The problem of penetration of a fluid into a porous medium containing a more viscous liquid is investigated. It is known that the displacement front may become unstable in this case because it may break up into "fingers". The problem of inception of fingers has been treated previously in the literature by describing the displacement front in terms of its Fourier transform. In the present paper, we generalize earlier procedures by making allowance for an arbitrary elemental growth law. Furthermore, we assume that the phenomenon of fingering is not solely governed by the prevailing flow potentials, but also by the spectrum of heterogeneities in the porous medium. This is achieved by introducing a constant characteristic of the frequency of the heterogeneities in the porous medium. It then turns out that the maximum rate of growth as a function of wave length is considerably shifted from that predicted in the literature. At the same time it is also shown that the difficulty encountered by other workers, which consists of small wave lengths growing at an infinitely high rate, is being avoided.
When a fluid enters a porous medium displacing a more viscous liquid, an interesting kind of instability may occur at the displacement front. Protuberances may arise which shoot through the porous medium at relatively great speed, leaving behind the large amounts of the liquid intended to be displaced. This phenomenon is commonly referred to as "fingering".
The problem of fingering is an extremely involved one owing to the complexity of the phenomenon. To treat it theoretically, drastic simplifications have to be made. One way to do this is to confine one's attention to the very beginning of the occurrence of the instabilities. The displacement equations can then be linearized, the displacement front can be described by its Fourier transform and the growth law for each spectral component can be deduced.
An attempt along these lines has recently been published by Chuoke, et al., who showed how the prevailing flow potentials affect the various spectral components of a displacement front on the verge of instability. Chuoke's formula contains a capillary pressure term as an essential feature; if the limit is taken with this term being set equal to zero, a disconcerting difficulty arises. The spectral components with the smallest wave lengths are found to grow at the fastest rate; in fact, the rate becomes infinite for the wave length approaching zero.
