  For the Saffman-Taylor instability, the inertia of the fluid may become
important for large Reynolds numbers Re. We investigate the effects of inertia
on the width of the viscous fingers experimentally. We find that, due to
inertia, the finger width can increase with increasing speed, contrary to what
happens at small Re. We find that inertial effects need to be considered above
a critical Weber number We. In this case it can be shown that the finger width
is governed by a balance between viscous forces and inertia. This allows us to
define a modified control parameter 1/B', which takes the corrections due to
inertia into account; rescaling the experimental data with 1/B', they all
collapse onto the universal curve for the classical Saffman-Taylor instability.
Subsequently, we try and rationalize our observations. Numerical simulations
taking into account a modification of Darcy law to include inertia, are found
to only qualitatively reproduce the experimental findings, pointing to the
importance of three-dimensional effects.
