  Harmonic moments are integrals of integer powers of z = x+iy over a domain.
Here the domain is an exterior of a bubble of air growing in an oil layer
between two horizontal closely spaced plates. Harmonic moments are a natural
basis for such Laplacian growth phenomena because, unlike other
representations, these moments linearize the zero surface tension problem
(Richardson, 1972), so that all moments except the lowest one are conserved in
time. For non-zero surface tension, we show that the the harmonic moments decay
in time rather than exhibiting the divergences of other representations. Our
laboratory observations confirm the theoretical predictions and demonstrate
that an interface dynamics description in terms of harmonic moments is
physically realizable and robust. In addition, by extending the theory to
include surface tension, we obtain from measurements of the time evolution of
the harmonic moments a value for the surface tension that is within 20% of the
accepted value.
