scholarly journals Contact Angle for Spherical Nanodroplet in Cylindrical Cavity with Quadratic Curve Generatrix

2016 ◽  
Vol 6 (1) ◽  
pp. 96
Author(s):  
Ai-Jun Hu ◽  
Bao-Zhan Lv
Keyword(s):  
Contact Angle ◽  
Line Tension ◽  
Equilibrium Contact Angle ◽  
Cylinder Surface ◽  
Quadratic Curve ◽  
Dividing Surface ◽  
Solid Liquid ◽  
Young Equation ◽  
Homogeneous Cylinder ◽  
Young's Equation

<p class="1Body">Wetting of a spherical nanodroplet in smooth and homogeneous cylinder surface rotated by quadratic curve was studied by methods of thermodynamics. The solid-liquid-vapor system was separated into six parts using Gibbs method of dividing surface. The system free energy was calculated. A generalized Young equation for the equilibrium contact angle is proposed taking the line tension effects into consideration. On the basis of some assumptions, this generalized Young equation is the same as the classical Young’s equation.</p>

The contact angle for a droplet on homogeneous and spherical concave surfaces

2016 ◽  
Vol 30 (07) ◽  
pp. 1650078
Author(s):  
Ai-Jun Hu ◽  
Bao-Zhan Lv ◽  
Xiao-Song Wang ◽  
Long Zhou
Keyword(s):  
Contact Angle ◽  
Chemical Potential ◽  
Rough Surfaces ◽  
Line Tension ◽  
Equilibrium Contact Angle ◽  
Precursor Film ◽  
Phase System ◽  
Spherical Droplet ◽  
Dividing Surface ◽  
Young's Equation

Wetting of droplets on homogeneous and spherical concave rough surfaces is investigated based on thermodynamics. In this study, neglecting the droplet gravity and the thickness of the precursor film of the liquid–vapor interface, the three-phase system is divided into six parts using Gibbs concept of dividing surface. The system Helmholtz free energy is established based on thermodynamics. Supposing the temperature and chemical potential to be constant, a new generalized Young’s equation of the equilibrium contact angle for a spherical droplet on a spherical concave rough surfaces is obtained including the line tension effects. Under certain conditions, this generalized Young’s equation is the same as the Rusanov’s equation.

Generalized Young Equation for Cylindrical Droplets within a Homogeneous and Smooth Regular Triangular Prism Filled with Gas in Three Convex Corners

2016 ◽  
Vol 6 (1) ◽  
pp. 14
Author(s):  
Long Zhou ◽  
Guang-Hua Sun ◽  
Ai-Jun Hu ◽  
Xiao-Song Wang
Keyword(s):  
Line Tension ◽  
Phase System ◽  
Triangular Prism ◽  
Gas Phases ◽  
Three Phase ◽  
Dividing Surface ◽  
Solid Liquid ◽  
Wetting Behaviors ◽  
Young Equation ◽  
Dividing Line

<p class="1Body">Based on the approaches of Gibbs’s dividing surface and Rusanov’s dividing line, the wetting behaviors of cylindrical droplets that at equilibrium are sitting inside a homogeneous and smooth regular triangular prism filled with gas in three convex corners are studied. For the three-phase system, which is composed of solid, liquid and gas phases, a generalized Young equation for cylindrical drops in a homogeneous and smooth regular triangular prism imbued with gas within three apex corners has been successfully derived including the effects of the line tension.</p>

Line Tension-Based Modification of Young's Equation for Rock-Oil-Brine Systems

2009 ◽  
Vol 12 (05) ◽  
pp. 702-712 ◽  
Author(s):  
Dayanand Saini ◽  
Dandina N. Rao
Keyword(s):  
Contact Angle ◽  
Oil Recovery ◽  
Adhesion Force ◽  
Line Tension ◽  
Intermolecular Forces ◽  
Petroleum Engineering ◽  
L Systems ◽  
Solid Liquid ◽  
Young's Equation ◽  
Liquid Vapor

