$C_B$	correction coefficient
$C_D$	drag coefficient
d	diameter, m
${\overrightarrow{F}}_{Ba}$	Basset force, N
${\overrightarrow{F}}_D$	drag force, N
${\overrightarrow{F}}_{c,ij}$	contact force, N
${\overrightarrow{F}}_{nc,ik}$	noncontact force, N
${\overrightarrow{F}}_{bf}$	Bubble–fluid interaction force, N
${\overrightarrow{F}}_G$	gravity force, N
${\overrightarrow{\mathrm{f}}}_{\mathrm{bf}}$	reacting force of bubble–fluid interactions, N
h	releasing depth, m
$I$	moment of inertia
$\stackrel{=}{I}$	identity matrix
${\overrightarrow{M}}_{r,ij}$	rolling friction moments, N·m
${\overrightarrow{M}}_{t,ij}$	tangential friction moments, N·m
m	mass, kg
P	pressure, Pa
Q	flow rate, L/h
Re	Reynolds number
$t$	time, s
$t_0$	initial time, s
$t_s$	time to reach liquid surface, s
$t_i-t_e$	the time differences between the simulation and the experiment, s
$\overrightarrow{u}$	fluid velocity, m/s
$V$	volume, m3
$\overrightarrow{v}$	bubble/particle velocity, m/s
$v_b$	bubble velocity in the case with Basset force, m/s
$\overrightarrow{v_i}$	translation velocity of the bubble, m/s
$v_r$	rising velocity, m/s
$v_i-v_e$	the velocity differences between the simulation and the experiment, m/s
Greek symbols
$a$	volume fraction,
$\rho$	density, kg/m3
$\mu$	dynamic viscosity, Pa·s
${\overrightarrow{\omega }}_i$	angular velocity of the bubble, rad/s
${\mu }_{\mathrm{q}}$	shear viscosity of phase-q, Pa·s
${\lambda }_{\mathrm{q}}$	bulk viscosity of phase-q, Pa·s
Subscripts
b	bubble phase
f	fluid phase
q	phase-q