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Comptes Rendus
Géoscience — Sciences de la Planète
Supplementary material to the article available at:
https://doi.org/10.5802/crgeos.214
Supplementary material: Bubble connectivity in
experimentally-sheared crystal-bearing silicic melts
Camille Daffosa, CarolineMartel ∗, a, Laurent Arbaret a and Rémi Champallier a
a Institut des Sciences de la Terre d’Orléans (ISTO), Univ. Orléans, CNRS, BRGM,
UMR 7327, Orléans, France
E-mails: camille.daffos@univ-orleans.fr (C. Daffos), caroline.martel@cnrs-orleans.fr
(C. Martel), laurent.arbaret@univ-orleans.fr (L. Arbaret),
remi.champallier@cnrs-orleans.fr (R. Champallier)
1. Methods
The experiments consisted in three main phases:
(i) synthesis of a crystal-bearing hydrated glass by
melt hydration in an internally-heated pressure ves-
sel and mixing of the obtained hydrated glass with
plagioclase crystals, (ii) H2O-bubble formation by
decompression in the Paterson-type apparatus, and
(iii) subsequent deformation in simple shear of the
three-phase magma.
1.1. Experimental methods
1.1.1. Synthesis of crystal-bearing hydrated glasses
The anhydrous starting glass is a haplogranite
(HPG8, prepared by Schott AG, Germany) with the
eutectic composition of the quartz–albite–orthoclase
system [Holtz et al., 1992; composition in wt%: 78.6
SiO2, 12.5 Al2O3, 4.6 Na2O, 4.2 K2O). About 10 g of
the powdered (<90 µm) anhydrous HPG8 glass was
mixed with either about 1 g or 0.5 g deionized H2O,
and sealed in 20-mm diameter and 30-mm long Au
capsules. The HPG8 hydrations were performed in
∗Corresponding author.
internally-heated pressure vessels pressurized with
argon (at ISTO) at T of 750 and 950 °C and P of
400 MPa (for the capsules containing 1 g H2O) and P
of 170 MPa (for the capsules containing 0.5 g H2O).
The H2O contents introduced in the capsules were
enough to ensure H2O solubilities at P of 400 MPa
and 170 MPa (950 °C) according to the H2O solubil-
ity model of Newman and Lowenstern [2002], i.e. 9.6
and 5.0 wt% H2O, respectively. Hydration durations
were 48 to 96 h, which is long enough to homog-
enize H2O by diffusion in the HPG8 glass powder,
according to Zhang and Behrens [2000]. The sam-
ples were isobarically quenched by shutting down
the furnace, in order to avoid H2O exsolution from
the melt. The recovered hydrated HPG8 glasses were
ground in an agate mechanical grinder to obtain a
∼20-µm grain size powder, to which plagioclase crys-
tals were added. We purchased commercially a pla-
gioclase block of labradorite (anorthite content of
50 to 70 mol%) whose composition was tested for
chemical resistance at the contact of the HPG8 hy-
drated melt under the elected run conditions. The
labradorite block was reduced into pieces using a
high-voltage pulsed power fragmentation apparatus
(Selfrag, at BRGM, Orléans, France). The main advan-
tage of the Selfrag is to crush rocks at the grain joints,
so that we were expecting more or less elongated bits,
ISSN (electronic) : 1778-7025 https://comptes-rendus.academie-sciences.fr/geoscience/
2 Camille Daffos et al.
Supplementary Figure S1. The 50–90 µm frac-
tion size of the plagioclase crystals.
i.e. resembling the natural plagioclase shapes. The
recovered fragments were sieved to 50–90 µm (Sup-
plementary Figure S1), before manual mixing with
the hydrated HPG8 glass powder following differ-
ent weight proportions. Very minor amounts of crys-
tals other than plagioclase (presumably Fe–Ti oxides
and pyroxenes) have been found in the fragments,
likely coming from mineral inclusions trapped in the
labradorite block. Recalculated to volume propor-
tions using a 2.7 density for labradorite, four series
based on their crystal contents (Φc_melt_3D) have been
chosen: 0, 21, 50, and 70 vol%.
