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Although the Af calculation is obvious by analogy with that for gravitational field and osmotic pressure, it is interesting to confirm it by a method which can be generalized to include related effects.

Consider a shear field with a height of H and a cross-sectional area of A opposed by a manometer with a height of H ( referred to the same base as H ) and a cross-sectional area of A.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

Af is the work necessary to fill the manometer column from the reference height to H.

The total volume of the system above the reference height is Af, and H can be eliminated to obtain an equation for the total potential energy of the system in terms of H.

The minimum total potential energy is found by taking the derivative with respect to H and equating to zero.

This gives Af, which is the pressure.

This is interesting for it combines both the thermodynamic concept of a minimum Gibbs function for equilibrium and minimum mechanical potential energy for equilibrium.

This method can be extended to include the concentration differences caused by shear fields.

The relation between osmotic pressure and the Gibbs function may also be developed in an analogous way.