Non-equilibrium distribution of adsorbing ions along the diffuse layer

Non-Equilibrium Distribution of Adsorbing Ions Along the Diffuse Layer and Quasi-Equilibrium Distribution of Counterions 

We will consider the stationary distribution of concentration of surfactant anions within DL under conditions when the flux of these ions to the surface differs from zero. Under these conditions c(x) is the solution of the equation 

The aim now is to derive an equation for the flow of surfactant anions to the surface of a rising bubble. To do so, we have to calculate the integral on the right hand side of Eq. (7.22) 

If the concentration of coions deep inside DL is neglected, the distribution of the electric potential this region is described by the simplified Poisson-Bolt2mann equation (cf Section 

This result is valid under condition (7.11) and at z-z 2) 0. The flux of surfactant anions under discussion can be expressed in terms of K(i /s,), 

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