The Effect of Thermo-Solutal Capillary Transport on the Dynamics of Liquid Bridge

Volume 1 ◽  
2004 ◽  
Author(s):  
Fre´de´ric Joly ◽  
Wei Shyy ◽  
Ge´rard Labrosse
Keyword(s):  
Surface Tension ◽  
Liquid Bridge ◽  
Soret Effect ◽  
Stability Limit ◽  
Solute Concentration ◽  
Transport Dynamics ◽  
Separation Ratio ◽  
Prandtl Numbers ◽  
The Stability ◽  
Pseudo Spectral Method

The transport dynamics and stability limit of the axisymmetric steady flow driven by a surface tension variation in a liquid bridge configuration is studied numerically. The surface tension variation results from both thermal and solutal gradients, and varies linearly with both temperature and solute concentration. The pseudo-spectral method is employed to investigate the solutions under different combinations of Marangoni, Prandtl and Lewis numbers, and separation ratio. Steady bifurcations for low Prandtl numbers are observed. The Soret effect has important influence on the stability of the basic flow, as it can change the symmetry of the most destabilizing perturbations and affect the threshold for 3D convection. It is also shown that for large Prandtl number, the Hopf bifurcation observed for pure fluid is replaced by a steady one for negative separation ratio.

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.

A thermodynamic approach to mechanical stability of nanosized particles

Open Physics ◽  
2003 ◽  
Vol 1 (2) ◽  
Author(s):  
Vladimir Samsonov ◽  
Nikolay Sdobnyakov
Keyword(s):  
Surface Tension ◽  
Free Energy ◽  
Stability Condition ◽  
Mechanical Stability ◽  
Noble Gas ◽  
Stability Limit ◽  
Gas Clusters ◽  
The Stability ◽  
The Second Variation ◽  
Nonpolar Organic

AbstractThermodynamic stability conditions for nanoparticles (resulting from non-negativity of the second variation of the free energy) have been analyzed for two cases: (i) a nonvolatile nanosized particle with the size-dependent surface tension; (ii) the limiting case of larger objects when the surface tension takes its macroscopic value. It has been shown that the mechanical stability of a nanoparticle, i.e. its stability relative to the volume fluctuations, is defined by an interplay between the excess (“surface”) free energy and the volumetric elastic energy. According to the results obtained, noble gas clusters and metal nanoparticles satisfy the mechanical stability condition. At the same time, water nanodrops, as well as nanoparticles presented by nonpolar organic molecules, correspond to the stability limit. Among the investigated systems, the stability condition is not carried out for n-Pentane clusters.

Convective instability in liquid pools heated from below

1971 ◽  
Vol 47 (4) ◽  
pp. 779-787 ◽  
Author(s):  
Harvey J. Palmer ◽  
John C. Berg
Keyword(s):  
Surface Tension ◽  
Heat Flux ◽  
Stability Analysis ◽  
Convective Instability ◽  
Temperature Drop ◽  
Stability Limit ◽  
Liquid Pool ◽  
Silicone Oils ◽  
Liquid Pools ◽  
The Stability

The linear hydrodynamic stability analysis of liquid pools heated from below combining surface tension and buoyancy effects as presented by Nield (1964) is confirmed by experiment for a series of silicone oils. The experimental method used is an adaptation of the Schmidt–Milverton technique, in which the stability limit is located by the change of slope in the plot of heat flux versus temperature drop across the liquid pool.

On the stability limit of charged droplets

1989 ◽  
Vol 422 (1863) ◽  
pp. 319-328 ◽  
Keyword(s):  
Surface Tension ◽  
Particle Size ◽  
Light Scattering ◽  
Stability Limit ◽  
Prolate Spheroid ◽  
Charged Droplets ◽  
Electric Stress ◽  
The Stability ◽  
Stability Limits

Single, highly charged droplets of dioctylphthalate and sulphuric acid of radius between 1 and 10 μm are suspended in vacuum in a quadrupol trap. As the droplets evaporate their radius is monitored continuously by light scattering and their charge is determined periodically by weight balancing. The droplets break when the electric stress exceeds that of surface tension. The largest fragment remains trapped allowing a determination of the change in volume and charge. The fraction of volume and charge lost is found to be independent of particle size and sign of charge and is variable. The oil drops lose (15.0 ± 3.9)% of their charge on breakup and (2.25 ± 0.96)% of their mass. The acid droplets lose (49.4 ± 8.3)% of their charge and less than 0.1% of their mass. The acid results are compared with those from a model of field emission based upon prolate spheroid deformation and the formation of Taylor cones. For both oil and acid droplets the stability limits are in agreement with those predicted by Lord Rayleigh.

