The Four Measurable Contact Angles

It has been known in the literature for a long time that there are three measurable contact angles, 6, Ga, and Gr for a given liquid-solid system [17-19], The static 

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Fig. 3.7 Schematic of the four measurable contact angles for a given sessile droplet...

Fig. 3.9 A schematic showing the wetting process and the flee energy relationship among the four measurable contact angles...

Table II presents the results of some wettability measurements on adsorbed monolayers prepared from molten Compound D on pure, polished, clean, chromium surfaces after solvent treatment had been used to remove all surplus solidified acid. A series of successive solvent treatments was applied to each coated specimen (see first four columns of Table II) using liquids which have been shown to be good solvents for Compound in the bulk (9). These liquids were either absolute ethyl alcohol or benzene at or above 20°C., or n-hexane at or above 60°C. In the remaining columns are listed the average values of the slowly advancing contact angles measured by the drop-buildup method on from three to five different drops. Measurements were made on sessile drops of water, thiodiglycol, and methylene iodide. These three diagnostic liquids were chosen because of their high surface tensions (72.8, 54.0,...

Section II.D, each material was finished by several methods, such as lathing and polishing, in order to measure contact angles for various surface roughnesses. The test liquids were water and 15% ethanol solution for the measurement of the contact angle and water, four kinds of ethanol solution of different concentrations, and two kinds of machine oils for the measurement of the liquid-vapor interfacial tension. 

Measurement of the flow by a heated membrane with connected thermocouples has been proposed by van Oudheusden [6, 7]. The schematic setup is shown in Rg. 3. Comparing the four measured temperatures allows not only measuring the flow near the wall, but can also determine the angle of attack of the main direction of flow. More details of the analysis have been given by van Oudheusden [7]. The sensor contacts also serve as mechanical hinges and guarantee a good thermal insulation for the heated membrane. 

In Table 3.2, these approaches are applied to our systems methylated solid surfaces and four characteristic nonpolar liquids. The adhesion energy Wvalues are estimated as mentioned above W=Gs + (Jl- F/2. W values are independently obtained data on the work of adhesion for considered nonpolar phases on the basis of contact angle of wetting measurements [20, 34] as W = 0l(1 + cos i ) 0 evaluations of interfacial energy in these systems as 05 = 0s—<7lCosi3. W a) and W(p), 0sl(A) and 0sl(F) are the estimations calculated for the same systems following Antonov and Fowkes, respectively, with the same 0s and 0l. 

Methods of Measurement Methods of characterizing the rate process of wetting include four approaches as illustrated in Table 20-37. The first considers the ability of a drop to spread across the powder. This approach involves the measurement of a contact angle of a drop on a powder compact. The contact angle is a measure of the affinity of the fluid for the solid as given by the Young-Dupre equation, or... 

The four-to-six day duration of the dynamic Wilhelmy tests (wherein equilibrium actually occurred after one day) were much shorter than the times generally required for the sessile drop test. The conventional contact angle measurements on oil from the fields mentioned above required up to 48 days (12). 

Recently, Heiberg et al. [26] have studied polarizabilities of the intermolecular contacts in bis(ethylenedithiolo)tetrathiafulvalene (BEDT-TTF) and bis(ethylenedioxy)tetrathiafulvalene (BEDO-TTF) molecular crystals by polarizing microscope techniques. The principal refractive indices and the corresponding optical axes have been calculated by tensorial addition of the bond polarizabilities of all bonds in the molecules. Comparison of calculated and measured values of the relative polarizabilities showed that the polarizabilities of the molecules only cannot yield the measured indicatrix and axes angle. Thus polarizabilities with other orientations must be involved. From the crystal structure of the molecular crystals it is known that 10 and four different contacts exist between the molecules of BEDT-TTF and BEDO-TTF, respectively, with contact distances lower than van der Waals distances. Assigning of polarizabilities of these contacts can explain the measured behavior. 

FIGURE 2.1.16 (a) Polar plot of the mobility at the rubrene a-b surface (the angle is measured between the b axis and the direction of current flow), (b) The four-probe measurements of the channel conductivity and the contact resistance (inset) as a function of along the b and a axes the p. values measured along the b and a axes are 15.4 cmWs and 4.4 cmWs, respectively. (From Sundar V. C. et ah, Science, 303, 1644, 2004.)... 

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