The above analysis shows that the formation of a genuine cusp is possible for both Newtonian and second order fluids. Thus it seems very unlikely that the jump discontinuity in the bubble velocity can be attributed to the cusp formation. It is most likely due to a discontinuity in the surface forces, as pointed out recently by Rodrigue and De Kee (1999). Thus a study of the convection of adsorbed surfactants at the surface is desirable.
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