Spherical Drop Revisited

Previously the drag on a spherical droplet falling through an infinite fluid was obtained at Equation 7.25. On balancing this force with gravity, the terminal velocity U = U is obtained as 

There are two different ways of accounting for y or Vjy. The first consists of postulating a physical mechanism, which in this case is the effect of the presence of minute quantities of surface active impurities. The second is to define an effective surface viscosity, a matter considered further in Section 8. 

With the first of these models, y is the change in y due to adsorption of the impurities. The transport of these materials in bulk is governed at steady state by the conservation equation 

Finally, one has the equation of conservation of the adsorbed species, which at steady state simplifies from Equation 6.2 to 

In this special case it is considered that the adsorption-desorption is the rate limiting step, consequently c a) = the bulk concentration. It is further assumed that F deviates only a little from the equilibrium given by 

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