Table 2.

Example adsorption and desorption fluxes for the isotherms detailed in table 1. Because only the ratio of j_a and j_d is constrained by equilibrium thermodynamics, each pair (j_a and j_d) in this table may be multiplied by any function of C and Γ without changing its equilibrium isotherm. Different surfactants with identical isotherms may respond very differently under dynamic conditions.

Isotherm	Adsorption flux, ja	Desorption flux, jd
Henry	kaC	kdΓ
Freundlich	kaKm−1Cm	kdΓ
Langmuir	kaC (Γ∞ − Γ)	kdΓ
Volmer	kaC (Γ∞ − Γ)	$k_d\Gamma \text{exp}\left[\frac{\Gamma }{{\Gamma }_{\infty }-\Gamma }\right]$
Frumkin	kaC (Γ∞ − Γ)	$k_d\Gamma \text{exp}\left[-\frac{\beta \Gamma }{k_{B}T}\right]$
van der Waals	kaC (Γ∞ − Γ)	$k_d\Gamma \text{exp}\left[\frac{\Gamma }{{\Gamma }_{\infty }-\Gamma }-\frac{\beta \Gamma }{k_{B}T}\right]$