A soap film bounded by a wire frame has the shape determined by the
minimization of its internal energy. The shape of the film is described
by the height u(x,y) over a given domain.
The height is fixed at the domain boundary, by the height of
the wire frame g
If the film is homogeneous, minimizing the internal energy is equivalent
to minimizing its area, the integral of
s(u) = sqrt(1+|grad(u)|^2)
This in its turn is equivalent to finding u such that
In this example you look at a wire frame with two circular components.
The inner frame is at height 0 while the outer frame is given by
g(x,y) = x^2.
The wire frame for a soap bubble. The computational domain
First you draw the domain which is an annulus (a two-dimensional doughnut),
i.e. the region between two concentric circles:
An annulus obtained by subtracting the small disk from the
large one. This is expressed by the set formula C1-C2
Boundary conditions dialog box.
In the soap bubble problem, you have a = f = 0 and
c = 1./sqrt(1+ux.^2+uy.^2).
A triangularization of the domain
Mesh generation is done automatically, but it you can also steer it by setting parameters. In this example the default mesh is initialized and then uniformly refined. The fine mesh contains 590 nodes and 1096 triangles.
The shape of the soap film