Contact angle Young’s equation

The liquid-solid or liquidj-solid-liquidz system is both a contact angle (Young s equation) and capillary phenomena (Laplace equation). These two parameters are... 

In this section, we consider the influence of a gravitational field on the shape of a liquid droplet residing on a solid substrate (see Fig. 8). This topic was already addressed some 100 years ago by Bashforth and Adams [29], who supplied numerical tables for the shape of the liquid droplet. Their analysis is based on two equations the Laplace equation to describe the shape of the droplet, and Young s equation to determine the contact angle. Young s angle. 

Consider a glass tube of small internal diameter dipped vertically into a liquid which wets the glass. A film of liquid will creep along the wall until the angle of contact satisfies Young s equation, ffius causing the surface of liquid near the wall to be concave upwards. From (1.14) it follows that ffie internal pressure below this portion of liquid is less than... 

The preceding definitions have been directed toward the treatment of the solid-liquid-gas contact angle. It is also quite possible to have a solid-liquid-liquid contact angle where two mutually immiscible liquids are involved. The same relationships apply, only now more care must be taken to specify the extent of mutual saturations. Thus for a solid and liquids A and B, Young s equation becomes... 

Since both sides of Eq. X-39 can be determined experimentally, from heat of immersion measurements on the one hand and contact angle data, on the other hand, a test of the thermodynamic status of Young s equation is possible. A comparison of calorimetric data for n-alkanes [18] with contact angle data [95] is shown in Fig. X-11. The agreement is certainly encouraging. 

Fig. 4. Definition of contact angle showing the derivation of Young s equation, Eq.. 8, using a balance of horizontal forces at the three-phase interline.

Since —1 < cos < 1, Young s equation is valid only when the right hand side of Eo 3 or Eq. 3a lies between these limits, i.e. the observed contact angle is finite. In le event that the measured contact angle is 0°, i.e. full spreading occurs, one may conclude only that... 

A requirement underlying the validity of Zisman plots is that there be no specific interactions, such as acid-base interactions, between the solid surface and the probe liquids. Such interactions, however, can, in principle, be taken into account by Young s equation, provided the contact angle remains finite. Their... 

The phenomenon of wetting of a solid by a liquid depends on the surfaces and interfacial energies. When a liquid droplet is in contact with an ideally smooth solid surface, as shown schematically in Fig. 9, according to the Young s equation [72], the contact angle (6) of the liquid is given by... 

Fig. 9. Schematic of contact angle of a liquid on a solid. By balancing components of interfacial free energies in the horizontal direction, we can obtain the Young s equation.

Many of the most widely used methods are based on measuring the contact angles of a series of test liquids on the solid surface, and evaluating the surface energies via Young s equation, Eq. 4 above. 

It is well known that when liquid droplets form on a flat substrate they adopt spherical cap shapes (neglecting gravity effects) with a contact angle 6. This angle depends solely on the interfacial energies as described by the Young s equation ... 

Equilibrium at the triple line satisfies Young s equation [Eq. (1)], but if the contact angle as a function of time, 0(0, is greater than 6o, then there is a net spreading force acting per nnit length of triple line and given by [5] ... 

Young s equation is a plausible, widely used result, but experimental verification is often rendered difficult e.g., the two terms which involve the interface between the solid and the two other phases cannot be measured independently. Furthermore, many complications can arise with contact angle measurements ys values of ionic solids based on contact angle measurements are different from those estimated from solubility (Table 6.1) (cf. Table A.4.1). 

The contact angle 0 of a liquid on a solid is the reflection of its wetting power. If 0 = 0, the liquid spreads freely on the solid surface and wets it. The relationship between the contact angle of a liquid on a solid and the surface tensions in the presence of saturated vapor of the liquid, is given by the Young s equation, Eq. (2). 

Good, R.J, (1952). A thermodynamic derivation of Wenzel s modification of Young s equation contact angles Together with a theory of hysteresis. J. Am. Chem. Soc. 74, 5041-5042. 

Young s equation at liquid —solid l iq uid2 has been investigated in various systems where it has been found that the liquid-solid-liquidi surface tensions meet at a given contact angle. For example, the contact angle of water drop on Teflon is 50° in octane (Chattoraj and Birdi, 1984 see Figure 5.3). 

In practice, the contact angle can be experimentally determined in a rather routine manner, as can the liquid surface tension and even the solid surface energy. The interfacial energy for the liquid-solid system of interest, ysi, can then be calculated using Young s equation. Alternatively, if ysL, Yl, and ys are known as a function of temperature, the contact angle can be predicted at a specified temperature. 

Fig. 14. Schematic illustration of a drop ofliquid spreading in contact with a solid surface, showing the relations between the relevant parameters the contact angle, 0 the solid/vapor interfacial free energy, Ysv the liquid/vapor interfacial free energy, yLV and the solid/liquid interfacial free energy, ySL. Young s equation describes the relationship between these parameters for a stationary drop at thermodynamic equilibrium [175]...

Accepting Equation (54) and Young s equation, on which it is based, suggests calorimetry as a method for measuring contact angles. At this time this is not practical, but the implication that contact angle is a thermodynamic property is a very important realization. 

Although we established the thermodynamic significance of y early in the chapter, 0 has been allowed to drift. Its role is clear when we think of surface tension as a force We use 0 to project 7 in a specified direction. In thermodynamic terms, contact angle has been an outsider in our presentation. Young s equation is the remedy to this. Rewriting Equation (44), we observe... 

Both of these conclusions are consistent with Young s equation. All other things being equal in Equation (55), the larger ysv ySo is, the larger cos 0 will be. Since the cosine increases as 0 decreases, large values of ys° result in smaller contact angles, and vice versa. We noted... 

Using 379.5 and 34.0 erg cm-2, respectively, as the values of y for the mercury-water and benzene-water interfaces, compare the observed contact angles with the predictions of Young s equation. Comment on the fact that constant values are used for yHg w and ybeniene.w... 

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