Free surface zone near front stagnant point

Free Surface Zone near Front Stagnant Point 

At high surface activity due to the residual surface mobility, the zone of low surface concentration can appear near the front stagnation point. In other words the angle )/ characterising the dimension of the stagnant cup can be slightly less than n and 

For the sake of simplicity we introduce the special term front stagnation free zone (f.s.f.z.). 

When the bubble is sufficiently big and the Marangoni number (see Section 8.3) is sufficiently small, the viscous compression forces far exceed the linear surface pressure, which decreases the cup. The decrease of the cup angle at bubble velocity increase can be described by Eq. (8.41) at small Reynolds numbers. It turns out that a f.s.fz. appears at small Reynolds number in sufficiently clean water only. 

In contaminated water an f s.f z. can appear at sufficient large Reynolds numbers only. Due to the absence of a quantitative theory of the stagnant cup at high Reynolds numbers one can only estimate the condition of the existence of an f s.f.z.. 

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Bubble Buoyancy for a Wide Range of Reynolds Numbers and Different Degrees of Water Contamination, and the Free Surface Zone near the Front Stagnant Point... 

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