The influence of the curvature dependence of the surface tension on the geometry of electrically charged menisci

We evaluate how the curvature dependence of surface tension affects the shape of electrically charged interfaces between a perfectly conducting fluid and its vapour. We consider two cases: i) spherical droplets in equilibrium with their vapour; ii) menisci pending in a capillary tube in presence of a conducting plate at given electric potential drop. Tolman-like dependence of surface tension on curvature becomes important when the “nucleation radius” is comparable with the interface curvature radius. In case i) we prove existence of the equilibrium minimal radius and estimate its dependence on the electric fields and Tolman-like curvature effects. In case ii) the menisci are subject to the gravitational force, surface tension and electrostatic fields. We determine the unknown surface of the menisci to which the potential is assigned using an iterative numerical method and show that Tolman-like corrections imply: 1) a variation of the height (up to 10% in some cases) of the tip of the menisci; 2) a decrease of the maximum electrical potential applicable to the menisci before their break-down amounting to 40V over 800V in the considered cases. We conjecture that these effects could be used in new experiments based on electric measurements to determine the dependence of the equilibrium surface tension on curvature. Received January 19, 1998     

A one-dimensional theory for viscoelastic fluid jets,with application to extrudate swell and draw-down under gravity

A model is derived for a viscoelastic fluid jet based on a one-dimensional directed curve idealization. It incorporates the general influences on the free surface geometry of surface tension, inertia viscosity, elasticity and gravity. The model is applied to the special case of an axisymmetric torsionless jet, and the observed fluid jet phenomena of extrudate swell and draw-down under gravity are described. In particular: (a) When gravity is neglected in the model, the jet outer radius asymptotically approaches a final value which depends on the radius and velocity of the jet at the nozzle, the stress state in the fluid at the nozzle, certain material constants characterizing the fluid, and surface tension; (b) When gravity is included, the jet swells to a maximum radius, then necks down to zero radius at infinity. Some planned future applications of the model and these special solutions are indicated.     

Precise viscosity measurements of Newtonian liquids withv < 1 mm2/s for the selection of suitable standards

The application of long capillary Ubbelohde viscometers in the determination of low viscosities is described. Corrections and measurement uncertainties are discussed. Viscosity and density data are given for 18 Newtonian liquids of commercially available purity, with viscosities below about 1 mm²/s. For several liquids the commonly used purity specifications were found to be sufficient to qualify these liquids as viscosity standards, which can be used for viscometer calibration.     

Molecular-dynamical study of surface tension in nanostructures

In the present paper, we perform a molecular-dynamical study of the surface tension in nanodimensional structures. In this case, we find three types of surface characteristics corresponding to different mechanisms of the surface reaction to the external actions:

Kinetic description of Brownian movement of heated particles in rarefied gas

Translational and rotational Brownian movement of a spherical particle in a rarefied gas is considered. It is assumed that the particle radius is much less than the free path of the molecules in the gas. The collision integral of the considered particles and the gas molecules is generalized to the case of an arbitrary law of interaction between the molecules and the particle surface, this making it possible to consider the situation when there is no thermodynamic equilibrium between the particles and the gas, in particular, the particle temperature differs from the gas temperature. By expansion with respect to the small parameter — the ratio of the molecule and particle masses — the kinetic equation of the Boltzmann type reduces to the Fokker-Planck equation for the particle distribution function. The coefficients of the equation are calculated in an explicit form for the case of diffuse interaction between the molecules and the particle surface. A dependence of the diffusion coefficients on the ratio of the particle and gas temperatures is obtained.     

A crack along the interface of a circular inclusion embedded in an infinite solid

The two-dimensional problem of an arc shaped crack lying along the interface of a circular elastic inclusion embedded in an infinite matrix with different elastic constants is considered. Based on the complex variable method of Muskhelishvili, closed-form solutions for the stresses and the displacements around the crack are obtained when general biaxial loads are applied at infinity. These solutions are then combined with A.A. Griffith's virtual work argument to give a criterion of crack extension, namely the de-bonding of the interface. The critical applied loads are expressed explicitly in terms of a function of the inclusion radius and the central angle subtended by the crack arc. In the case of simple tension the critical load is inversely proportional to the square-root of the inclusion radius. By analyzing the variation of the cleavage stress near the crack tip, the deviation of the crack into the matrix is discussed. The case of uniaxial tension is worked out in detail.     

