Youngs Equation Again

FIGURE 17.7. Young s equation for determining the contact angle was originally based on an analysis of the force balance among the three surface tensions involved. 

While Young s equation provides a thermodynamic definition of the contact angle, its experimental verification is prevented by the fact that the values of Ssi and Ss2 cannot be directly determined experimentally. In this sense, the contact angle of a hquid on a sohd differs from that of a hquid on a second liquid since in the latter case all three interfacial tensions can be determined independently and the relationship can therefore be verified directly. 

In terms of the mechanical (hydrostatic) equilibrium derivation of Young s equation, this equation appears nonsensical, since the three-phase wetting line for which it describes the equilibrium does not exist. That is, there is no three-phase contact hne at which the two fluid phases contact each other and the sohd surface. Thermodynamically, however, one can show that the equation is exactly obeyed when spreading occurs. 

If Equation (17.6) is rewritten to take into account the microscopic mechanism of spreading, the situation can be clarified. For example, spreading proceeds first by a molecular level spreading of hquid on the sohd surface. If it is assumed that the second fluid (2) is air and the only component adsorbed at the S2 interface is the vapor of hquid 1, Equation (17.6) can be written 

If spreading occurs, the spreading pressure 7752,1 will increase, reducing 052 until Equation (17.8) is exactly satisfied. At that point the thickness of the adsorbed film will be such that only the SI and 1-2 interfaces exist. Further thickening of the spread film may then occur by spreading of hquid 1 on itself. 

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The kinetic observations reported by Young [721] for the same reaction show points of difference, though the mechanistic implications of these are not developed. The initial limited ( 2%) deceleratory process, which fitted the first-order equation with E = 121 kJ mole-1, is (again) attributed to the breakdown of superficial impurities and this precedes, indeed defers, the onset of the main reaction. The subsequent acceleratory process is well described by the cubic law [eqn. (2), n = 3], with E = 233 kJ mole-1, attributed to the initial formation of a constant number of lead nuclei (i.e. instantaneous nucleation) followed by three-dimensional growth (P = 0, X = 3). Deviations from strict obedience to the power law (n = 3) are attributed to an increase in the effective number of nuclei with reaction temperature, so that the magnitude of E for the interface process was 209 kJ mole-1. 

Once again, we may use Young s equation to decide what adsorption situation is most conducive to values of 02 >90°... 

Now assume that by some means we cause liquid L2 to solidfy on solid Si in such a manner that we again have an equilibrium system, this time of solid S1 in contact with solid S2 in the presence of saturated vapor of S2. The Young-Dupre equation for this system is... 

If the interface between A and B in the large region outside the tube is flat, we can again invoke the Young-Laplace equation at the height of this interface ... 

Again, the Halpin Tsai equations give a set of elastic constants to a good approximation, provided that the axial Young s modulus 3 is modified to... 

Role of Suifactants in Biological Enhancement 585 Again using the Young s equation, one obtains the following expression for W, ... 

We now address again the work of adhesion that we defined in its general form in Chapter 3. The general equation (Equation 3.1) is applied to all interfaces. In the case of solid-liquid interfaces, the work of adhesion is given by the Young-Dupre equation ... 

If this approximation is accepted, the Young and Dupre equations may be again introduced in O Eq. 6.20b yielding... 

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