The case Pe

If the Peclet number is small, Pe l, two simplifying approximations are possible (Dukhin, 1965, 1981). As it will be shown in the following, if Pe l the surface concentrations differ negligibly from their equilibrium values, 

With these simplifications, it has been shown that the effect of the adsorption layer on the droplet hydrodynamic is quantitatively described by the introduction of a retardation coefficient. The velocity fields inside and outside the drop are respectively 

Explicit expressions for Ac, Af, Xb and v can be derived from the boundary condition (8.10), which under the present simplifications reads 

The final result for the surface concentration distribution at Pe l and the establishment of practically instantaneous adsorption equilibrium is derived from Eqs (8.20), (8.27), (8.28), and 

Condition (8.18) can or caimot be fulfilled at Pe l and the angular distribution dependence of adsorption and surfactant concentration is more complex than the functions given in Eq. (8.19). The concentration distribution must obey the convective diffusion equation. In spite of this, Frumkin Levich (1947) have proposed an approximate theory of the diffusion boundary 

---

One conclusion from these results is that the axial diffusion model begins to fail as Pe, - small, when an open boundary condition is used at the outlet. The case Pe, - small means increasing backmixing, or that the diffusive flux becomes increasingly significant compared with the convective flux. For an open boundary condition, it is also questionable whether the actual response C(e) can be identified with E(B). Furthermore, regardless of the boundary conditions chosen, it is difficult to envisage that cA... 

Statement of the problem. Following [367, 368], let us consider stationary diffusion to a particle of finite size in a stagnant medium, which corresponds to the case Pe = 0. We assume that the concentration on the surface of the particle and remote from it is constant and equal to Cs and C), respectively. The concentration field outside the particle is described by the Laplace equation... 

---