Cylindrical Droplets of Different Radii

Applying the same method of minimization of the excess free energy as in the preceding section, we obtain the following equations  

FIGURE 2.35 The equilibrium profile of interlayer t(x) = h. ix) - /t2 ( ) between two droplets of different radii, and R, in the general case (a) and in the simplified case (b), when the transition region is neglected. 

In a similar way, we may solve the same problem for two droplets of different composition with different interfacial tensions, y, and 72, of the first and the second droplet, respectively. In this case, even for the droplets of the same radius, the interlayer on the whole proves to be curved owing to the appearance of a capillary pressure drop, AP = (yj - 72)// . 

In the case of a not strongly curved interlayer between droplets, the term (h Y may be neglected as compared with 1. From Equation 2.149, Equation 2.150, and Equation 2.153, taking into account that t(x) = h (x) - h ix) and t (x) = H[(x) -h x), we obtain  

This equation should be subjected to the following boundary conditions  

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Let us now consider a more complicated case of interaction of cylindrical droplets of different radii, R2 > R (Figure 2.35a). 

Calculation of the interaction of cylindrical droplets of different radii (1 2 > R ) can be simplified if we assume that the interlayer is of a constant thickness. This means that the effect of a transition zone is neglected, which is justified only at Xq t,. 

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