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

Abstract

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.

Atomic Force Microscope‐Based Meniscus‐Confined Three‐Dimensional Electrodeposition

“…Regarding the first phenomenon, it has been reported that a small tip‐to‐substrate distance combined with a 1:2 inner‐to‐outer tip diameters ratio cause the formation of larger meniscus, and as a result, a larger deposition area . Similarly, the larger base size can be attributed to a small tip‐to‐substrate distance and approach speed, as well as to the hydrophilic nature of Cu …”

Protein adsorption in three dimensions

“…Solid tensions are not typically accessible to tensiometry (at least not without additional theory [14, 210] and the inevitable assumptions/simplifications embodied therein). Also, interpretation of solid interfacial tensions almost always depends on the reliability of the Young equation, which is of dubious merit for reasons mentioned in Section 6.1.…”

Energy Transport by Thermocapillary Convection during Sessile-Water-Droplet Evaporation

“…1 (color online). In each experiment, an evaporating water droplet with a three-phase-line radius of 9 AE 0:01 mm was maintained on a polished Cu substrate (roughness 53 nm [19]) and in steady state by a syringe pump that injected deionized, degassed water into the droplet base through a small (0.6-mm-diameter) tube at the same rate that vapor was removed from the enclosing chamber. The droplet height and the temperature in the liquid and vapor phases were measured with a U-shaped thermocouple (25 m bead diameter) that was mounted on a positioning micrometer.…”

“…If zð0Þ and C cl are known, but the evaporation ignored, the contact angle of an equivalently sized equilibrium droplet e may be determined by the methods described in [19]. The values of e correlate with , but are always less, Table I. The pressures in the liquid and vapor phases at the interface were obtained as part of the procedure to predict the droplet shape, and the temperatures in each phase at 10 points along the interface were measured.…”