79 resultados para Equilibrium Surface Tension


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Nucleation at large metastability is still largely an unsolved problem, even though it is a problem of tremendous current interest, with wide-ranging practical value, from atmospheric research to materials science. It is now well accepted that the classical nucleation theory (CNT) fails to provide a qualitative picture and gives incorrect quantitative values for such quantities as activation-free energy barrier and supersaturation dependence of nucleation rate, especially at large metastability. In this paper, we present an alternative formalism to treat nucleation at large supersaturation by introducing an extended set of order parameters in terms of the kth largest liquid-like clusters, where k = 1 is the largest cluster in the system, k = 2 is the second largest cluster and so on. At low supersaturation, the size of the largest liquid-like cluster acts as a suitable order parameter. At large supersaturation, the free energy barrier for the largest liquid-like cluster disappears. We identify this supersaturation as the one at the onset of kinetic spinodal. The kinetic spinodal is system-size-dependent. Beyond kinetic spinodal many clusters grow simultaneously and competitively and hence the nucleation and growth become collective. In order to describe collective growth, we need to consider the full set of order parameters. We derive an analytic expression for the free energy of formation of the kth largest cluster. The expression predicts that, at large metastability (beyond kinetic spinodal), the barrier of growth for several largest liquid-like clusters disappears, and all these clusters grow simultaneously. The approach to the critical size occurs by barrierless diffusion in the cluster size space. The expression for the rate of barrier crossing predicts weaker supersaturation dependence than what is predicted by CNT at large metastability. Such a crossover behavior has indeed been observed in recent experiments (but eluded an explanation till now). In order to understand the large numerical discrepancy between simulation predictions and experimental results, we carried out a study of the dependence on the range of intermolecular interactions of both the surface tension of an equilibrium planar gas-liquid interface and the free energy barrier of nucleation. Both are found to depend significantly on the range of interaction for the Lennard-Jones potential, both in two and three dimensions. The value of surface tension and also the free energy difference between the gas and the liquid phase increase significantly and converge only when the range of interaction is extended beyond 6-7 molecular diameters. We find, with the full range of interaction potential, that the surface tension shows only a weak dependence on supersaturation, so the reason for the breakdown of CNT (with simulated values of surface tension and free energy gap) cannot be attributed to the supersaturation dependence of surface tension. This remains an unsettled issue at present because of the use of the value of surface tension obtained at coexistence.

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A heterotroph Paenibacillus polymyxa bacteria is adapted to pyrite, chalcopyrite, galena and sphalerite minerals by repeated subculturing the bacteria in the presence of the mineral until their growth characteristics became similar to the growth in the absence of mineral. The unadapted and adapted bacterial surface have been chemically characterised by zeta-potential, contact angle, adherence to hydrocarbons and FT-IR spectroscopic studies. The surface free energies of bacteria have been calculated by following the equation of state and surface tension component approaches. The aim of the present paper is to understand the changes in surface chemical properties of bacteria during adaptation to sulfide minerals and the projected consequences in bioflotation and bioflocculation processes. The mineral-adapted cells became more hydrophilic as compared to unadapted cells. There are no significant changes in the surface charge of bacteria before and after adaptation, and all the bacteria exhibit an iso-electric point below pH 2.5. The contact angles are observed to be more reliable for hydrophobicity assessment than the adherence to hydrocarbons. The Lifschitz–van der Waals/acid–base approach to calculate surface free energy is found to be relevant for mineral–bacteria interactions. The diffuse reflectance FT-IR absorbance bands for all the bacteria are the same illustrating similar surface chemical composition. However, the intensity of the bands for unadapted and adapted cells is significantly varied and this is due to different amounts of bacterial secretions underlying different growth conditions.

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Experiments involving heating of liquid droplets which are acoustically levitated, reveal specific modes of oscillations. For a given radiation flux, certain fluid droplets undergo distortion leading to catastrophic bag type breakup. The voltage of the acoustic levitator has been kept constant to operate at a nominal acoustic pressure intensity, throughout the experiments. Thus the droplet shape instabilities are primarily a consequence of droplet heating through vapor pressure, surface tension and viscosity. A novel approach is used by employing Legendre polynomials for the mode shape approximation to describe the thermally induced instabilities. The two dominant Legendre modes essentially reflect (a) the droplet size reduction due to evaporation, and (b) the deformation around the equilibrium shape. Dissipation and inter-coupling of modal energy lead to stable droplet shape while accumulation of the same ultimately results in droplet breakup. (C) 2013 Elsevier B.V. All rights reserved.

