Abbreviations
AEM	anion-exchange membrane
CEM	cation-exchange membrane
KHT	potassium hydrogen tartrate
ED	electrodialysis
Subscript
1	counterion
A	Co-ion
Symbols
${\rho }_{H_{2}O}$	volumetric density of water, g cm–3
$G^0$	Gibbs hydration energy, J mol
d	thickness of the membranes, μm
h	hydration number
Q	ion-exchange capacity of the membrane, mmol g–1
$\overline{V}$	partial molar volume of water, 18 cm3 mol–1
$\sigma$	interfacial surface tension, 0.072 N m–1
θ	contact angle, degree
nw	number of water molecules per fixed group of AEM, molH2O mol–1 f.gr
V	integral volume of sorbed water per gram of dry membrane, cm3 g–1dry
Vt	total water content in the test sample, cm3 g–1dry
A	binding energy of water, J mol–1
r	pore effective radius, nm
P	integral coefficient of diffusion permeability, cm2 s–1
P*	differential coefficient of diffusion permeability, cm2 s–1
$\overline{P}$	diffusion permeability of the membrane gel phase, cm2 s–1
D	diffusion coefficient of the electrolyte, cm2 s–1
α	structural parameter
$\overline{t_i}$	transport numbers of ions i in the gel phase
$t_i$	transport numbers of ions i in the electrolyte
f 1	volume fraction of gel phase in the membrane
f 2	volume fraction of intergel spaces in the membrane
${\overline{c}}_A$	concentration of co-ions of the gel phase, M
${\overline{D}}_A$	diffusion coefficient of co-ions in the gel phase, cm2 s–1
zi	charge number of ion i
KD	Donnan constant
$K_j^i$	ion-exchange equilibrium constant for i and j counterions