A novel numerical scheme for the investigation of surface tension effects on growth and collapse stages of cavitation bubbles

In the present study the effects of surface tension on the growth and collapse stages of cavitation bubbles are studied individually for both spherical and nonspherical bubbles. The Gilmore equation is used to simulate the spherical bubble dynamics by considering mass diffusion and heat transfer. For the collapse stage near a rigid boundary, the Navier–Stokes and energy equations are used to simulate the flow domain, and the VOF method is adopted to track the interface between the gas and the liquid phases. Simulations are divided into two cases. In the first case, the collapse stage alone is considered in both spherical and nonspherical situations with different conditions of bubble radius and surface tension. According to the results, surface tension has no significant effects on the flow pattern and collapse rate. In the second case, both the growth and collapse stages of bubbles with different initial radii and surface tensions are considered. In this case surface tension affects the growth stage considerably and, as a result, the jet velocity and collapse time decrease with increasing surface tension coefficient. This effect is more significant for bubbles with smaller radii.     

Effect of the mass-transfer intensity on the dynamic relations on a phase interface

The dynamic relations on the phase interface are derived in the isothermal approximation for liquids in which the dependence of the surface energy on the mass flux across the phase interface must be taken into account. The criterion of stability of subsonic phase-transition fronts with plane waves with respect to small perturbations is determined. The dependence of the surface tension on the mass flux is calculated for the well-known exact solution to the problem of the structure of isothermal phase transition within the framework of the generalized van der Waals model.     

Structure and stability of the interface in a magnetizable fluid

The problems of interface stability in magnetizable and polarizable fluids are considered in the case of the surface tension tensor dependent on the electromagnetic field strength. For describing this dependence the model proposed by A.N. Golubyatnikov (1986) is used. The investigation of the internal interface structure showed that for single-component systems, as a rule, the dependence of the surface tension on the field strength corresponds to surface phase properties paramagnetic in the normal and diamagnetic in the tangential direction. It is shown that within the framework of the model adopted the thermodynamic stability of the surface depends on the thickness of the interphase layer. Necessary stability conditions are obtained for plane interfaces in media with a constant magnetic permeability outside the interphase layer. The problem of stability of the horizontal free surface of an ideal magnetic field in an external magnetic field (similar to the problem of stability of the horizontal interface of two polarizable fluids in an external electric field) is solved for an arbitrary orientation of the external field relative to the interface. The stability loss is now accompanied by qualitative effects absent in the case of the surface tension tensor independent of the electromagnetic field strength.     

Structure and stability of the interface between magnetic and conventional fluids. Model of a three-component medium

The structure of a flat interphase boundary between a magnetic suspension and a conventional immiscible fluid is investigated within the framework of the model of a three-component medium taking the dependence of the free energy of the system on the concentration gradients into account. It is shown that for certain values of the constitutive parameters the bulk magnetic particle concentration increases significantly inside the interfacial layer, i.e., the particles are significantly adsorbed on the interface. The dependence of the surface tension on the magnetic field strength is determined. It is shown that for certain problem parameters this dependence qualitatively corresponds to that obtained experimentally and described in the phenomenological theory developed by Golubyatnikov and Subkhankulov in 1986. In the case of strong particle adsorption the dependence of the surface tension on the magnetic particle concentration on the phase interface is significantly nonlinear. A refined model of the interface as a two-dimensional continuum with surface magnetization is constructed. Constitutive equations, conditions on the interface, and necessary stability conditions are obtained.     

Statics of a magnetic fluid containing magnetic field concentrators

Various static surface shapes of a magnetic fluid containing bodies made of easily magnetizable materials (magnetic field concentrators) in a uniform applied magnetic field are numerically calculated with account for the gravity force, surface tension, and the dependence of the magnetic-fluid magnetization on the magnetic field strength. The possibility of a sudden change in surface shape is shown. Hysteresis in the surface shape with a cyclic increase and decrease in the applied field is predicted.     

