$\overrightarrow{u}$	velocity vector (m/s)
$P$	pressure (Pa)
$\overrightarrow{g}$	gravity vector (m/s2)
$\overrightarrow{F}$	external force (N)
$J_i$	diffusion flux (kg/m2·s−1)
$D$	diffusion coefficient(m2/s)
$c_i$	concentration of phase i (mol/L)
$M$	mixing index (−)
$C_i$	concentration of ethanol of sampling point (mol/L)
$C_0$	average concentration of ethanol of cross-section (mol/L)
$E$	extraction efficiency (−)
$q$	volume ratio of water to n-butanol (−)
$m$	partition coefficient (−)
KLa	volumetric mass transfer coefficient (s−1)
$C_{w,i}$	concentration of succinic acid in the water phase at the inlet (mol/L)
$C_{w,0}$	concentration of succinic acid in the water phase at the outlet (mol/L)
$C_{0,i}$	concentration of succinic acid in the organic phase at the inlet (mol/L)
$C_w^{*}$	equilibrium concentration of succinic acid in the water phase (mol/L)
$C_0^{*}$	equilibrium concentration of succinic acid in the organic phase (mol/L)
$d$	hydraulic diameter at the inlet (m)
Greek symbols
${\alpha }_i$	volume fraction of phase i (−)
${\rho }_i$	density of phase i (kg/m3)
${\rho }_m$	average density (kg/m3)
${\rho }_w$	water phase density (kg/m3)
${\rho }_0$	organic phase density (kg/m3)
$\mu$	viscosity (Pa·s)
${\mu }_m$	viscosity (Pa·s)
${\mu }_w$	water phase viscosity (Pa·s)
${\mu }_0$	organic phase viscosity (Pa·s)
$\tau$	residence time (s)
Dimensionless numbers
Re	Reynolds number (−)