Hypothesis of incomplete retardation

Hypothesis of Incomplete Retardation of a Bubble Surface at Re 1 and Presence of a Dynamic Adsorption Layer 

Up to = 0.03 cm bubbles float up like solid spheres even in distilled water. This is possible both at a complete and at a strong (incomplete) retardation of the bubble surface. At a complete retardation the velocity at any point of the surface (in a system associated with the bubble movement) is equal to zero. A strong retardation means a small surface velocity as compared with the bubble velocity, 

Under condition (8.90), the viscous stress tensor, and therefore, the bubble rising velocity depends very weakly on the motion of the surface. Thus, the merging of curves 1 to 4 in Fig. 

3 at a 0.03 cm does not exclude the possibility of slow bubble surface motion. At the same time it points to the presence of some uncontrollable factors causing a strong or complete retardation of the surface at a 0.03 cm. The fact that at a 0.03 cm this factor is weak is difficult to understand along with its unexpectedly strong effect, which supposedly results in a 

Papers by Frumkin Levich (1947) and by Derjaguin Dukhin (1961) are apparently only of methodical nature, since they do not take into account the bubble surface effect which causes retardation at a 0.03 cm. Indeed if at a 0.03 cm a strong but not complete retardation of the bubble surface takes place, the discussed theories cannot be applied directly, but can be transformed to the hypothesis of incomplete retardation. 

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When deposition of emulsion drops is investigated, sedimentation can be neglected so that the first term in Eq. (10.27) dominates even at strong retardation. Retardation of the surface becomes less efficient with increasing bubble dimensions and, respectively, Reynolds number. Therefore, the experimental verification of the hypothesis of incomplete retardation of the surface at intermediate Reynolds numbers is of interest. A maximum removal of impurities fi om the water used is important in such experiments. 

The consideration made is of semi-quantitative nature, and is justified both at moderate and large Reynolds numbers. At moderate Reynolds numbers, a refinement of the theory seems to be premature since the notion of the incomplete retardation of the surface is a hypothesis which needs an experimental check. At large Reynolds numbers, a quantitative consideration of the effect of DAL on the elementary flotation act will prove to be possible generally only after the quantitative theory of DAL has been developed. The given evaluations confirm that the effect of DAL on the transport stage of microflotation is high at large Reynolds munbers and, possibly, also at moderate values. 

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