Simulations of free surface flows with implementation of surface tension and interface sharpening in the two-fluid model

Two-fluid model used for free surface flows with large characteristic scales is improved; the smeared interface is sharpened with conservative level set method and the surface tension force with wetting angle is implemented. Surface tension force is split between two phases with several models. Detailed analysis showed the splitting of surface tension force with volume averaging as the most appropriate. The improved two-fluid model with interface sharpening and implemented surface tension is validated on several test cases. The pressure jump over a droplet interface test case showed that the pressure jump in simulation converges with grid refinement to the analytical one. The parasitic currents in simulation are one order of magnitude larger than in simulation with volume of fluid model. In the oscillating droplet test case the time period of oscillating droplet with initially ellipsoid or square shape is similar to the analytical time period. In the rising bubble test case, the rising bubble position, terminal velocity, and circularity are similar to the one observed in simulations with level set model. The wetting angle is implemented in the two-fluid model with interface sharpening and surface tension force. Model is tested in the simulation of droplet in contact with wall with different wetting angles.     

Rheology of polymer blends: linear model for viscoelastic emulsions

 Kerner's model for flow of composite elastic media is extended to an emulsion of viscoelastic phases with interfacial tension undergoing deformations of small amplitude. A privileged internal structure inside the suspended drops is discussed in terms of fluid circulation across the interface. It is shown that for usual drop radius and interfacial tension values of emulsions, the rheological behavior predicted by the model, with very simple expression for the complex shear modulus, is quantitatively similar to that predicted by Palierne's model. Predictions of the model are compared with experimental data obtained on a polystyrene/polyethylene blend sheared in a small-amplitude oscillatory mode. Received: 10 August 1998 Accepted: 18 December 1998     

Strength analysis of an elastic plane containing a square lattice of circular holes under mechanical loading

The strength characteristics of an elastic plane weakened by a square lattice of circular holes are considered. The stress concentrations in three distinct lattices under the conditions of uniaxial tension/compression in various directions are studied. The minimum and maximum values of the stress concentrations are calculated, and the stress fields in various lattices are considered. We show that under the compression conditions fracture can occur inside the material rather than on the hole boundaries. It is demonstrated that in dense lattices the stress concentrations exhibit power-law dependence on the structure parameter equal to the ratio of the length of the interval between the holes to the hole radius.     

拉扭耦合作用下柱形纤维与基底的界面黏附性能研究

受壁虎刚毛可逆黏附性能的启发,本文建立了单根弹性圆柱纤维与刚性基底黏附接触的理论和数值模型,同时考虑了拉伸和扭转载荷的耦合作用及纤维半径对界面黏附性能的影响.研究发现耦合载荷作用下柱形纤维同样存在一个临界半径,当纤维半径小于该临界尺寸时,界面应力达到均匀的理论强度分布,接触边界应力集中消失,出现缺陷不敏感现象;当纤维半径大于该临界尺寸时,界面以裂纹扩展而失效.在耦合载荷作用下纤维的临界半径小于纯拉伸而大于纯扭转时的临界尺寸,且该临界半径随着施加扭转载荷的增大而减小.表明在纯拉伸载荷下使界面黏附强度达到最优的柱形纤维,在拉伸和扭转载荷耦合作用下,由于界面失效形式的转变使界面易发生脱黏,并且界面脱黏时的拉脱力随着扭转载荷的增大而减小,理论和数值结果一致.本文结果进一步应用揭示了壁虎可以通过调控施加在其最小黏附单元上的载荷形式实现纯拉伸载荷下强黏附及耦合载荷下易脱黏的力学机制.     

