Two Identical Cylindrical Drops or Bubbles

Note that, in general, the system of two droplets is thermodynamically unstable with regard to coalescence. Therefore, the following calculations give the conditions of the metastable equilibrium of droplets separated by a thin interlayer of the surrounding liquid. 

The excess free energy of the two cylindrical drops (per unit length of cylindrical droplets), O, is equal to O = yS -h + P V, where S is the total 

FIGURE 2.33 The equilibrium profile of interlayer,/jfx), between two cylindrical droplets of the same radius, R. 

Substitution of the latter expression into the excess free energy results in 

A variation of the excess free energy with respect to h(x), h, (x), (x), and 

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First, let us consider a case of two identical cylindrical drops or bubbles (Figure 2.33). It is assumed for simplicity that the radius of action of surface forces is limited to a certain distance, t,. Beyond this distance, the surface of droplets retains a constant curvature radius, R, and is not disturbed by surface forces. The interacting droplets are considered as being surrounded by a liquid with constant pressure, F,. 

For this purpose, let us consider the line tension in the simplest possible case contact of two identical cylindrical drops or bubbles. In this case, the corresponding excess free energies given by Equation 2.194 and Equation 2.197 take the following form ... 

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