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# Gull Wing Lead Example gullwing-2 for the Surface Evolver

[Click for the gullwing-2.fe datafile in a second window.]

This file adds the liquid solder, completely surrounded by facets. Surrounding the solder with facets is easier conceptually than going immediately to edge integrals, and provides an accuracy check on the integral form in gullwing-3.fe.

### Design steps:

• Solder parameters: We need to define the physical properties of the liquid solder, so we put in some appropriate parameters:
```   parameter gamlv = 0.45    // Liquid-vapor surface energy of solder (Kg/s^2)
parameter den = 1.3e-10   // Density of solder (Kg/mil^3)
parameter mr_grav= 385000 // Acceleration of gravity  (mil/s^2)
```
The internal gravitational constant is set to the proper value with
```   gravity_constant mr_grav
```
The values look a little strange because of the unusual mil-Kg-sec system of units. Also we need to specify the contact angles:
```   //Contact angles on sides, foot, and bottom surfaces of lead, and pad
parameter theta_side = 20  // Contact angle on sides of the gull wing (degrees)
parameter theta_lower = 20 // Contact angle on the bottom surface of the gull wing (degrees)
parameter theta_toe = 20   // Contact angle on the toe of the gull wing (degrees)
parameter thetap = 20      // Wetting angle on the pad (degrees)
```
A contact angle is actually used to specify an equivalent contact surface tension of the form -gamlv*cos(angle). In this datafile, this type of tension will be applied to the contact facets; in gullwing-3.fe, it will be incorporated into edge integrals.
• Solder geometry:
• A full new set of constraints is needed to define the various contact surfaces of the solder: the pad (constraint 5), the toe of the lead, the underside of the lead, and the bottom of the lead.
• Also needed are a set of one-sided constraints to keep the pad contact lines inside the pad. If the pad were to be perfectly wetting, then we could just fix the contact line to the edge of the pad, and life would be simple. However, we are doing a non-zero contact angle on the pad, so we need the constraints. There are four sides on the pad, so we could use four one-sided constraints. Or we could mathematically combine the constraints into two formulas, or even one. I initially chose to combine into one formula to start off with, and see if it causes any problems:
```   constraint 6 nonnegative  // Keep inside pad edges
```
But it turned out later in evolution that some vertices escaped to undesired regions, so I made it two constraints:
```   constraint 6 nonnegative  // Keep inside pad edges in x direction

constraint 7 nonnegative  // Keep inside y direction
```
These will be applied to all vertices, edges, and facets on the pad. It might not seem necessary to apply them to the facets on the pad, since the ultimate effect is to apply them to interior vertices resulting from refinement. But experience has shown me that interior vertices can do strange things when the evolution does not go right, so it is better to keep them under control. Besides, the interior vertices will be gone when we get to serious evolution in gullwing-3.fe.
• Also need one-sided constraints to keep contact lines from going above or below or sideways off the lead. These are constraints 20-23. Constraints 22 and 23 use conditional expressions to do 3-way piecewise definitions of the formulas. Each could have been expanded into three constraints with simpler formulas, but then we would have problems when vertices want to slide back and forth between sections. Better to have the complexity once here than repeatedly in evolution.
• Now we put in a full new set of vertices, edges, and faces to define the liquid solder. Also one body to prescribe the volume of the solder. All the faces are oriented with outward normals, for easy incorporation into the body. The solder facets are all given tensions to provide the proper surface energies and contact angles.
• I have started the solder fairly low on the lead, since I have found it usually works better for solder to spread rather than shrink. Shrinking leads to short edges and tiny triangles that can stall the evolution until they are dealt with.
• Visually check that everything is right with the contact facets by displaying only them with
```   show facet where color == white
```
Also, refine a couple times to check all the constraints on edges and facets.
• I have set the body volume to 3780, simply because this was the volume of the initial configuration as shown by the 'v' command.
• If you try evolving this datafile, you will see the problems caused by the interface facets. Contact lines tend to cross over interior vertices, and since contact facets have negative tension, they tend to explode when they get overrun. Fixing the contact facets so the interior vertices can't move doesn't help, since there is still the overrunning problem.
• We're not even going to try to evolve this datafile, but go on to gullwing-3.fe, and just use this datafile to verify energies there.