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In Incompressible Smooth Particle Hydrodynamics (ISPH), a pressure Poisson equation (PPE) is solved to obtain a divergence free velocity field. When free surfaces are simulated using this method a Dirichlet boundary condition for pressure at the free surface has to be applied. In existing ISPH methods this is achieved by identifying free surface particles using heuristically chosen threshold of a parameter such as kernel sum, density or divergence of the position, and explicitly setting their pressure values. This often leads to clumping of particles near the free surface and spraying off of surface particles during splashes. Moreover, surface pressure gradients in flows where surface tension is important are not captured well using this approach. We propose a more accurate semi-analytical approach to impose Dirichlet boundary conditions on the free surface. We show the efficacy of the proposed algorithm by using test cases of elongation of a droplet and dam break. We perform two dimensional simulations of water entry and validate the proposed algorithm with experimental results. Further, a three dimensional simulation of droplet splash is shown to compare well with the Volume-of-Fluid simulations. (C) 2014 Elsevier Ltd. All rights reserved.

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An arbitrary Lagrangian-Eulerian (ALE) finite element scheme for computations of soluble surfactant droplet impingement on a horizontal surface is presented. The numerical scheme solves the time-dependent Navier-Stokes equations for the fluid flow, scalar convection-diffusion equation for the surfactant transport in the bulk phase, and simultaneously, surface evolution equations for the surfactants on the free surface and on the liquid-solid interface. The effects of surfactants on the flow dynamics are included into the model through the surface tension and surfactant-dependent dynamic contact angle. In particular, the dynamic contact angle (theta(d)) of the droplet is defined as a function of the surfactant concentration at the contact line and the equilibrium contact angle (theta(0)(e)) of the clean surface using the nonlinear equation of state for surface tension. Further, the surface forces are included into the model as surface divergence of the surface stress tensor that allows to incorporate the Marangoni effects without calculating the surface gradient of the surfactant concentration on the free surface. In addition to a mesh convergence study and validation of the numerical results with experiments, the effects of adsorption and desorption surfactant coefficients on the flow dynamics in wetting, partially wetting and non-wetting droplets are studied in detail. It is observed that the effects of surfactants are more in wetting droplets than in the non-wetting droplets. Further, the presence of surfactants at the contact line reduces the equilibrium contact angle further when theta(0)(e) is less than 90 degrees, and increases it further when theta(0)(e) is greater than 90 degrees. Nevertheless, the presence of surfactants has no effect on the contact angle when theta(0)(e) = 90 degrees. The numerical study clearly demonstrates that the surfactant-dependent contact angle has to be considered, in addition to the Marangoni effect, in order to study the flow dynamics and the equilibrium states of surfactant droplet impingement accurately. The proposed numerical scheme guarantees the conservation of fluid mass and of the surfactant mass accurately. (C) 2015 Elsevier Inc. All rights reserved.

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The relationship between the parameters in a description based on a mesoscale free energy functional for the concentration field and the macroscopic properties, such as the bending and compression moduli and the permeation constant, are examined for an asymmetric lamellar phase where the mass fractions of the hydrophobic and hydrophilic parts are not equal. The difference in the mass fractions is incorporated using a cubic term in the free energy functional, in addition to the usual quadratic and quartic terms in the Landau–Ginsburg formulation. The relationship between the coefficient of the cubic term and the difference in the mass fractions of the hydrophilic and hydrophobic parts is obtained. For a lamellar phase, it is important to ensure that the surface tension is zero due to symmetry considerations. The relationship between the parameters in the free energy functional for zero surface tension is derived. When the interface between the hydrophilic and hydrophobic parts is diffuse, it is found that the bending and compression moduli, scaled by the parameters in the free energy functional, do increase as the asymmetry in the bilayer increases. When the interface between the hydrophilic and hydrophobic parts is sharp, the scaled bending and compression moduli show no dependence on the asymmetry in the bilayer. The ratio of the permeation constant in between the water and bilayer in a molecular description and the Onsager coefficient in the mesoscale description is O(1) for both sharp and diffuse interfaces and it increases as the difference in the mass fractions is increased.