Summary The two-century-old Young's equation has been widely used in petroleum engineering to depict the reservoir wettability in terms of contact angle, which is a function of surface free energies of the system. For solid/liquid/vapor (S/L/V) systems, Young's equation has been modified in the recent literature to include a line-tension term. This modification was sought to accommodate the imbalance of intermolecular forces experienced by the three-phase confluence zone. Also, Young's equation does not account for the vertical component of liquid/vapor surface tension. The present study aims to experimentally investigate the applicability of the line-tension-based modification of Young's equation to solid/liquid/liquid (rock/oil/brine) (S/L/L) systems of interest to the petroleum industry. Both the ambient- and reservoir-condition optical cells were used, with stock-tank and live oil, respectively, to determine the drop-size dependence of dynamic contact angle subtended by the oil/brine interface with the rock surface. The experimental data were correlated with the modified Young's equation to determine the magnitude of line tension for different rock/oil/brine systems. To the best of our knowledge, this is the first attempt to apply the modified Young's equation to rock/oil/brine systems and to measure line tension for a rock/live-crude-oil/brine system at reservoir conditions of pressure and temperature. The measured line tension for S/L/L systems, while being positive and of the same order of magnitude as in S/L/V systems, correlates well with the water-advancing contact angle and the adhesion number, a ratio of adhesion force to capillary force. This experimental study indicates that the extent of deviation from Young's equation exhibited by rock/oil/brine systems may be directly related to the rock/oil adhesion interaction. This study reinforces the need to include the rock/oil adhesion force in our consideration of rock/fluid interactions, wettability, and their impact on enhanced-oil-recovery (EOR)/improved-oil-recovery (IOR) processes.

Dependence of the Contact Angle on Adsorption at the Solid-Liquid Interface

2010 ◽  
Author(s):  
C. A. Ward
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Pressure Range ◽  
Line Tension ◽  
Liquid Interface ◽  
Fluid Interfaces ◽  
Phase Line ◽  
Three Phase ◽  
Solid Liquid Interface ◽  
Solid Liquid

A method for determining the surface tension of solid-fluid interfaces has been proposed. For a given temperature and fluid-solid combination, these surface tensions are expressed in terms of material properties that can be determined by measuring the amount of vapor adsorbed on the solid surface as a function of xV, the ratio of the vapor-phase pressure to the saturation-vapor pressure. The thermodynamic concept of pressure is shown to be in conflict with that of continuum mechanics, but is supported experimentally. This approach leads to the prediction that the contact angle, θ, can only exist in a narrow pressure range and that in this pressure range, the solid-vapor surface tension is constant and equal to the surface tension of the liquid-vapor interface, γLV. The surface tension of the solid-liquid interface, γSL, may be expressed in terms of measurable properties, γLV and θ: γSL = γLV(1 − cosθ). The value of θ is predicted to depend on both the pressure in the liquid at the three-phase, line x3L, and the three-phase line curvature, Ccl. We examine these predictions using sessile water droplets on a polished Cu surface, maintained in a closed, constant volume, isothermal container. The value of θ is found to depend on the adsorption at the solid-liquid interface, nSL = nSL(x3L,Ccl). The predicted value of θ is compared with that measured, and found to be in close agreement, but no effect of line tension is found.

THE MODIFIED YOUNG'S EQUATION FOR THE CONTACT ANGLE OF A SMALL SESSILE DROP FROM AN INTERFACE DISPLACEMENT MODEL

1999 ◽  
Vol 13 (27) ◽  
pp. 3255-3259 ◽  
Author(s):  
HARVEY DOBBS
Keyword(s):  
Contact Angle ◽  
Sessile Drop ◽  
Unit Length ◽  
Excess Free Energy ◽  
Line Tension ◽  
Rigid Substrate ◽  
Three Phase ◽  
Interface Displacement ◽  
Displacement Model ◽  
Young's Equation

We derive the modified Young's equation for the contact angle of a fluid droplet on a rigid substrate using an interface displacement model and identify the line tension with the excess free energy per unit length calculated previously for a straight three-phase contact line.

scholarly journals MODELLING AND INVESTIGATION OF THE DEPENDENCE OF SUPERHYDROPHOBIC PROPERTIES OF NANOSURFACES ON THE TOPOLOGY OF MICROCHANNELS

2019 ◽  
Vol 3 ◽  
pp. 52
Author(s):  
Sharif E. Guseynov ◽  
Jekaterina V. Aleksejeva
Keyword(s):  
Contact Angle ◽  
Interphase Boundary ◽  
Slip Length ◽  
Superhydrophobic Surfaces ◽  
Equilibrium Contact Angle ◽  
Three Phase ◽  
Quantitative Understanding ◽  
Air Cushion ◽  
Local Slip ◽  
Solid Liquid

