The theory of short range hydrodynamic interaction

The theory of short range hydrodynamic interaction (SRHI) 

When a particle moves along a bubble surface the conditions for the particle/bubble interaction changes and the short range interaction becomes unsteady. However, in local coordinates linked to the particle the interaction can be considered as quasi steady. The system of cylindrical coordinates can be used with its centre on the bubble surface and a z-axis crossing the centre of the moving particle. Such cylindrical coordinates simplify the description of 

The equations describe that stage of the particle movement when the liquid interlayer is thin and the distance between the centres of a particle and the bubble is equal to a. The rates of interlayer thinning and particle movement are identical and are controlled by the action of the pressing force F and the resistance force (product of Stokes drag coefficient and the 

The function f3(H) yields the dependence on the film thickness. After the substitution into Eq. (11.103) we obtain 

The functions fpf2,f3 are determined by Goren (1970), Goren O Neil (1971), Goldman et al. (1967), Spielman Fitzpatrick (1973). At a distance of the order of the particle size, i.e. at H 1, we can assume fjfj/fjwl and the particle trajectory coincides with the liquid streamline. 

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