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The Effect of Surface Tension on the Stability Criterion

Saffman and Taylor showed that including a surface tension-induced pressure difference across the interface led to a modification of the stability criterion: in this case instead of being unstable to all wavelengths, surface tension stabilizes perturbations of small wavelength and overall the interface is unstable to disturbances of wavelength greater than

eqnarray112

tex2html_wrap_inline453 is maximized with respect to n, i.e. the perturbation grows fastest, when the wavelength is tex2html_wrap_inline507 . In practice, this is the disturbance which will be observed as the instability develops.



brenner@math.mit.edu