## File: column.htm

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 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200` `````` Surface Evolver Documentation - Column Example

Surface Evolver Documentation

Example: Column of liquid solder

Here we have a tiny drop of liquid solder that bridges between two parallel, horizontal planes at z = 0 and z = ZH. On each plane there is a circular pad that the solder perfectly wets, and the solder is perfectly nonwetting off the pads. This would be just a catenoid problem with fixed volume, except that the pads are offset, and it is desired to find out what aligning force the solder exerts. The surface is defined the same way as in the catenoid example, except the lower boundary ring has a shift variable SHIFT in it to provide an offset in the y direction. This makes the shift adjustable at run time. Since the top and bottom facets of the body are not included, the constant volume they account for is provided by content integrals around the upper boundary, and the gravitational energy is provided by an energy integral. One could use the volconst attribute of the body instead for the volume, but then one would have to reset that every time ZH changed.

The interesting part of this example is the calculation of the forces. One could incrementally shift the pad, minimize the energy at each shift, and numerically differentiate the energy to get the force. Or one could set up integrals to calculate the force directly. But the simplest method is to use the Principle of Virtual Work by shifting the pad, recalculating the energy without re-evolving, and correcting for the volume change. Re-evolution is not necessary because when a surface is at an equilibrium, then by definition any perturbation that respects constraints does not change the energy to first order. To adjust for changes in constraints such as volume, the Lagrange multipliers (pressure for the volume constraint) tell how much the energy changes for given change in the constraints:

DE = L*DC
where DE is the energy change, L is the row vector of Lagrange multipliers and DC is the column vector of constraint value changes. Therefore, the adjusted energy after a change in a parameter is