As a final example of a useful Evolver calculation, consider the case of an assembly of small spheres which have a liquid phase wetting the contact points and interstices.
This is a reasonable idealization of a drying powder compact or liquid-phase sintering. In each case, the forces which the liquid menisci apply to the assembly of spheres can cause local rearrangement, shrinkage, or result in crack-like features where the menisci become unstable and break. In addition, the meniscus curvature will depend on the wetting angle, liquid volume, and the local arrangement of the solid particle. Thus, the local vapor pressures within the compact may vary considerably and influence drying behavior.
Evolver can be used to calculate such forces and curvatures[9].
Consider three spheres with a fixed amount of volume of fluid located in the
interstice as in the top of Figure 3.
If the total energy E of such a system can be calculated as the upper two
spheres in Figure 3 are rotated away from each other by some angle 
,
then the torque T that the meniscus applies to the spheres can be calculated by
.
Similarly, if the energy is calculated as the volume of fluid is increased, then
the mean curvature can be calculated as 
and the
vapor pressure can be inferred through the Gibbs-Thomsen equation.
The Evolver code in 9 illustrates how to do such a calculation. Parameters are defined for the wetting angle, the sphere opening angle, and the meniscus volume. To model the entire system, three constraints must be defined and vector integrands must be obtained for the energy and volume content on each; the results are given in the code which follows.
Macro functions are defined at the end of the file in 9 which allows the
program to run on its own.
These may provide some useful examples for other similar problems.
The macro run_this given at the end of the file does the following:
increments ; iterates toward a solution while doing some mesh
cleaning operations; stops iterating when the energy decrease falls below
a chosen tolerance; writes data to a file; saves the surface every ten
increments; repeats.
Some results are plotted in Figure 3 for two 
.
The end of the curves signify opening angles where no Evolver solution could be
found and are thus an estimate for the critical opening angle for each 
The torques are such that the particles tend to be drawn back together; this
is probably not the case for 
.
The solid vertical curve in the plot can be used to calculate the curvatures
in the collapsed configuration.
Such calculations could be done for many different values of and
and placed in a look-up table for a simulation of a many particle compact.
The solutions for bridges between two spheres are well-known and have been
worked out.[10].
An Evolver calculation for a meniscus in a tetrahedral interstice would be
a nice contribution to the literature.
The same method of taking derivatives can be applied to the first example
of the grain boundary phase.
Using that same program and varying the height of the cell, the force
exerted by the top grain boundary constraint could not be numerically
distinguished from 0.
However, the second derivative of energy with respect the height is
negative-indicating that this
particular symmetric geometry is unstable.
The total surface potential, 
, was also numerically
determined to be 
and the potential
is a decreasing function of density; so the system will be unstable to
coarsening.
