Liquid Bridge Volume Research Articles

Linear-stability analysis of thermocapillary convection in liquid bridges with highly deformed free surface

The float-zone crystal-growth process is studied in the framework of the half-zone model. Linear-stability analysis is used to compare the onset of oscillations in liquid-bridge thermocapillary convection upon liquid-bridge volume with experimental data for high-Prandtl fluid. Well-known structure of neutral stability curve for high-Prandtl fluid, consisting of two branches separated by an “overstability” gap, has been clearly reproduced. Moreover, for low-volume branch there is a good quantitative correspondence between experimental data and linear-stability analysis. Travelling hydrothermal waves with unit azimuthal wave number correspond to critical perturbations for both branches. In addition, an influence of temperature-dependent viscosity on stability limits is determined.

A scheme for micro-manipulation based on capillary force

As the size of object diminishes, the effect of adhesional forces grows stronger for micro-manipulation and so. The capillary force generated by a liquid bridge can be greater than both the capillary force generated by another bridge and the adhesional force because the capillary force can be controlled by regulation of the liquid volume. We propose a micro-manipulation method based on the regulation of liquid bridge volume. A numerical investigation to estimate the capillary force from a given liquid volume is also presented, and four phases of capillary force curves are obtained from it. If an object is supported by two liquid bridges, we can predict which bridge collapse by a stability analysis for the wide range of liquid volume using the force curve.

Influence of liquid bridge volume on the floating zone convection

AbstractThe liquid bridge volume is a critical geometrical parameter in addition to the aspect ratio for onset of oscillation in the floating zone convection. The oscillatory features are generally divided into two characteristic regions: slender liquid bridge region and fat liquid bridge region. The oscillatory modes in two regions are discussed in the present paper.

Linear dynamics of axisymmetric liquid bridges

The dynamical response of an axisymmetric liquid bridge to small-magnitude perturbations is studied in the framework of the Cosserat model. A numerical procedure to deal with this problem is proposed. The method is found to provide very accurate results from a comparison with the analytical predictions for the cylindrical configuration. The frequencies and damping rates characterizing the oscillation modes are obtained numerically for arbitrary axisymmetric liquid bridge shapes, considering the combined effects of residual gravity, the liquid bridge rotation, the inequality of the disks, and the liquid bridge volume. The results are compared with the predictions obtained from the three-dimensional model for inviscid liquid bridges.

Theoretical Analysis of the Vibration of Axisymmetric Liquid Bridges of Arbitrary Shape

A liquid bridge consists of a mass of liquid sustained by the action of capillary forces between two parallel disks. The dynamics of these liquid columns has been extensively analysed both theoretically and experimentally over the last decades. Many of the studies have focused on the dynamical response of cylindrical liquid bridges subjected to the action of an oscillatory microgravity field due to, for instance, an in-phase vibration of the supporting disks. There have been fewer studies dealing with the vibration of axisymmetric liquid bridges of arbitrary shape. In this paper the dynamics of rotating inviscid axisymmetric liquid bridges is analysed considering the combined effect of residual gravity, the inequality of the disks and the liquid bridge volume. The results are calculated numerically by using the one-dimensional Cosserat model and the full three-dimensional description. The excitation is assumed to be of small amplitude and harmonic, so that the theoretical models are linearized and the analysis is performed in the frequency domain. The details of the numerical methods proposed are discussed. Comparison between the values of the first resonance frequency obtained from both models shows an excellent agreement for long liquid bridges, the discrepancies increasing as the value of the slenderness decreases.

Two bifurcation transitions of the floating half zone convection in a fat liquid bridge of larger Pr

The transient process of the thermocapillary convection was obtained for the large Pr floating half zone by using the method of three-dimensional and unsteady numerical simulation. The convection transits directly from steady and axisymmetric state to oscillatory flow for slender liquid bridge, and transits first from steady and axisymmetric convection to the steady and non-axisymmetric convection, then, secondly to the oscillatory convection for the fatter liquid bridge. This result implies that the volume of liquid bridge is not only a sensitive critical parameter for the onset of oscillation, but also relates to the new mechanism for the onset of instability in the floating half zone convection even in case of large Prandtl number fluid.

A New Method for the Characterization of Electrically Conducting Liquid Bridges

An electrical conductance technique is employed in investigating the behavior of constant volume liquid bridges when their length is altered. The liquid bridges are edge-pinned between two vertical, identical rods with a variable separation distance. Rods of different radius, material, and edge geometry are examined as they play a role in the response of the system. It is shown that liquid bridge volume and rod radius are the parameters that mainly influence the conductance signal. A mathematical framework is developed for the identification of the geometrical characteristics of liquid bridges explicitly from conductance data. The role of gravity is discussed in both the experiments and the theoretical analysis. The theoretical predictions obtained show a close agreement with measurements.

Influence of liquid bridge volume on the onset of oscillation in floating-zone convection: III. Three-dimensional model

An unsteady and three-dimensional model of the floating-half-zone convection on the ground is studied by the direct numerical simulation for the medium of 10 cSt silicon oil, and the influence of the liquid bridge volume on the critical applied temperature difference is especially discussed. The marginal curves for the onset of oscillation are separated into two branches related, respectively, to the slender liquid bridge and the fat liquid bridge. The oscillatory features of the floating-half-zone convection are also discussed.

