When a drop of liquid is placed on the flat surface of a solid, it may: 1) spread out to form a thin film; or 2) remain as a drop forming a finite angle with the solid surface. The angle, measured in the liquid, is defined as the contact angle, Θ.
The concept also applies to a system consisting of two immiscible liquids in contact with a solid. In this case, Θ may apply to either liquid.
Fox et al. (1950) has designed a system in which a small drop of the liquid is placed on the surface of a flat solid in a small chamber which has optically worked faces or windows. The chamber is placed on a table which forms part of an optical bench. The drop is illuminated by a collimated beam of monochromatic light. The silhouette of the drop is then examined using a telescope fitted with a goniometer eyepiece or it may be photographed and measured later. In Fox and Zisman's device, the chamber could be evacuated or filled with an inert atmosphere. Hysteresis of the contact angle can be determined by adding or removing fluid from the drop.
When the amount of liquid available is not important and the solid is available as a transparent plate, the plate may be partially immersed in the liquid and rotated about an axis parallel to the surface of the liquid until the liquid remains flat right up to the surface of the plate. This position may be ascertained by viewing a grid immersed in the liquid, which should show no distortion.
For very small angles of contact, collimated monochromatic light may be used to illuminate the edge of the film. Light rays reflected from the liquid-vapor interface and from the solid-liquid interface will interfere and produce Fizeau fringes, from the spacing of which the angle made by the film on the solid may be determined.
Jones and Porter (1967) have devised a method suitable for routine measurements on fibers. The fiber is stretched between two holders fixed to a sliding table (see Figure 2). An eyelet is fitted round the fiber and filled with the liquid. The meniscus is viewed with a microscope having vertical illumination. Only rays incident perpendicular to the surface are reflected back to the microscope and a pin-point of light is observed at P.
The system is rotated until the point P just reaches F, where the liquid touches the solid surface. At this point, the spot vanishes. The method is suitable for angles up to about 75°. Hysteresis of the contact angle may be measured by sliding the fiber forwards and backwards.
If the surface of a packed bed or compressed powder touches the surface of a liquid which wets or partially wets the solid, the liquid will flow into the system under the action of the Laplace pressure. If the system has an effective pore radius of r, then . The volume rate of flow w is given by the Poiseuille equation
where η is the viscosity of the liquid and h, the height to which the liquid has risen. The rate of advance of the liquid front, dh/dt, is:
This is the Washburn equation [Washburn (1921)]. By making measurements using a liquid, which completely wets the solid, one may obtain a value for the average pore radius. The system may then be used to measure Θ for any other liquid. In a modification of Washburn's method made by Bartell (1932), the pressure needed to prevent the liquid from penetrating the capillary system is measured.
Measured values of the contact angle show that they are dependent on the direction of liquid motion before coming to rest, i.e., hysteresis occurs. When the liquid is advancing over the surface, the advancing angle, ΘA, is measured and as liquid withdraws from the surface the receding angle, ΘR, is obtained. There are five main causes of hysteresis:
Heterogenity in surface energy of the solid surface;
The liquid may remove adsorbed molecules from the solid surface;
Molecules of the liquid may form an oriented adsorbed layer at the solid-liquid interface;
Molecules of the liquid may form an oriented monomolecular film on the solid surface, which is not wetted by the liquid;
The surface may be rough.
The work of adhesion between a liquid and a solid may be defined in a similar way to that between two liquids, viz.:
The angle of contact is an excellent measure of the wettability of a solid surface. If the liquid spreads over the surface without limit, it is zero; otherwise, a finite angle is formed. The interfacial free energies, σSV and σSL, are not in general easy to measure. Young has derived an expression which relates these quantities to the contact angle.
The contact line between three phases in equilibrium – solid, liquid, and vapors – is shown in Figure 3. Consider a virtual displacement which causes Δ m2 of solid surface to be covered by the liquid. Then the solid-liquid and liquid-vapor interfacial energies increase by σSLΔ and σSV cos Θ Δ , respectively, while the solid-vapor interfacial energy decreases by σSVΔ .
By the principle of virtual work,
where π is the reduction in the surface free energy of the solid due to the adsorption of vapor. This is the Young-Dupre equation.
and the spreading coefficient S is then
Zisman and his coworkers (1964) made a systematic study of the variation of contact angle of a series of liquids, in particular solid surfaces. They observed a linear relationship between the surface tension of the liquids and the cosine of the angle of contact formed by them on any particular solid [see Figure 4.] , RX: , alkylbenzenes; , n-alkanes; , dialkyl ethers; , siloxanes; , miscellaneous polar liquids.
They extrapolated the lines to cos Θ = 1. Zisman defined this corresponding value of σLV; as the critical surface tension of the solid. It is the surface tension of a liquid which just spreads on the surface and is characteristic of the solid. It is not the surface free energy of the solid since if the interaction between the solid and the liquid is high, the solid has a high surface energy and a large value of sSL could exist. If the critical surface tension is to equal solid surface tension, sSL would be zero.
Bartell, F. E. and Miller, P. L. (1932) Industr. Engin. Chem., 24, 335.
Fox, H. W. and Zisman, W. A. (1950) J. Coll. Sci., 5, 514.
Jones, W. C. and Porter, M. C. (1967) J. Coll. Int. Sci., 24, 1-3.
Washburn, E. W. (1921) Phys. Rev. Ser., 2, 17, 273.
Zisman, W. A. (1964) Advances in Chemistry, No. 43, American Chemical Society, Washington D. C.
- Bartell, F. E. and Miller, P. L. (1932) Industr. Engin. Chem., 24, 335.
- Fox, H. W. and Zisman, W. A. (1950) J. Coll. Sci., 5, 514.
- Jones, W. C. and Porter, M. C. (1967) J. Coll. Int. Sci., 24, 1-3.
- Washburn, E. W. (1921) Phys. Rev. Ser., 2, 17, 273.
- Zisman, W. A. (1964) Advances in Chemistry, No. 43, American Chemical Society, Washington D. C.
Heat & Mass Transfer, and Fluids Engineering