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.

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.

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

2015 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Robust Stability ◽  
Optimal Parameter ◽  
Stability Limit ◽  
Boundary Function ◽  
Lower Envelope ◽  
Computation Method ◽  
Parameter Region ◽  
Dynamical Parameters ◽  
The Stability ◽  
Machining Parameter

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

Numerical Analysis of Thermal-Solutal Convection in Heterogeneous Porous Media

2005 ◽  
Vol 73 (1) ◽  
pp. 21-25 ◽  
Author(s):  
Charles-Guobing Jiang ◽  
M. Ziad Saghir ◽  
M. Kawaji
Keyword(s):  
Porous Media ◽  
Thermal Diffusion ◽  
Soret Effect ◽  
Heterogeneous Porous Media ◽  
Soret Coefficient ◽  
Solutal Convection ◽  
Coefficient Distribution ◽  
Separation Ratio ◽  
Diffusion In Porous Media ◽  
Vertical Cavity

Thermal diffusion, or Soret effect, in porous media is mathematically modeled with the Firoozabadi model based on non-equilibrium thermodynamics. The Soret effect in a binary mixture is investigated in a vertical cavity with heterogeneous permeability, where natural convection can occur. The thermo solutal convection with heterogeneous permeability was studied in terms of flow pattern, concentration distribution, component separation ratio, and Soret coefficient distribution. A consistent analysis was conducted and it is concluded that the Soret coefficient of thermal diffusion in porous media strongly depends on the heterogeneity of permeability.

Some difficulties associated with the limit equilibrium method of slices

1983 ◽  
Vol 20 (4) ◽  
pp. 661-672 ◽  
Author(s):  
R. K. H. Ching ◽  
D. G. Fredlund
Keyword(s):  
Slope Stability ◽  
Factor Of Safety ◽  
Limit Equilibrium ◽  
Stability Limit ◽  
Limit Equilibrium Method ◽  
Soil Conditions ◽  
Side Force ◽  
Limit Equilibrium Methods ◽  
Equilibrium Method ◽  
The Stability

Several commonly encountered problems associated with the limit equilibrium methods of slices are discussed. These problems are primarily related to the assumptions used to render the inherently indeterminate analysis determinate. When these problems occur in the stability computations, unreasonable solutions are often obtained. It appears that problems occur mainly in situations where the assumption to render the analysis determinate seriously departs from realistic soil conditions. These problems should not, in general, discourage the use of the method of slices. Example problems are presented to illustrate these difficulties and suggestions are proposed to resolve these problems. Keywords: slope stability, limit equilibrium, method of slices, factor of safety, side force function.

Double-diffusive instabilities in a vertical slot

1999 ◽  
Vol 392 ◽  
pp. 213-232 ◽  
Author(s):  
OLIVER S. KERR ◽  
KIT YEE TANG
Keyword(s):  
Temperature Difference ◽  
Salinity Gradient ◽  
Stability Boundary ◽  
Large Temperature ◽  
Vertical Slot ◽  
Stability And Instability ◽  
Heat Diffusivity ◽  
Prandtl Numbers ◽  
The Stability ◽  
Double Diffusive

A fluid stably stratified by a salinity gradient and enclosed between two vertical boundaries can become unstable when it is subjected to a temperature difference between the walls. The linear stability of such a fluid in a vertical slot is investigated. Errors in earlier results are found, confirming recent results of Young & Rosner (1998). Four different asymptotic regimes on the stability boundary are identified. One of these, the limit of a strong salinity gradient, has previously been analysed. The analyses of the separate asymptotic limits of weak salinity gradient, large temperature difference and small wavenumber are also given. These four cases make up much of the total boundary between stability and instability for double-diffusive instabilities in a vertical slot, and so most of this boundary can be mapped out for general Prandtl numbers and salt/heat diffusivity ratios using these results.

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