Calculation of the Liquid Bridge Volume and Bulk Saturation from the Half-filling Angle

The volume of a liquid bridge between two spherical particles can be used to calculate the critical separation distance and the rupture energy. There exist a number of explicit but very complex equations for the calculation of the bridge volume as a function of the half-filling angle. In this paper, an empirical equation is presented that strongly simplifies these calculations. In addition, the presented approach leads to a calculation of the half-filling angle from the bulk liquid saturation which may be used for the estimation of the tensile strength of a wet powder.

Effect of liquid bridge volume on the instability in small-Prandtl-number half zones

A perturbation method is used to examine the linear instability of thermocapillary convection in a liquid bridge of floating half-zone filled with a small Prandtl number fluid. The influence of liquid bridge volume on critical Marangoni number and flow features is analyzed. The neutral modes show that the instability is mainly caused by the bulk flow that is driven by the nonuniform thermocapillary forces acting on the free surface. The hydrodynamic instability is dominant in the case of small Prandtl number fluid and the first instability mode is a stationary bifurcation. The azimuthal wave number for the most dangerous mode depends on the liquid bridge volume, and is not always two as in the case of a cylindrical liquid bridge with aspect ratio near 0.6. Its value may be equal to unity when the liquid bridge is relatively slender.

Numerical simulation of cohesive powder behavior in a fluidized bed

A numerical simulation model was developed for wet powder fluidization in the scope of investigation on cohesive powder behavior. The model was developed based on the discrete element method (DEM) with the inter-particle cohesive interaction due to liquid bridging. To take into account the liquid bridge force between particles and between a particle and a wall, a regression expression for the liquid bridge force was developed as a function of the dimensionless liquid bridge volume and the separation distance based on numerical solutions of the Laplace–Young equation. The critical rupture distance, i.e. the maximum separation distance where the liquid bridges rupture between particles or between a particle and a wall, was also correlated in the similar manner. For gas motion the Anderson–Jackson local averaged Navier–Stokes equations were integrated by the SIMPLE method employing the staggered grid system. For the particle motion the Newtonian equations of motion of individual particles were integrated, where the Hooke’s repulsive and damping forces for particle collision, the gravity force, the drag force and the particle cohesion force were taken into account. Example computations were conducted for a two-dimensional bed of spherical particles of 1 mm in diameter, density of 2650 kg/m 3, moisture content of 0.27 wt% and gas velocity of 1.2 m/s. Both dry and wet powder behavior in a fluidized bed was successfully reproduced. It was observed that such a wet powder was fluidized forming agglomerates. The fluctuations of the pressure drop and the minimum fluidizing velocity for wet powder were higher than those for dry particles in the present computer experiment. The granular temperature was obtained from particle velocity. The high granular temperature area below a rising bubble and above a forming bubble could be found for both dry and wet particles

Influence of liquid bridge volume on instability of floating half zone convection

Thermocapillary instabilities on floating half zone convection in microgravity environment were investigated by linear instability analysis method. The critical Marangoni numbers were obtained and compared with the experimental ones. The influences of the liquid bridge volume and the aspect ratio on the critical Marangoni number were analyzed. It is found that the liquid bridge volume and the aspect ratio have great influence on the critical Marangoni number. There was a gap region where the oscillatory convection will not be observed in present analyses and in experiments in the curve of the critical Marangoni number vs the liquid bridge volume for the case of large Prandtl number and small aspect ratio.

Investigation on a simulation model of floating half zone convection—II. Experiment

A simulation model of floating half zone with non-uniform temperature distribution at the upper rod and uniform temperature distribution at lower rod was discussed by numerical investigation in a previous paper. In the present paper, the experimental investigation of the simulation model is given generally. The results of the present model show that the temperature profile is quite different and the critical applied temperature difference is lower than the one of usual model with same geometrical parameters in most cases. The features of critical Marangoni number depending on the liquid bridge volume are also different from the ones of usual model.

Stability of an isorotating liquid bridge between equal disks under zero-gravity conditions

The stability of the relative equilibrium of an isorotating axisymmetric liquid bridge between two equal-radius coaxial disks under zero-gravity conditions has been investigated in detail. The free surface is assumed to be pinned to the edges of the disks and in equilibrium and only perturbations compatible with this pinning are considered. In the plane of the dimensionless variables characterizing the liquid bridge length and the liquid bridge volume, the stability regions for a set of values of the Weber number have been calculated. The stability region structure and the nature of critical perturbations change when the Weber number, W, passes through the values W0 (2.05<W0<2.06) and W1 (2.44<W1<2.45). It has been found that, for W<W0, the stability region is connected, and the neutral stability may take place with respect to nonaxisymmetric perturbations as well as to axisymmetric ones. In the latter case, it has been established whether the critical axisymmetric perturbations are reflectively symmetric or reflectively antisymmetric about the equatorial plane. When the increasing Weber number passes through the value W0, the stability region breaks into two disconnected parts. The first exists for all Weber numbers larger than W0. For the states belonging to the boundary of this part, only nonaxisymmetric perturbations are critical. The second part exists only for Weber numbers between W0 and W1. Its boundary is determined by the states that may be neutrally stable to nonaxisymmetric perturbations or to axisymmetric ones. The characteristics of the shape of the neutrally stable surfaces have been calculated for a wide range of the Weber number.

