Bubble shapes in rotating two-phase fluid systems: a thermodynamic approach

Elliott, Janet A.W.; Ward, C. A.; Yee, D.

doi:10.1017/s0022112096007239

Cited by 7 publications

(4 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Bashforth and Adams procedure is modified to impose the necessary conditions for thermodynamic equilibrium at the droplet apex. ,− The turning angle, ϕ, the radial position on the liquidvapor interface, y (ϕ), and the height of the liquid−vapor interface above the Cu substrate, z (ϕ) − z b , are indicated in Figure . We assume the liquid phase is axisymmetric.…”

Section: System Definitionmentioning

confidence: 99%

Sessile-Water-Droplet Contact Angle Dependence on Adsorption at the Solid−Liquid Interface

Ghasemi¹,

Ward²

2010

J. Phys. Chem. C

Self Cite

View full text Add to dashboard Cite

We investigate both analytically and experimentally the possible role of line tension in determining the contact angle of sessile water droplets on a polished Cu substrate. In a closed system with constraints that make the Helmholtz function the thermodynamic potential, the curvature of the three-phase line and the height of an axisymmetric droplet on its center line could be measured. The adsorption on each of the surfaces used to construct the experimental chamber was taken into account, and the value of the total number of water moles in the system was determined from the minimum in the Helmholtz function. The number of water moles was then changed to a new value and the system allowed to come to equilibrium again. The contact angle in the second state could be both measured and predicted with the adsorption at the solid−liquid and solid−vapor interfaces fully taken into account but with line tension completely neglected. The predicted values of the contact angle compared closely with those measured, indicating line tension played no role in determining the contact angle of mm-sized water droplets on a polished Cu surface, and that the dependence of the contact angle on the curvature of the three-phase line could be predicted by including adsorption. The contact angle values ranged from 38.3 to 76.5°, indicating that the contact angle cannot be viewed as a material property of a fluid−solid combination, but must be viewed as a thermodynamic property. The surface tension of the solid−vapor interface was approximately constant and equal to the surface tension of the adsorbing fluid; thus, the Young equation could be simplified. The surface tension of the solid−liquid interface was changed by more than a factor of 3.3 in the experiments.

show abstract

Section: System Definitionmentioning

confidence: 99%

Sessile-Water-Droplet Contact Angle Dependence on Adsorption at the Solid−Liquid Interface

Ghasemi¹,

Ward²

2010

J. Phys. Chem. C

Self Cite

View full text Add to dashboard Cite

show abstract

“…If the chemical potential in phase j is denoted as µ j , the potential energy per unit mass as ξ, a second condition for equilibrium may be written 28,29 where λ is a constant. For a system exposed to a gravitational field of intensity g and to a centrifugal field corresponding to an angular speed of ω, at a height z and radial position y, ξ may be written When eq 2 is applied at a position on a liquid-vapor interface, z and y have the same values in each phase; thus If the molar specific volume of the liquid at saturation is denoted as V f , the saturation vapor pressure as P s (T), the ratio of the liquid-phase pressure to the saturation vapor pressure as x L (y, z), and the isothermal compressibility as κ T , then provided |κ T P s [x L (y, z) -1]| , 1, the chemical potential in the liquid may be expressed If the vapor phase is approximated as an ideal gas:…”

Section: Contact Angle Dependence On the Pressure At The Three-phase ...mentioning

confidence: 99%

“…Each of the cylinders is assumed to be maintained isothermal while exposed to gravitational and centrifugal fields. A modified turning-angle method 28,31,32 was used to determine the functional relation between x 3 L and θ. The turning angle, φ, is indicated in Figure 1.…”

Section: Functional Relation Between X 3 L and θmentioning

confidence: 99%

Measurement of the Adsorption at Solid−Liquid Interfaces from the Pressure Dependence of Contact Angles

