Adsorption kinetics model for the maximum bubble pressure method

Adsorption Kinetics Model for the Maximum Bubble Pressure Method 

The idea of a maximum bubble pressure instrument is that the pressure inside a growing bubble passes through a maximum. The pressure maximum is reached at a hemispherical bubble size. After the maximum has passed the bubble grows fast and finally detaches. For quantitative interpretation of bubble pressure experiments details are required on the time scale of the bubble growth (cf Fig. 5.8). First of all, the dead time, needed by a bubble to detach after it has 

The time for bubble growth to a hemisphere t, is the difference between the total bubble time Tb and the dead time x, p and L are pressure and gas flow rate and p and are the respective values at a critical point. From considerations discussed above about adsorption processes at the surface of growing drops it is concluded that the situation with the growing bubble is comparable, at least until the state of the hemisphere. Then, the process runs without specific control and leads to an almost bare residual bubble after detachment due to the very fast bubble growth. 

Fainerman et al. (1993c, 1994b) presented an analysis of the adsorption proeess at the bubble surface in order to derive a relation between the bubble life time and the effective surface age Tj. The basis of this analysis is the condition of constant pressure p at any moment of bubble life in the time interval 0 t t. 

cp is the angle between the bubble surface and the front area of the capillary of tip diameter 2r p. The bubble growth in the time after having reached the hemisphere is very fast, 

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