Gibbs phase rule curved interfaces

The fact that the curvature of the surface affects a heterogeneous phase equilibrium can be seen by analyzing the number of degrees of freedom of a system. If two phases a and are separated by a planar interface, the conditions for equilibrium do not involve the interface and the Gibbs phase rule as described in Chapter 4 applies. On the other hand, if the two coexisting phases a and / are separated by a curved interface, the pressures of the two phases are no longer equal and the Laplace equation (6.27) (eq. 6.35 for solids), expressed in terms of the two principal curvatures of the interface, defines the equilibrium conditions for pressure ... 

Equation (6.42) introduces a new independent variable of the system the mean curvature c = (c1 +C2). This variable must be taken into account in the Gibbs phase rule, which now reads F + Ph = C + 2 + 1. The number of degrees of freedom (F) of a two-phase system (Ph = 2) with a curved interface is given by... 

Example 2.9 Gibbs Phase Rule for curved interfaces Deri ve the phase ru 1 e for a composite system of p phases and c components with curved interfaces F = c + l where F is the number of degrees of freedom. If some of the interfaces are flat, then F = c + 1 — I, w here 7 is the number of flat interfaces between the bulk phases. 

Solution The Gibbs Phase Rule for a fiat interface between the phases, which W as established in Example 1.9 of Chapter 1, is based on the assumption that the PdV work is the only mode of work. As W c have seen in this chapter, the equilibrium conditions for systems with curved interfaces and under the influence of gravity are different from the equilibrium conditions of systems with flat interfaces and negligible gravity. For systems with curved interfaces and also with gravity effect, the Gibbs Phase Rule should be modified. In this example, we will only consider the effect of the curved interface. 

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