. 2019 Aug 22;9(9):106. doi: 10.3390/membranes9090106

Table 3.

Model equations for permeate and reverse solute flux using an ALDS membrane orientation.

Model	Permeate Flux	Reverse Solute Flux	Ref.
I	$J_{w} = \frac{D_{F S}}{S} l n (\frac{B + A π_{D S} \exp [- \frac{J_{w}}{k}] - J_{w}}{B + A π_{F S}})$	$J_{s} = B \frac{c_{D S} \exp (- \frac{J_{w}}{k_{D S}}) - π_{F S} \exp (\frac{J_{w} S}{D_{F S}})}{1 + \frac{B}{J_{w}} [\exp (\frac{J_{w} S}{D_{D S}}) - e x p (- \frac{J_{w}}{k_{D S}})]}$	[16] mod., [44]
II_ALDS	$J_{w} = A \frac{π_{D S} \exp (- \frac{J_{w}}{k_{D S}}) - π_{F S} \exp (\frac{J_{w} S}{D_{F S}})}{1 + \frac{B}{J_{w}} [\exp (\frac{J_{w} S}{D}) - e x p (- \frac{J_{w}}{k_{D S}})]}$		[16] mod., [44]
III	$J_{w} = A \frac{π_{D S} \exp (- \frac{J_{w}}{k_{D S}}) - π_{F S} \exp [J_{w} (\frac{1}{k_{F S}} + \frac{S}{D_{F S}})]}{1 + \frac{B}{J_{w}} [\exp [J_{w} (\frac{1}{k_{F S}} + \frac{S}{D_{F S}})] - e x p (- \frac{J_{w}}{k_{D S}})]}$	$J_{s} = B \frac{c_{D S} \exp (- \frac{J_{w}}{k_{D S}}) - c_{F S} \exp [J_{w} (\frac{1}{k_{F S}} + \frac{S}{D_{F S}})]}{1 + \frac{B}{J_{w}} [\exp [J_{w} (\frac{1}{k_{F S}} + \frac{S}{D_{F S}})] - e x p (- \frac{J_{w}}{k_{D S}})]}$	[47]

water permeability A, solute permeability B, structural parameter S, osmotic pressure π, concentration c, diffusion coefficient D, mass transfer coefficient k, feed solution indexed FS, draw solution indexed DS.