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The surface tension gradient driven flow that occurs during laser melting has been studied. The vorticity-streamfunction form of the Navier-Stokes equations and the energy equation has been solved by the ‘Alternative Direction Implicit’ method. It has been shown that the inertia forces in the melt strongly influence the flow pattern in the melt. The convection in the melt modifies the isotherms in the melt at high surface tension Reynolds number and high Prandtl number. The buoyancy driven flow has been shown to be negligible compared to the surface tension gradient driven flow in laser melting.

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Bubble formation under constant pressure conditions has been investigated for wide range of variation of liquid properties.Air bubbles were formed from single horizontal orifices submerged in liquids whose viscosity varied from 1·0 to 600 cPs and surface tension from 37 to 72 dyn/cm. Air flow rate was varied from 2 to 250 cm3/sec and the orifice diameter from 0·0515 to 0·4050 cm.

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The stability of an incompressible inviscid, perfectly conducting cylindrical plasma against azimuthal disturbances in the presence of a monotonic decreasing magnetic field having a constant pitch is discussed by using energy principle. The results obtained by this principle are compared for m = 1 mode (which is a dangerous mode in which there is a lateral shift of the entire column) with that obtained by normal mode analysis. It is found that m = 1 mode is always unstable. Further, an axial line current, external axial field and the surface tension tend to stabilise m ≠ modes.

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Bubble formation from porous discs submerged in liquids of different physical properties has been investigated. It is found the number of sites effective for bubble formation is much smaller than the total potentially available sites. The number of effective sites is found to be a function of the surface tension, viscosity, and density of the liquid and the gas flow rate through the disc. A model proposed on the basis of bubble formation from an isolated nozzle and the close packed arrangement of the formed bubbles, explains the phenomenon adequately. © 1970.

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A study of atomization has been made with an external mixing-type pneumatic atomizer. The drops were sampled on Vaseline-coated cells using a shutter arrangement and their sizes were measured under a microscope. The effects of liquid viscosity, liquid surface tension, liquid flow rate, air velocity, and nozzle angle on drop size have been studied. A model, which explains adequately the influence of various factors, has been proposed. This model predicts the values of average drop sizes over a wide range of operating conditions. The model also explains the data of other investigators who have used other kinds of pneumatic atomizers.

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A complete analytical solution is obtained, by using an integral transform method, for the porous-wavemaker problem, when the effect of surface tension is taken into account on the free surface of water of finite-depth in which surface waves are produced by small horizontal oscillations of a porous vertical plate. The final results are expressed in the form of convergent integrals as well as series and known results are reproduced when surface tension is neglected.

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An analysis involving a transformation of the velocity potential and a Fourier Sine Transform technique is described to study the effect of surface tension on incoming surface waves against a vertical cliff with a periodic wall perturbation. Known results are recovered as particular cases of the general problem considered. An analytical expression is derived for the surface elevation, at far distances from the shore-line, by using Watson's lemma and a representative table of numerical values of the coefficients of the resulting asymptotic expansion is also presented.

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Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

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Hypo-eutectic Ti-6.5 wt % Si alloy modified by separate additions of misch metal and low surface tension elements (Na, Sr, Se and Bi) has been examined by microscopic study and thermal analysis. Addition of third element led to modification of microstructure with apparently no significant enhancement of tensile ductility, with the exception of bismuth. Bismuth enhanced the ductility of the alloy by a factor of two and elastic-plastic fracture toughness to 9 MPa m–1/2 from a value of almost zero. The improved ductility of bismuth modified alloy is attributed to the reduced interconnectivity of the eutectic suicide, absence of significant suicide precipitation in the eutectic region and increase in the volume fraction of uniformly distributed dendrites. These changes are accompanied by a decrease in the temperature of eutectic solidification.