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A new general class of exact solutions is presented for the time evolution ofa bubble of arbitrary initial shape in a Hele-Shaw cell when surface tensioneffects are neglected. These solutions are obtained by conformal mapping theviscous flow domain to an annulus in an auxiliary complex-plane. It is thendemonstrated that the only stable fixed point (attractor) of the non-singularbubble dynamics corresponds precisely to the selected pattern. This thus showsthat, contrary to the established theory, bubble selection in a Hele-Shaw celldoes not require surface tension. The solutions reported here significantlyextend previous results for a simply-connected geometry (finger) to adoubly-connected one (bubble). We conjecture that the same selection rulewithout surface tension holds for Hele-Shaw flows of arbitrary connectivity. Wealso believe that this mechanism can be found in other, similarly described,selection problems.

Selection of the Taylor-Saffman Bubble does not Require Surface Tension