There is a maximum size for the first detaching bubble,
Bubble Rise and Break-up in Volcanic Conduits A. Soldati 1, K. V. Cashman 2, A. C. Rust 2, M. Rosi 1
1 Department of Earth Sciences, University of Pisa (Italy) 2 School of Earth Sciences, University of Bristol (United Kingdom)
Conclusions • System geometry controls rise
velocity, which in turn controls
break-up
• There is a specific size to the
bubbles a system of a certain size
and geometry can deliver
• Being able to measure that size
(through geophysical techniques)
we can invert it to infer upper
conduit geometry
Bubble rise through magma
inside a volcanic conduit is
effectively described by an
appropriate flow regime,
therefore eruptive dynamics
can be studied in the
framework of two-phase flow.
e.g. slug flow will result into
Strombolian paroxysms.
strombolian
paroxysm
slug
flow
Flow Regimes
How: Volume Distribution
1st daughter bubble: 50-95% total volume
2nd daughter bubble: 5-45%
micro bubble: up to 5%
but dependent on the slope geometry
0
20
40
60
80
100
9 11 13 15
dau
gh
ter
bu
bb
les
vol
(%)
original slug volume (ml)
bigger bubble
more even partition
Bubble vs. Slug Size (%)
independent of the original slug size
100
125
150
175
200
100 125 150 175 200 225
up
per
dau
gh
ter
are
a (
mm
2)
original slug area (mm2)
Bubble vs. Slug Size (abs)
Rationale
Existing models of volcanic degassing consider
the feeder conduit to be cylindrical, while
there is strong evidence that it is flattened
instead, like a dyke; such approximation
affects our interpretation and understanding
of deep magmatic processes.
This study aims at determining the impact of
system geometry on active degassing dynamics
in terms of bubbles’ rise velocity and stability.
Analogue Modelling
Flexible set-up
Analogue melt:
golden syrup-water
mixtures (17<η<59 Pa∙s)
Analogue volcanic gas:
air bubbles manually
injected with a syringe
Why: Gas Motion Why: Syrup Motion
0
15
30
45
60
0 3 6 9 12 15 18
slop
e (°
)
original bubble volume (ml)
60
45
30
15
Regime Diagram
stability
field
break-up
field
time
Break-up
undisturbed
rise
head
bulging
middle
thinning
break-up
nose
pointing
Bubbles rise faster in wider spaces.
The shallower the slope, the higher the difference in velocity
between the head and tail of the bubble.
Shallower slopes promote a faster syrup re-occupation
of the channel cross sectional area after the slug passage.
-10
-8
-6
-4
-2
0
0 15 30 45 60 75
bre
ak
-up
lev
el (
mm
)
slope angle (°)
Where
The syrup displaced by the slug, descending along the slope, has
to change direction at the slope-break level to enter the channel;
however, the actual break-up occurs slightly below it.
A steeper slope determines a steeper downward syrup flux,
therefore the steeper the slope, the deeper the break-up level.
Scaling
0
50
100
150
200
0 15 30 45 60
are
a (m
m2
)
slope (°)
15 30 45 60
200
150
100
50
0
slope angle (°)
up
per
dau
gh
ter
size
(m
m2)
Bubble Size vs. Slope
0
10
20
30
40
50
60
70
0 0,5 1 1,5
tim
e (s
ec)
film width (cm)
15p15
30p15
45p15
60p15
Film Width (at y=0)
Temporal Evolution
film
wid
th i
n t
he
chan
nel
-0,5
0,0
0,5
1,0
1,5
0 5 10 15 20 25
Δv (
nm
m/s
ec)
time (sec)
15° 30° 45° 60°
Δvt-h
Geometrical Slug volume → slug lenght/channel width
→ slug lenght/channel cross sectional area
Slope → 1/sin(slope)
Wall Roughness Effect (neglegible)
infrasounds
Experimental Work
Model
Field
Measurements
Better understanding
of volcanic degassing
Improved risk and
hazard assessment
…
Applications
infrasounds
measure emerging
bubble size
invert for
conduit geometry
established correlation between
system geometry and bubble size Kynematical Newtonian Fluid → Non-Newtonian Fluid
Pure Silicate Melt → Real Magma
Golden Syrup → + sugar xls, bubbles
ρ w v Re = ———— < 2300 η
η-dominated
system
laminar flow
conditions
Dynamical
