Analysis of the terms in the dispersion relation
Consider the terms inside the braces in Eq. (3.13).
I st Term:
It represents the effect of gravity. If
 ,
this term would be positive and have a destabilizing effect (Rayleigh-Taylor instability). This situation could occur when, for example, there is a heavier liquid on top of a lighter one on a surface.
II Term:
It represents the effect of surface tension. For any positive interfacial tension this term would be negative and thus would have a stabilizing effect.
III Term:
If  , it would have a destabilizing effect.
 has the units of energy per unit volume. And  is known as Hamaker constant and depends on the properties of the material.
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