How to determine critical marangoni number in half floating zone convection

In the present paper, the coordinated measurements of the temperature profile inside the liquid bridge and the boundary variation of free surface, in addition to other quantities, were obtained in the same time for the half floating zone convection. The results show that the onset of free surface oscillation is earlier than the one of temperature oscillation during the increasing of applied temperature difference, and the critical Marangoni numbers, defined usually by temperature measurement, are larger than the one defined by free surface measurement, and the difference depends on the volume of liquid bridge. These results induce the question, “How to determine experimentally the critical Marangoni number?”

Influence of liquid bridge volume on the onset of oscillation in floating zone convection II. Numerical simulation

The onset of oscillation in the floating zone convection driven by the gradient of surface tension was studied numerically for an unsteady and two-dimensional model, and studies were concentrated on the influence of liquid bridge volume on the onset of oscillation in comparison with the experimental results in the Paper I. The numerical results agree with the experimental ones presented in the previous paper, in which the distributions of critical applied temperature difference depending on the volume of liquid bridge and a gap range of liquid volume in marginal stability curve were obtained.

Influence of liquid bridge volume on the onset of oscillation in floating zone convection I. Experiments

The onset of oscillation in the floating zone convection driven by the gradient of surface tension was experimentally studied, and discussions were concentrated on the influence of liquid bridge volume on the onset of oscillation. Distributions of critical applied temperature difference and frequency depending on the volume of the liquid bridge were obtained, and there was a gap range of liquid volume which separated the curve of marginal stability into two parts for fixed rod diameter and aspect ratio. The results imply that the volume of the liquid bridge is a sensitive critical parameter for the onset of oscillation. The implication on the instability is also discussed in the present paper.

A Theoretical Study of the Liquid Bridge Forces between Two Rigid Spherical Bodies

This paper is concerned with liquid bridges between two spherical rigid bodies of equal radii under conditions where the effects of gravity are negligible. Previous work on the necessary condition for the stability of such bridges is examined and the minimum free-energy formulation applicable to any contact angle is proven. It is shown that this formulation is a more fundamental criterion for specifying the stable numerical solutions of the Laplace-Young equation, although equivalent to previous conjectures based on the liquid bridge neck diameter and filling angle. At relatively low contact angles, say <40°, the critical separation for rupture is given by the cube root of the liquid bridge volume to a good approximation. The toroidal approximation provides a simple method of estimating the total liquid bridge force. The "gorge method" of evaluation leads to errors of <10% for all stable separations and a wide range of bridge volumes. The accuracy is independent of contact angle because of geometrical self-similarity. Simple scaling coefficients can be introduced into the toroidal approximation to allow force estimations to be made with relatively high accuracy.

Liquid bridges between spheres in a gravitational field

A theoretical study has been made of the properties of a liquid bridge between spheres of equal and unequal radii taking into account the effect of gravity on the meniscus shape and capillary attractions. The interfacial shape of the bridge is obtained by a numerical solution of the Young-Laplace equation employing the Runge-Kutta method for a given sphere pair, liquid bridge volume, and contact angle. The capillary force, sphere separation, minimum neck diameter, and filling angle of the liquid on both spheres are calculated numerically for interfacial shapes which exhibit the minimum neck diameter. The equal bridge volume problem at different sphere separations for a given set of spheres is solved with the two point boundary-value condition which must be satisfied on the sphere surfaces. This new solution, which takes into consideration gravitational disortion, enables large spheres to be used in experimental studies, and permits accurate measurements of the bridge volumes and the maximum amount of liquid that can be deposited between the spheres in a given system. It is found that the capillary attraction and maximum liquid bridge volume increases as the contact angle decreases and, also, as the radius of the bottom sphere increases. The effects that changing the bridge volume, sphere radii, and contact angle have on the capillary force, the maximum sphere separation, and other factors affecting the system are investigated.

Measurement of the variation of interfacial tension with temperature between immiscible liquids of equal density

For the measurement of interfacial tensions between liquids of equal densities, methods like drop weight, Wilhelmy plate etc. fail. A method is developed using a liquid bridge between a glass tip and a freely hanging piece of density higher than that of the fluids. The volume of liquid bridge that can sustain a piece of given weight cannot exceed some maximal value. This maximal volume is determined experimentally. A computer program makes it possible to tabulate the maximal volumes of the liquid bridge as a function of the interfacial tension for a given tip and metal piece. The program uses iteratively the circle segment approximation for the calculation of the meridian curve given by Kelvin. Results are given for the system aqueous ethanol/paraffin oil of equal densities.