Abstract
An important problem concerning the Hele-Shaw displacements is to minimize the Saffman - Taylor instability. To this end, some constant viscosity fluid layers can be introduced in an intermediate region (I.R.) between the displacing fluids. However, we prove that very small (positive) values of the growth rates can be obtained only for a very large (unrealistic) I.R. On the contrary, when the I.R. length is constrained by certain conditions (for instance, geological), then the maximum value of the growth constants can not fall below a certain value, not depending on the number of layers. This maximum value is not so small.
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