Contact angle tilting plate method

FIG. 6.2 Illustrations of liquid film formation, contact angle, and measurement of contact angle (a) a wire loop with a slide wire on which a liquid film might be formed and stretched by an applied force F. (b) profile of a three-phase (solid, liquid, gas) boundary that defines the contact angle 0. (c) the tilted plate method for measuring contact angles. 

For a plate of rectangular cross section having length f and thickness t, P = 2(f + t) these dimensions can be accurately measured. By suspending the plate from a sensitive balance, we can also measure w with considerable accuracy. The apparatus is called a Wilhelmy balance, and the technique the Wilhelmy plate method. Thus, if the contact angle is known from an independent determination by, say, the tilted-plate method, then 7 can be evaluated by Equation (2). 

All the techniques described here are easily conducted, so that both 0a and 0, may be observed. When the tilted plate method is used to evaluate the contact angle, 6r values are obtained if the plate has been pulled out (emersion) from the liquid 0a results if the plate is pushed into the liquid (immersion). Likewise, both values of 0 may be obtained from the Wilhelmy method, depending on whether the liquid is making an initial contact (0a) with the plate or is draining from it (6r). 

If a moderately large area of flat solid surface is available, contact angles are usually measured directly from a projection of a sessile drop of the liquid. Alternatively, the tilting-plate method illustrated... 

Figure 6.3 Tilting plate method for the measurement of contact angles...

Two common methods for measuring contact angles are the sessile drop and tilting plate methods. 

Figure 3.17 Illustration of the tilting plate method for measuring contact angle.

Figure 5.24. Contact angle by the tilted plate method.

Advancing and receding contact angle should be determined by the drop expansion/ contraction technique. The tilting plate method has significant shortfall particularly with high hysteresis samples and should be avoided if possible. 

Figure 9.2 Determination of contact angle from the sliding drop on an inclined plate method. The advancing contact angle, 9 , is the measured angle at the downhill edge of the drop, the receding contact angle, 0r is measured at the uphill edge, and 0, is the tilt angle.

There are a variety of simple and inexpensive techniques for measuring contact angles, most of which are described in detail in various texts and publications and will be mentioned only briefly here. The most common direct methods (Fig. 17.4) include the sessile drop (a), the captive bubble (b), the sessile bubble (c), and the tilting plate (d). Indirect methods include tensiometry and geometric analysis of the shape of a meniscus. For solids for which the above methods are not applicable, such as powders and porous materials, methods based on capillary pressures, sedimentation rates, wetting times, imbibition rates, and other properties, have been developed. 

Experimentally, contact angle is measured based on geometry of the droplet or the interfacial tension across the contact line using various techniques such as tilting plate, sessile bubble and drop, captive bubble, the Wilhelmy method, and so on. Similarly, in simulation, three methods are generally used to find the contact angle. 

FIG. 24 Principle of the method for the measurement of contact angle using tilted plate based on geometrical instability of two-dimensional meniscus (a) receding contact angle (b) advancing contact angle. 

FIG. 34 Comparison of contact angles measured by the proposed method using tilted plate with those by a commercially available contact angle meter (a) advancing contact angle (b) receding contact angle. 

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