magnetic field, , Vadasz number,  and solutal Rayleigh number,  delay the onset of instability.

The stability of pendent liquid drops. Part 2. Axial symmetry

1974 ◽  
Vol 63 (3) ◽  
pp. 487-508 ◽  
Author(s):  
E. Pitts
Keyword(s):  
Surface Tension ◽  
Energy Change ◽  
Maximum Volume ◽  
Experimental Conditions ◽  
Liquid Drops ◽  
Stable Equilibria ◽  
Equilibrium Shapes ◽  
The Stability ◽  
The Many ◽  
Horizontal Support

In a drop of liquid which hangs below a horizontal support or a t the end of a tube, the forces due to surface tension, pressure and gravity are in equilibrium. Amongst the many possible equilibrium shapes of the drop, only those which are stable occur naturally. The calculus of variations has been used to determine theoretically the stable equilibria, by calculating the energy change when the liquid in equilibrium experiences axially symmetrical perturbations under physically realistic constraints. If the energy change can be made negative, the drop is unstable. With this criterion, stable equilibria have been identified through which the naturally growing drops evolve until they reach a maximum volume, when they become unstable. These results are illustrated by calculations relating to typical experimental conditions.

Sign in / Sign up

Export Citation Format

Share Document