Energy release or absorption due to simultaneous rotation of two nano voids in plane elastic materials as influenced by both surface effect and interacting effect

In this paper, the L-integral analysis for two nano-sized voids in plane elasticity under uniaxial loading is present. Three surface parameters are considered including the surface tension and two surface Lamé constants. Attention is focused on the mutual influence on the L-integral from both the surface effect at voids’ rims and the interacting effect between voids. A close-form expression of L-integral for multiple nano voids is obtained. Comparing with those in macro fracture mechanics, the L-integral shows some different features when the surface effect is taken into account. It is concluded that under tensile loading and due to the mutual influence, the L-integral might be either positive or negative, depending on the loading level. The numerical results show that the surface tension is the dominant one in surface parameters on impacting the L-integral. It is also concluded that the surface effect shields the energy release (positive L-integral value) while enhances the energy absorption (negative L-integral value). The two-state L-integral analysis is performed to clarify the way that the surface effect impacts the L-integral. It is concluded that the contribution to L-integral from the voids’ configuration could either be negative or positive, while that from the surface effect is always negative. Besides, the size dependence in the present problem is studied in detail.     

Shape of the free surface of a magnetic fluid containing a cylindrical concentrator of the magnetic field

The shape of the surface of a magnetic fluid containing a cylindrical body made of a well-magnetizable material (magnetic field concentrator) in a uniform applied magnetic field is studied experimentally and theoretically. Various static shapes of the surface are calculated numerically taking into account the gravity forces, the surface tension, and the dependence of the magnetic fluid magnetization on the magnetic field strength. It is found that there exists several equilibrium shapes of the magnetic fluid surface. Abrupt changes in the magnetic fluid surface and its hysteresis are predicted theoretically and observed experimentally. The theoretical and experimental results are compared.     

Displacement of a viscous fluid from an annular Hele–Shaw cell with a sink within the framework of the Brinkman model

The stability of the radial front of viscous fluid displacement from an annular Hele–Shaw cell with a sink of finite radius is analyzed. It is shown that in the absence of the surface tension and at a minimal manifestation of molecular diffusion the role of the stabilizing factor determining the displacement front structure can be played by small viscous forces in the cell plane. The viscous fingers formed in this case turn out to be wider than those in a rectangular cell.     

Dynamic detachment of a gas bubble from a solid flat substrate performing normal harmonic vibrations

This paper presents an investigation of the detachment of a bubble from a solid flat substrate according to a dynamic scenario, i. e., due to strong vibrations of the surface shape of the bubble caused by normal nonacoustic harmonic vibrations of the substrate. The Layzer’s model based on an analysis of single-mode solutions near the bubble top was used to study its detachment in microgravity, where the dynamics of the bubble surface is due to competition between liquid inertia forces and surface tension forces. Detachment of the bubble from the substrate was determined from the condition of its elongation during vibrations by a magnitude comparable to the radius of the bubble in equilibrium. The dependence of the vibration intensity required for the detachment of the bubble on the problem parameters was determined using a number of empirical assumptions. The volume of the detached bubbles was estimated.     

Time periodic viscosity of concentrated kaolin suspensions at constant shear rates

Knowledge of the viscosity of concentrated suspensions is required for several technical applications, e.g. process control in mechanical engineering, casting of ceramics and pipeline transport of solids. Our previous viscometric investigations of concentrated suspensions showed, under particular shear conditions, an apparent viscosity that was periodic in time for a constant shear rate and temperature. These results were obtained with rotational viscometers with a set coaxial geometry. The inner cylinder was rigidly coupled to the viscometer driving axis. In this paper we describe a viscosity time behavior which was found using another type of coupling. Measurements were performed with rotational viscometers with a non-rigidly linked inner cylinder (small sample adapter supplied by Brookfield). Using kaolin suspensions of 30% solid mass content, viscosity oscillations appear. They show a regular time pattern at certain intervals of low shear rates. The amplitudes reach up to 20% of the viscosity mean value. In addition a motion of the inner cylinder away from the coaxial position is observed. This dislocation is followed by a relocation into the coaxial position. A maximum in the viscosity value is correlated with a maximum of the dislocation position. The process of dislocation and relocation of the inner cylinder is assumed to be caused by local anisotropically distributed inhomogeneities, which originate from shear-induced agglomeration and deglomeration of suspended particles. The motion of the inner cylinder is described by introducing a perturbation term into the equation of motion. The parameters of the perturbation term are fitted to the experimental data. Received: 10 September 1998 Accepted: 28 April 1999