  We analyze the effect of frequency on the width of a single finger displacing
a viscoelastic fluid. We derive a generalized Darcy's law in the frequency
domain for a linear viscoelastic fluid flowing in a Hele Shaw cell. This leads
to an analytic expression for the dynamic permeability that has maxima which
are several orders of magnitude larger than the static permeability. We then
follow an argument of de Gennes to obtain the smallest possible finger width
when viscoelasticity is important. Using this, and a conservation law, we
obtain a lowest bound for the width of a single finger displacing a
viscoelastic fluid. Our results indicate that when a small amplitude signal of
the frequency that maximizes the permeability is overimposed to a constant
pressure drop, gigantic variations are obtained for the finger width.
