  We reconsider the radial Saffman-Taylor instability, when a fluid injected
from a point source displaces another fluid with a higher viscosity in a
Hele-Shaw cell, where the fluids are confined between two neighboring flat
plates. The advancing fluid front is unstable and forms fingers along the
circumference. The so-called Brinkman equations is used to describe the flow
field, which also takes into account viscous stresses in the plane and not only
viscous stresses due to the confining plates like the Darcy equation. The
dispersion relation agrees better with the experimental results than the
classical linear stability analysis of radial fingering in Hele-Shaw cells that
uses Darcy's law as a model for the fluid motion.
