Table 1.

Dimensional variables.

symbol	units	description
${\tilde{L}}_x$, ${\tilde{L}}_y$	m	macroscopic and microscopic length scales
$\tilde{\mathrm{\lambda }}$	m	fluid–fluid interface thickness
${\tilde{\eta }}^{(0)}$, ${\tilde{\eta }}^{(1)}$, $\tilde{\eta }$	Pa s	viscosity of phase 0, phase 1 and the combined phase
${\tilde{\rho }}^{(0)}$, ${\tilde{\rho }}^{(1)}$	kg m−3	density of phase 0 and phase 1
$\tilde{\gamma }$	N m−1	surface tension at fluid–fluid interface.
${\tilde{F}}_b$, ${\tilde{F}}_s$, $\tilde{F}$	N m	bulk, surface and total free energies
${\widetilde{\mathit{\text{u}}}}^{(0)}$, ${\widetilde{\mathit{\text{u}}}}^{(1)}$, $\widetilde{\mathit{\text{u}}}$	m s−1	velocity of phase 0, phase 1 and the combined phase
$\tilde{\zeta }$	kg m−3 s−1	fluid–fluid drag coefficient
$\tilde{p}$	kg m−1 s−2	combined fluid pressure
$\tilde{\sigma }$	kg m−1 s−2	combined stress tensor
$\tilde{R}$	N m s−1	Rayleighian
$\tilde{\mu }$	kg m−1 s−2	capillary pressure
$\tilde{t}$	s	time coordinate
$\widetilde{\mathit{\text{x}}}$	m	space coordinate