A and B	Dimensional constants in Equations (6) and (7);
Cb	The concentration of adsorbed substance in the bulk of the solution in Equation (1);
C 0	The value of Cb at t = 0;
C S0	The number of free adsorption sites per the surface unit before the beginning of the adsorption process in Equation (1);
C(t)	Time-dependent dimensional parameter in Equations (6) and (7);
d′	Dipole moment of complex “MB + water”;
D	The diffusivity of adsorbing particles in Equation (3);
E	The electric field strength vector near the Nafion surface;
n i0	The equilibrium volume number density of ions in MB solution;
n	The number of adsorbed molecules on the surface unit in Equation (1);
RD	The Debye screening radius;
Y 01	The equilibrium percentage of MB, removed from the solution based on natural water;
Y 02	The equilibrium percentage of MB, removed from the solution based on DDW;
σ	The area of adsorbed molecules in Equation (1);
σ′(t)	The surface charge density on the Nafion membrane;
φ	The subsurface concentration of adsorbed substance in Equation (4);
κ(t)	The absorption coefficient of MB solution;
κ′(t)	The absorption coefficient of Nafion after removing from MB solution;
η and ξ	Variables of integration in Equation (4);
τ 1	The characteristic time of MB adsorption from MB solution based on natural water;
τ1′	The characteristic time of water desorption from MB solution based on natural water;
τ 2	The characteristic time of MB adsorption from MB solution based on DDW;
τ2′	The characteristic time of water desorption from MB solution based on DDW;
ω	The oscillator frequency.