Tilting plate method

When the drop just about to slide at a, F=f. From Eqs. (2.4) and (2.5), plot of sina versus (cos0r-cos0a) should yield a linear relationship if 0a=9wb and R=9n. Experimentally, a very scattered plot was obtained (Fig. 5.13), indicating that AT max and The fundamental related to the inequality between 9J9ma. and 

0R/0min will be addressed in Sect. 5.3. In any event, the inequality suggests that the use of the titling plate method to determine sliding angle is technically incorrect. 

2 Contact Angle Measurements and Surface Characterization Techniques 

This observation is in agreement with the theoretical modeling study reported by Krasovitski and Marmur [49], who predicted inequality between and d lQ  

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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.

Also shown in Fig. III.3 is the dependence of the experimental accuracy on the nonuniformity of particle diameter in the dust fractions (curve 1). With Ad/d v = 0.05, the error of the method is 15%. Hence, the tilt-plate method will give accurate results only if the particles are monodisperse. If the particle size varies significantly within the fraction, the method is less accurate, becoming unsuitable in practice for the determination of particle adhesive force for example, with d = 40-60 /rm, we find that Adld y = 0.2 and B = 60%. 

For partially oriented uniaxial samples, two linearly independent spectra can be obtained from an experiment, irrespective of the mode of measurement and the polarization state of the absorbed light. The obvious procedure is to record two absorption spectra, one with the electric vector of light parallel to U, the unique axis of the sample Ei), the other with the electric vector perpendicular to the unique axis (Ey). The spectra must be baseline-corrected by subtracting the curves recorded on pure solvents. This yields the largest difference between the tow linearly independent spectra. Other alternatives are also possible. A combination of Ey or Ey with the spectrum of an isotropic sample, E =[E + 2Ey]/3) is easily obtained in liquid crystal. In cases where the sample geometry precludes the measurement of both Ey and the isotropic spectrum (membranes), the two spectra are Ey and the latter recorded with the incidence angle nlZ-co, and with the plane of polarization containing the U axis (the tilted plate method ). 

Eiso = absorbance in an isotropic sample Ey = absorbance with the electric field vector parallel to the unique axis, U Ey = absorbance with the electric field vector perpendicular to the unique axis (parallel to the perpendicular axis, V)i U= the unique optical axis (o = angle complementary to the incidence angle in the tilted plate method . 

Table 2.1 Comparison of the 0 and values from the drop expansion/contraction method to the, values from the tilting plate method (data from [45])...

Drop expansion/contraction method Tilting 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. 

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