$C$	Concentration (mol m−3)
$C_{mean}$	Mean value of $C$ (mol m−3)
$c_K$	Membrane coefficient based on the Knudsen diffusion model (mol m−2 pa−1 s−1)
$c_M$	Membrane coefficient based on the molecular diffusion model (kg m−2 Pa−1 s−1)
$c_m$	Membrane permeation coefficient (mol m−2 pa−1 s−1)
$D_a$	Diffusion coefficient of CO2 in gas feed stream (m2 s−1)
$D_b$	Diffusion coefficient of CO2 in MEA absorbent feed stream (m2 s−1)
$d$	Channel thickness (m)
$d_{h,i}$	Equivalent hydraulic diameter of channel (m), $i=spiral, empty$
$E$	Deviation of experimental results from the theoretical predictions
$E_P$	Further absorption flux enhancement
$f_F$	Fanning friction factor
$H_c$	Dimensionless Henry’s constant
$H_i$	Hydraulic dissipate energy (J kg−1), $i=spiral, empty$
$I_N$	Absorption flux improvement
$I_P$	Power consumption relative index
$k_a$	Mass transfer coefficient in the CO2/N2 gas feed stream (m s−1)
$k_b$	Mass transfer coefficient in the MEA absorbent feed stream (m s−1)
$K_{ex}$	Equilibrium constant
$K_{ex}^{\prime }$	Reduced equilibrium constant
$K_m$	Overall mass transfer coefficient of membrane (m s−1)
${\mathcal{l}w}_{f,i}$	Friction loss (J kg−1), $i=\mathrm{C}{\mathrm{O}}_2/{\mathrm{N}}_2, \mathrm{M}\mathrm{E}\mathrm{A}$
$L$	Channel length ($\mathrm{m}$)
$M_w$	Average molecular weight of CO2 and N2 gas mixture (${\mathrm{k}\mathrm{g} \mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$)
$N_{exp}$	Number of experimental measurements
$P_1$	Saturation vapor pressure in the gas feed flow side ($\mathrm{P}\mathrm{a}$)
$P_2$	Saturation vapor pressure in the liquid absorbent flow side ($\mathrm{P}\mathrm{a}$)
$q_a$	Volumetric flow rate of the gas feed stream (${\mathrm{m}}^3 {\mathrm{s}}^{-1}$)
$q_b$	Volumetric flow rate of the MEA absorbent stream (${\mathrm{m}}^3 {\mathrm{s}}^{-1}$)
$R$	Gas constant (8.314 $\mathrm{J}{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1} {\mathrm{K}}^{-1}$)
$Re$	Reynolds number
$S_{N_{exp}^{″}}$	Precision index of an experimental measurements of absorption flux (mol m−2 s−1)
$S_{\overline{N_{exp}^{″}}}$	Mean value of $S_{N_{exp}^{″}}$(mol m−2 s−1)
$Sc$	Dimensionless Schmidt number
${Sh}^P$	Enhanced dimensionless Sherwood number
${Sh}_{lam}$	Dimensionless Sherwood number for laminar flow
$W_p$	Spiral-ring pitch width (m)
$W_{ratio}$	Ratio of the various promoter widths inserted
$J$	Absorption flux ($\mathrm{m}\mathrm{o}\mathrm{l} {\mathrm{m}}^{-2} {\mathrm{s}}^{-1}$)
${\left|Y_m\right|}_{\mathcal{l}n}$	Natural log mean CO2 mole fraction in the membrane
$z$	Axial coordinate along the flow direction ($\mathrm{m}$)
Greek letters
${\alpha }^P$	Mass-transfer enhancement factor
$\beta$	Aspect ratio of the channel
${\delta }_m$	Thickness of membrane (µm)
$\epsilon$	Membrane porosity
$\overline{v}$	Average velocity ($\mathrm{m} {\mathrm{s}}^{-1}$)
${\rho }_i$	Density ($\mathrm{k}\mathrm{g} {\mathrm{m}}^{-3}$), $i=\mathrm{C}{\mathrm{O}}_2/{\mathrm{N}}_2, \mathrm{M}\mathrm{E}\mathrm{A}$
${\gamma }_m$	Concentration polarization coefficients
Subscripts
1	Membrane surface in CO2/N2 gas feed side
$2\left(\mathcal{l}\right)$	Liquid phase on membrane surface on MEA feed stream
$2\left(g\right)$	Gas phase on membrane surface on MEA side
a	The CO2 /N2 gas feed stream
b	The MEA absorbent feed stream
cor	Correlated results
promoter	Inserting spiral rings as promoters
empty	Empty channel
exp	Experimental results
$g$	Gas feed stream
in	At the inlet
$\mathcal{l}$	MEA absorbent feed stream
out	At the outlet
theo	Theoretical predictions
Superscripts
uni	Uniform promoter widths
des	Descending promoter widths