Table 2.

Summary of the effective parameters introduced in the text, their definition, and the corresponding equation in the text

Parameter	Definition	Equation	Description
${\kappa }^{\mathrm{e}\mathrm{ff}}$	$\kappa -\overline{\kappa }{\lambda }_2/{\mathrm{\Lambda }}_2$	Below Eq. 10	Effective permeation coefficient
$P_{\mathrm{1,2}}^{\mathrm{e}\mathrm{ff}}$	${\mathrm{\Pi }}_{\mathrm{1,2}}^{\mathrm{e}\mathrm{x}\mathrm{t}}-P_{\mathrm{h}}^{\mathrm{c}}-\frac{J_{\mathrm{p},\mathrm{1,2}}}{K_{\mathrm{1,2}}}-\frac{2}{3}\left({\zeta }_0{\nu }_0+{\lambda }_3+\frac{{\mathrm{\Lambda }}_3{\lambda }_2+\left(3{\nu }_1/2-2{\nu }_0{\nu }_3\right){\mathrm{\Lambda }}_1}{{\mathrm{\Lambda }}_2}\right)$	Eq. 25a	Effective pressure
${\gamma }_{\mathrm{1,2}}^{\mathrm{a}\mathrm{p}\mathrm{p}}$	${\gamma }_{\mathrm{1,2}}\mp 4{\nu }_3{\mathrm{\Lambda }}_3/{\mathrm{\Lambda }}_2$	Eq. 25b	Apparent surface tension
${\gamma }_0^{\mathrm{a}\mathrm{p}\mathrm{p}}$	$\left(3{\nu }_1/2-2\left(2+{\nu }_0\right){\nu }_3\right)\left({\mathrm{\Lambda }}_3/{\mathrm{\Lambda }}_2\right)$	Eq. 25b	Apparent surface tension
${\lambda }^{\mathrm{e}\mathrm{ff}}$	${\lambda }_1-{\mathrm{\Lambda }}_1{\lambda }_2/{\mathrm{\Lambda }}_2$	Eq. 25c	Effective pumping coefficient
$R_0$	$K_2\overline{\eta }$	Eq. 12	Characteristic length
${\tau }_0$	$\overline{\eta }/\left|P_2^{\mathrm{e}\mathrm{ff}}\right|$	Eq. 12	Characteristic time
$Q_0$	$4\pi {\overline{\eta }}^2{K}_2^3\left|P_2^{\mathrm{e}\mathrm{ff}}\right|$	Eq. 12	Characteristic volumetric flux
$I_0$	$4\pi {\mathrm{\Lambda }}_2\overline{\eta }{K}_2\left|P_2^{\mathrm{e}\mathrm{ff}}\right|/\left|{\lambda }_2\right|$	Eq. 12	Characteristic electric current
${\delta }_{\mathrm{1,2}}$	$P_{\mathrm{1,2}}^{\mathrm{e}\mathrm{ff}}/\left|P_2^{\mathrm{e}\mathrm{ff}}\right|$	Eq. 18	Dimensionless effective pressure
$\widehat{\lambda }$	${\lambda }^{\mathrm{e}\mathrm{ff}}\overline{\eta }{K}_2/\left|P_2^{\mathrm{e}\mathrm{ff}}\right|$	Eq. 18	Dimensionless effective pumping
${\widehat{v}}_2$	$\left(3v_2-\left(2\left({\gamma }_2^{\mathrm{a}\mathrm{p}\mathrm{p}}+{\gamma }_0^{\mathrm{a}\mathrm{p}\mathrm{p}}\right)\right)/\overline{\eta }\right)/\left(K_2\left|P_2^{\mathrm{e}\mathrm{ff}}\right|\right)$	Eq. 18	Dimensionless effective velocity
$\widehat{Q}$	$Q^{\mathrm{e}\mathrm{x}\mathrm{t}}/Q_0$	Below Eq. 13	Dimensionless volumetric flow
$Î$	$I^{\mathrm{e}\mathrm{x}\mathrm{t}}/I_0$	Below Eq. 13	Dimensionless electric current
$w_{\mathrm{0,1}}$	$j_{\mathrm{0,1}}Î+u_{\mathrm{0,1}}\widehat{Q}$	Below Eq. 13	Dimensionless external contributions
$u_0$	$1-\frac{K_2}{1-\varphi }\left(3{\nu }_2-4{\nu }_0{\nu }_4+\frac{\overline{\kappa }}{{\mathrm{\Lambda }}_2}\left(3{\nu }_1-4{\nu }_0{\nu }_3\right)\right)$	Eqs. 14 and 15	—
$u_1$	${\kappa }^{\mathrm{e}\mathrm{ff}}\overline{\eta }{K}_2^2/\left(1-\varphi \right)$	Eq. 14	—
$j_0$	$\left(3{\nu }_1-4{\nu }_0{\nu }_3\right)/\left({\lambda }_2\overline{\eta }{K}_2\right)$	Eqs. 16 and 17	—
$j_1$	1	Eq. 16	—