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 |
|