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

Abstract

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.

Adsorption at the solid–liquid interface as the source of contact angle dependence on the curvature of the three-phase line

“…For an isothermal system, these results are consistent with those [33]. The upper data point on each curve is for a stationary cylinder.…”

“…7. By measuring the position of the liquidvapour interface on the centreline of a cylinder, and knowing the radius of the cylinder, the Laplace equation may be written as a differential equation, and integrated iteratively to determine the contact angle and the pressure in the liquid phase at the threephase line of the cylinder [33]. When the cylinder is stationary, the potential energy, Eq.…”

“…Although the effect of n SL on the contact angle has been neglected, with few exceptions [20,22,29,31,35], a recent study found that n SL is negative [33]. Although a negative value of n SL is consistent with the Gibbs method of defining the position of the interface [8,21,25], the prediction that follows is that, independently of any line tension, for a given curvature of the three-phase line, the contact angle increases as the pressure in the liquid at the three-phase line, P 3 L , is increased [35], but that, for a given value of P 3 L , the contact angle decreases as C cl increases [32].…”

“…If the system is accelerating parallel to the axis of the cylinder at a and is being rotated about the cylinder axis at an angular speed ω while exposed to the normal gravity field of intensity g 0 that is also parallel to the cylinder axis, then the potential energy per unit mass ξ at height z and radial position y, may be expressed [33] …”

“…The surface tensions, γ SV and γ SL , are related to the adsorptions through the Gibbs adsorption equations [33]:…”