A	Membrane area: m2	Sh	Sherwood number, dimensionless
Ad	Membrane area in cell, m2	Sc	Schmidt number, dimensionless
Cb	Bulk concentration, kgm−3	Pe	Peclet number, dimensionless
CCL	Boundary layer concentration, kgm−3	Wd	Stability factor with respect to deposition (parameter in No. 4.4, Table 4)
Cg	Gel concentration, kgm−3	s	Sedimentation coefficient
Cgv	Concentration gel layer in volume, m3	t	Time, s
Cm	Intrinsic concentration, kgm−3	tR	Fouling phase time, s
Cp	Permeated concentration, kgm−3	τ	Tortuosity, dimensionless
C0v	Feed concentration, kgm−3	T	Temperature, °C
Dm	Equivalent diffusion diameter of macromolecules (parameter in No. 1.11), m	U	Flow velocity, ms−1
D	Diffusivity, m2s−1	U0	Initial flow velocity, ms−1
d	Diameter of the module, m	v(L)	Average permeate velocity on the length of the filter channel, ms−1
dh	Hydraulic diameter, m	vf	Local filtrate velocity (parameter No. 1.8), ms−1
dp	Pore diameter, m	X(t)	Position change of the equilibrium zone (parameter in No. 4.5)
F	Intermolecular interactions	b	Radius of the stirred cell (parameter of No. 1.8)
fc	Marchetti correction factor	V	Permeate volume (parameter in No. 3.10), L
fcp	Capilar effect	Vc	Permeate volume at the reference time point (parameter in No. 3.10), L
b	Inverse of the solute density (parameter of No. 1.9)	V	Permeate volume, m3
H	Height of liquid over membrane (parameter of No. 1.9), m	V0	Initial permeate volume, m3
η	Non-dimensional distance (parameter of No. 1.9) = x/H	v	Specific partial volume, kgm3
ϕ	Non-dimensional concentration (parameter of No. 1.9) = c/co	v0	Specific partial initial volume, kgm3
fd	Dipole effect	VRF	Volume reduction factor, dimensionless
fe	Steric effect	v	Kinematic viscosity, m2s−1
H	Thickness of the gel layer, m	xi	Proportional parameter of permeability in No. 1.3
J	Permeate flux, ms−1	∆x	Membrane thickness, m
Jf	Final permeate flux, ms−1	X12	Flory-Huggins parameter
Jlim	Limit permeate flux, ms−1	z*	Axial position for osmotic pressure, m
J∞	Saturation (equilibrium) volumetric permeate flux, m3m−2s−1
Jss	Steady-state permeate flux, ms−1	Greek symbols
JW	Flux of pure water permeate, ms−1	δ	Thickness of the boundary layer, m
J*	Hydraulic lifting speed, ms−1	∆π	Osmotic pressure, Pa
Jo	Balance between solute input and output,	γ	Shear rate, ms−1
k	Mass transfer coefficient, ms−1	γm	Shear rate at the wall (parameter in No. 1.11), s−1
ko	Ideal mass transfer coefficient, ms−1	Ɛ	Porosity of the membrane, dimensionless
K	Boltzmann constant (parameter in No. 1.11), Jmol−1K−1	α	Specific resistance of the deposit on membrane, kgm2
L	Length of the module, m	ϵ	Specific gel resistance, m−2
Lp	Membrane permeability, mPa−1s−1	ƐCL	Boundary layer porosity, dimensionless
Lph	Effective permeability reverse flow,	β	Parameter of No. 1.5
mp	Deposited cake weight, kg	σ	Reflection coefficient
MW	Membrane cut-off limit, gmol−1	Ɛg	Solidity of the gel layer, %
∆P	Transmembrane pressure, Pa	εst	Steady-state value of the average solidity, %
Q	Flow rate, m3s−1	μ0	Initial viscosity, Pa s
Rm	Membrane resistance, m−1	μb	Viscosity in the bulk, Pa s
RM	Fouled membrane resistance, m−1	μ	Viscosity, Pa s
Rad,ss	Adsorption resistance, m−1	ρ	Feed density, kgm−3
Rcp	Concentration polarization resistance, m−1	ρpol	Membrane polymer density, kgm−3
Rcp,ss	Steady-state concentration polarization resistance, m−1	γa	Axial speed, ms−1
Re	Reynolds number, dimensionless	υpo	Osmotic pressure limiting flux (m3 m−2 s−1)
Rf	Irreversible resistance, m−1	X12	Flory–Huggins interaction parameter
Rg	Gel resistance, m−1	ϕ	Volume fraction of particles at the distance x from the membrane surface
Rm	Hydraulic resistance, m−1	ϕ	1/Jlim (parameter of No. 3.11), m2sm−3
${\mathrm{R}}_m^{*}$	Experimental resistance (constant ΔP), m−1
Rm i−1	Accumulated resistance at ti−1,
${\mathrm{R}}_{\mathrm{ps}}^{*}$	Concentration polarization differential resistance, dimensionless
Rt	Total resistance, m−1
rCL	Specific resistance of the boundary layer, m−1
ri	Cell radius, m
ro	Initial cell radius, m
rp	Particle radius, m
rpp	Membrane pore radius, m