Symbol Description Unit
a Bubble major axis [mm]
A Cross-sectional area [mm2]
AR Bubble aspect ratio (ratio of the major to minor axis) [-]
Ar Archimedes number [-]
BSD Bubble size distribution [-]
C Proportionality coefficient [-]
Ca Capillary number [-]
d Bubble diameter [mm]
D Column diameter [mm]
Eo Eötvös number [-]
F Force [kgms-2]
Fr Froude number [-]
g Gravitational acceleration [ms-2]
k Proportionality coefficient [-]
Mo Morton number [-]
n Number of bubbles in a sample population [-]
Oh Ohnesorge number [-]
P Input power from gas injection [kgm2s-3]
PDF Probability density function [-]
Q Volumetric flow rate [m3s-1]
r Average pore radius [μm]
Re Reynolds number [-]
RMS Standard deviation of bubble size distribution [mm]
S(db) Skewness of bubble size distribution [mm]
U Velocity [mms-1]
We Weber number [-]
Greek letters and symbols Greek letters and symbols Greek letters and symbols
Symbol Description Unit
∆H Vertical distance between two pressure taps [m]
∆p Differential pressure [kg m-1s-2]
ε Void fraction [-]
κ(db) Kurtosis of bubble size distribution [-]
μ Viscosity [kgm-1s-1]
ρ Density [kgm-3]
σ Surface tension [kgs-2]
Χ Froude number exponent in Equation (17) [-]
Ψ Archimedes number exponent in Equation (17) [-]
Ω Eötvös number exponent in Equation (17) [-]
Subscripts Subscripts Subscripts
10 Arithmetic mean diameter
32 Suater mean diameter
95 Maximum stable bubble size
b Bubble
B Buoyancy force
cap Capillary
cr Critical
D Drag force
eq Equivalent
G Gas phase
L Liquid (phase)
m Specific value
max Maximum
min Minimum
mf Most frequent
p Porous sparger
SG Superficial gas