Tension kills ... harmonic moments in viscous fingering

We measure the displacement of oil by air between two horizontal, closely-spaced glass plates to track the evolution of harmonic moments, which are integrals of integer powers of $z = x+iy$ over the oil domain. Richardson's theory (1972) predicts that the harmonic moments should be \emph{time invariant in the absence of surface tension}. When we extend the theory to include surface tension, the harmonic moments are predicted to \emph{decay in time because of surface tension}. From measurements of the time decay of the harmonic moments, we obtain a value for the surface tension within 5\% of the accepted value. To obtain such precise agreement, the effect of silicone oil wetting the glass plates must be included. Our results implicitly validate Richardson's theory and directly demonstrate that a full description of interface dynamics in terms of harmonic moments is physically realizable and robust. In addition, a novel growth method using feedback produces nearly n-fold symmetric bubbles.