This work is an extension of Taylor's earlier work on the instability of the interface between two fluids of equal viscosity when the less dense fluid is accelerated towards the more dense fluid. Rayleigh considered the buoyancy-driven instability of the static base state when a fluid of low density lies underneath a fluid of greater density, which came to be called the Rayleigh instability. In 1950 Taylor [9] published a paper explaining that this instability is identical to that which develops from the dynamic base state when one fluid of lesser density is accelerated towards another of greater density, whereupon the instability became known as the Rayleigh-Taylor instability.
The Saffman-Taylor instability is the over-damped analog of the Rayleigh-Taylor instability. In their paper, published in 1956, Saffman and Taylor derived the stability criterion based on viscous and gravitational effects. They showed that when the interface is unstable, surface tension will stabilize perturbations with sufficiently small wavelengths, and determined the fastest growing mode.
Saffman and Taylor also undertook experimental work. The velocity
field in a porous medium is equivalent to that in a Hele-Shaw cell
(two large flat plates separated by a narrow gap) averaged
perpendicular to the plates, and they used this apparatus to study the
flow. One of their observations was that when the finger developed in
a channel the ratio 
of the width of the finger to the width
of the channel was approximately one half except when the flow speed
was slow
.
Finally, Saffman and Taylor determined the shape of the interface for
one finger in a channel analytically. They found an infinite family
of solutions dependent on the value of the parameter which
was undetermined analytically. Taking 
in accordance
with experimental observations of systems in which the flow is not
slow yielded a solution which is in good agreement with what is
observed experimentally. When the flow is slow, however, the
experimental observations and the analytical results differed
significantly. Saffman and Taylor were unable to explain this
discrepancy.
When the effects of gravity are negligible, there is just one
nondimensional parameter which can be formed from the material
constants, 
, which represents the ratio of viscous to
surface tension effects. We shall see that this is an important
parameter in determining the behavior of the system.