Ward

Keshavarz

2007

J. Phys. Chem. B

Self Cite

View full text Add to dashboard Cite

Earlier studies have indicated that in an isothermal three-phase system, the liquid-phase pressure at the three-phase line, xL3, may be viewed as the independent variable of the contact angle, theta, and that adsorption at the solid-liquid interface is the mechanism relating them. When the liquid-vapor interface is axi-symmetric, we show that theta can be predicted as a function of xL3 and that by measuring theta(xL3), the amount adsorbed at the solid-liquid interface can be determined. We consider water in differently sized borosilicate glass cylinders. For progressively larger cylinders, xL3 increases with cylinder radius, but when a particularly sized cylinder is rotated about it longitudinal axis, xL3 is decreased. The observed value of theta in each case is found to be in close agreement with that predicted. A Gibbs model of the interphase is used, and the Gibbs adsorption at the solid-liquid interface is found to be negative. As xL3 increases above its value at wetting, the amount adsorbed at the solid-liquid interface becomes progressively more negative. Negative adsorption is shown to mean that the concentration of the fluid component is greater in the bulk liquid than in the interphase and that the difference in concentration increases as xL3 is increased. The data is used to investigate the hypothesis that the curvature of the three-phase line affects theta through line tension, but we find no relation between line tension and theta. There is an apparent relation between the curvature of the liquid-vapor interface, CLV and theta, but this is shown to be because CLV affects xL3.

show abstract

“…Thus, the total Helmholtz function for this phase must be written as an integral over the solid volume, V s . Following the treatment of systems exposed to an external field, , one finds: where f s is the Helmholtz function of the solid per unit volume and may be written where u s and s s are the internal energy and entropy of the solid, respectively, each per unit volume, T is the temperature, and φ is the potential energy of a unit volume of solid arising from the field generated by the adsorbed molecules. The potential energy is assumed to be a function of the number of adsorbed molecules, N σ , and the distance of the solid volume element from the surface, z…”

Section: System Descriptionmentioning

confidence: 99%

Chemical Potential of Adsorbed Molecules from a Quantum Statistical Formulation

Elliott

Ward

1997

Langmuir

Self Cite

View full text Add to dashboard Cite

When classical mechanics is used to treat an adsorption system involving a homogeneous surface, it is assumed that all adsorbed molecules have the same adsorption energy. In a quantum mechanical description of a homogeneous surface, the energy at an adsorption site could be any one of a discrete set of values and, at any time, a particular value would exist randomly at different adsorption sites. If the adsorbed molecules are allowed to have internal structure, to interact, and to change the substrate, then their energy spectrum becomes more complex. We report the result of approximating the adsorption of antisymmetric, diatomic molecules on a homogeneous substrate as quantum mechanical, double (two point masses) harmonic oscillators in a potential that changes with the amount of adsorption. The expression for the chemical potential is obtained from the canonical partition function and is examined by applying it to obtain the equilibrium adsorption isotherm for CO adsorbing on Ni(111). The expression for the chemical potential contains the unknown, coverage dependent, potential energy that results from both adsorbate−adsorbate and adsorbate−substrate interactions. In addition, four of the six characteristic frequencies of the harmonic oscillators are assumed not to be known. A procedure for obtaining this information from measured equilibrium isotherms allows independent sets of isotherm measurements to be quantitatively compared. Equilibrium properties, including the heat of adsorption and the adsorption-induced change in the surface tension, are predicted. As well, an approximate calculation of the minimum energy of bound molecules is made.

show abstract

Bubble shapes in rotating two-phase fluid systems: a thermodynamic approach

Cited by 7 publications

References 22 publications

Sessile-Water-Droplet Contact Angle Dependence on Adsorption at the Solid−Liquid Interface

Sessile-Water-Droplet Contact Angle Dependence on Adsorption at the Solid−Liquid Interface

Measurement of the Adsorption at Solid−Liquid Interfaces from the Pressure Dependence of Contact Angles

Chemical Potential of Adsorbed Molecules from a Quantum Statistical Formulation

Contact Info

Product

Resources

About