this is a summary of data generated from "bridge.fe"
suppose we fix some parameters for the pendant solder drops, say:
(pad spacing) (pad radius) (gravity:surface tension)
DD=1 RR=.8 GG=1
then, as we vary the parameter TT from pi/6 to pi/2, or rather
pi/TT from 6 to 2, we find the following behavior for the critical
volume fraction FF where the bridges break when we flow from our
intial surface (we also include the "pibridge.fe" data under 1)
pi/TT 6(hexagon) 4(square) 3(triangle) 2(linear) 1(dumbell)
FF 0.29 0.26 0.23 0.19 0.10
of course, more work will need to be done to see what further reduction
in FF is needed to break stable bridges which have already formed
but my preliminary conclusion is that not only do hexagonal arrays provide
about 20% more pads per unit area at the same pad spacing, but also permit
considerably larger solder volumes in the non-bridging regime
one caveat is that, with the assumption of pi/TT-fold symmetry, the bridges
are joining all neighbors - as is probably obvious, less FF is needed to
bridge with only some neighbors, so the above can be viewed as a verification
of this behavior: the limiting case (dumbell in "pibridge.fe") gives the
lower bound
rob kusner
6/2/94