In the Cassie-Baxter state anisotropic superhydrophobic surfaces have high lubricating properties. Such superhydrophobic surfaces are used in medical implants, aircraft industry, vortex bioreactors etc. In spite of the fact that quantitative understanding of fluid dynamics on anisotropic superhydrophobic surfaces has been broadened substantially for last several years, there still are some unsolved problems in this field. This work investigates dynamics of a liquid on unidirectional superhydrophobic surfaces in the Cassie-Baxter state, when surface texture is filled with gas and, consequently, the liquid virtually is located on some kind of an air cushion. Energy of the interphase boundary liquid-gas is much smaller than energy of the interphase boundary solid-liquid, that is why the contact angle at wetting such surfaces differs a lot from the Young contact angle and depends on contact area ratio of liquid-gas and liquid-solid in visible contact of liquid and surface. Considering difference in energy obtained if we slightly shift the three-phase contact line, expression for macroscopic equilibrium contact angle, which describes the Cassie-Baxter state, can be deduced. In the work the design formula for computing local-slip length profiles of liquid on the considered superhydrophobic surfaces is obtained.

scholarly journals Elastic Properties of Liquid Surfaces Coated with Colloidal Particles

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Edward Bormashenko ◽  
Gene Whyman ◽  
Oleg Gendelman
Keyword(s):  
Contact Angle ◽  
Interfacial Tension ◽  
Surface Density ◽  
Colloidal Particles ◽  
Physical Mechanism ◽  
Young Modulus ◽  
Line Tension ◽  
Equilibrium Contact Angle ◽  
Interfacial Effect ◽  
Liquid Surfaces

The physical mechanism of elasticity of liquid surfaces coated with colloidal particles is proposed. It is suggested that particles are separated by water clearings and the capillary interaction between them is negligible. The case is treated when the colloidal layer is deformed normally to its surface. The elasticity arises as an interfacial effect. The effective Young modulus of a surface depends on the interfacial tension, equilibrium contact angle, radius of colloidal particles, and their surface density. For the nanometrically scaled particles the line tension becomes essential and has an influence on the effective Young modulus.

A direct measurement of the influence of vapour, of liquid and of oriented monolayers on the interfacial energy of mica

1967 ◽  
Vol 301 (1464) ◽  
pp. 47-56 ◽  
Keyword(s):  
Contact Angle ◽  
Marked Reduction ◽  
Polar Medium ◽  
Monomolecular Layer ◽  
Interfacial Energies ◽  
A Value ◽  
Cleavage Energy ◽  
Solid Liquid ◽  
Work Done ◽  
Young's Equation

A cleavage technique has been used to measure solid/fluid interfacial energies, and to study directly the effect of various media on these energies. Solid/vapour and solid/liquid interfacial energies were measured by cleaving mica specimens first in an atmosphere of vapour and then in the corresponding liquid. In this way we have a direct means of checking the validity of Young’s equation. Results obtained with water, as representative of a polar medium, and hexane, as representative of a non-polar medium show that Young’s equation holds for systems with zero contact angle. The effect of the humidity of the surrounding atmosphere on the cleavage of mica was also investigated. Water vapour was found to produce a marked reduction in the cleavage energy. In another set of experiments the cleavage technique was used to determine the work done in separating mica surfaces covered with an adsorbed monomolecular layer of fatty acid. The results yield a value of 37 erg/cm 2 for the surface energy of a lauric acid monolayer on mica.

Sessile-Water-Droplet Contact Angle: the Effect of Adsorption

2010 ◽  
Author(s):  
H. Ghasemi ◽  
C. A. Ward
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Closed System ◽  
Water Droplet ◽  
Line Tension ◽  
Water Droplets ◽  
Three Phase ◽  
To Come ◽  
Predicted Values ◽  
Solid Liquid

A method has been recently proposed for determining the surface tension of solid-vapor interfaces. The proposed method was used in conjunction with Gibbsian thermodynamics to investigate both analytically and experimentally the possible role of line tension in determining the contact angle of sessile-water-droplets. After forming a sessile-water-droplet in a closed system, its contact angle was determined by measuring the curvature of three-phase contact line and the height of the axisymmetric droplet on its centerline. The total number of the moles in the closed system was determined from the minimum in the Helmholtz function. The total number of moles in the system was then changed to a new value and the system allowed to come to equilibrium again. The contact angle in the new equilibrium condition could be measured and predicted by taking the adsorption at the solid-liquid and solid-vapor interfaces into account but with line tension completely neglected. The predicted values of contact angle are in closed agreement with those measured indicating line tension plays no role in determining the contact angle of mm-sized water droplets on a polished Cu surface. The surface tension of the solid-vapor interface was approximately constant and equal to the surface tension of adsorbing fluid; that is, the Young equation could be simplified.

Sign in / Sign up

Export Citation Format

Share Document