The Limit of Fast Adsorption Kinetics

We now turn to a case in which the interface concentration is determined by the mass transfer process to and from the bulk fluids. We begin with the case in which the fastest of the surfactant transport processes is the adsorption desorption of surfactant between the exterior bulk fluid where it is assumed to be soluble and the interface, Bi 1. In particular, we assume that Bi (ca/V,Xjk)Pe, so that, according to (7-265), 

For the case of a drop rising by means of buoyancy through a quiescent Newtonian fluid, the velocity and concentration fields will be axisymmetric. Hence, because the Reynolds numbers are assumed to be low, the governing equations of motion are again 

For the mass transfer problem, we have the governing equation (7 260)  

The interfacial mass transport equation is (7 266). For convenience, we write this equation in the form 

The convenience of the form (7-300) will become evident shortly. In addition, we assume that the dimensionless bulk concentration 

---