in
is the region occupied by one of the fluids, which
contacts a fixed surface 
. In micro-gravity (i.e.,
gravity is negligible) the energy functional is
Capillary surfaces are closely related to minimal surfaces. In
fact, capillary surfaces minimize a more general functional than
do minimal surfaces. The standard mathematical model for volume
constrained capillary problems is as follows: a set in
is the region occupied by one of the fluids, which
contacts a fixed surface . In micro-gravity (i.e.,
gravity is negligible) the energy functional is
where 
is the free surface of 
(i.e., that
portion of 
which is not contained in 
),
is the portion of 
which is wetted by 
(i.e., 
), and 
is a constant
depending on the materials involved. We seek local minima of this
energy functional if 
is required to satisfy a volume
constraint, that is, we only consider volume conserving
perturbations. The first variation yields that the mean curvature
of 
is a constant H, and that the angle between the
normal to 
and the normal to 
along the curve of
contact is 
, at least when 
is
smooth enough to have a normal. A surface satisfying this first
order condition is called stationary. If gravity is included, the mean curvature is an affine function of height, but the contact angle condition remains the same.
For anyone interested in looking at these surfaces, Finn's book is a good place to start.