  A new kind of invasion percolation is introduced in order to take into
account the inertia of the invader fluid. The inertia strength is controlled by
the number N of pores (or steps) invaded after the perimeter rupture. The new
model belongs to a different class of universality with the fractal dimensions
of the percolating clusters depending on N. A blocking phenomenon takes place
in two dimensions. It imposes an upper bound value on N. For pore sizes larger
than the critical threshold, the acceptance profile exhibits a permanent tail.