1.1.2. Synthesis of bubble-bearing magmas
About 1.6–2.0 g of the crystal-glass mixtures were
sealed in 14-mm diameter and 12-mm long Cu cap-
sules in order to prevent H2O loss. The capsules were
sandwiched between alumina spacers, alumina and
zirconia pistons, and the whole assembly was coated
by an iron jacket (Figure 1b). The sample column was
placed at the hot spot of the internal Mo-furnace of
the gas-medium (argon) Paterson rig [Paterson and
Olgaard, 2000; Australian Scientific Instruments Pty
Ltd, at ISTO; Figure 1a]. The samples were (i) pressur-
ized to 240 MPa, (ii) heated to 850 °C (pressure will
reach 300 MPa) at a rate of 10 °C/min and maintained
during 15 min for thermal equilibration, then (iv) de-
compressed to 50 MPa within 9 to 20 min in order to
generate H2O bubble nucleation, (v) maintained for
45 min to let bubbles grow, and (vi) cooled to 650 °C
(crystal-free samples) or 750 °C (crystal-bearing
samples), in order to allow further deformation with-
out inconvenient jacket breakage, followed by a 15-
min dwell for thermal equilibration (Figure 1c). In the
Paterson rig, all samples were decompressed from
300 MPa (maximum pressure allowed in the Paterson
rig), so that the samples pre-hydrated at 400 MPa
(∼9.6 wt% H2O) nucleated between 300 and 50 MPa
[possibly during annealing at 300 MPa, although the
high supersaturations >100 MPa required for homo-
geneous nucleation in silica-rich melts would favour
nucleation at pressure below 300 MPa; Mourtada-
Bonnefoi and Laporte, 2002]. The samples hydrated
to 5.0 wt% H2O nucleated at pressure between 170
and 50 MPa.
1.1.3. Torsion experiments
Keeping the experimental setup as it was after
decompression, deformation in right-lateral simple
shear was carried out at T of 650 °C (crystal-free sam-
ples) or 750 °C, P of 50 MPa, and shear rate γr of
2× 10−4 s−1. Torsion durations were 1 or 2 h, which
led to bulk finite shear γ of 1 and 2, respectively, [see
Paterson and Olgaard, 2000, for γ calculation]; note
that in torsion, the sample centre experiences zero
torque and, therefore, zero strain; both strain and
strain rate increase radially toward the sample exte-
rior. Temperature, pressure, shear stress and angu-
lar displacement were live recorded on a computer.
The experiment was ended by relaxing the stress, fol-
lowed by an isobaric quench (shut of the furnace
while maintaining 50 MPa confining pressure) at a
rate of ∼40 °C/min from 750 to 200 °C. According to
Mader et al. [2013], the relaxation time (λ) of a bub-
ble writes as: λ = (a ×ηmelt)/σ, where a is the bub-
ble’s equivalent spherical radius, ηmelt is the viscosity
of the hydrated melt, and σ is the surface tension at
the bubble-liquid interface. Considering a = 10 and
100 µm (from the sample analyses), ηmelt = 106.3 Pa·s
[HPG8 melt with 2.9 wt% H2O at 50 MPa and 750 °C;
Hess and Dingwell, 1996], and σ= 0.2 N/m at 50 MPa
[Bagdassarov et al., 2000], λ would be about 2 and
17 min, respectively. At 700 °C, ηmelt = 106.9 Pa·s and
λ becomes 7 and 66 min for bubble radius of 10 and
100 µm, respectively. During quenching, about 42 s
are spent between 750 and 700 °C, so that we infer
that in our experiments, the small 10-µm radius bub-
bles fully relaxed (returned to sphericity), whereas
the larger 100-µm radius bubbles experienced lim-
ited relaxation during quenching. After experiment,
Camille Daffos et al. 3
Supplementary Figure S2. After run sample preparation for analyses. (a) Cutting, (b) polish section with
one outer piece of the sample, and (c) bore of a 3-mm cylinder in the middle piece.
the sample column was extracted from the vessel and
the extent of deformation was verified by the progress
of the pen-markers between the non-deformed (pis-
ton) and deformed (sample) parts. The iron jacket
was removed to release the Cu-capsule containing
the sample. Note that shear stress could not be de-
termined in-situ during deformation due to the low
viscosity (high temperature) of the samples, so that
bulk viscosity could not be measured.
1.2. Analytical methods
1.2.1. Microstructural analysis
After experiment, the Cu capsule containing the
sample was cut following two sections parallel to
the shear plane, in order to expose their longitudi-
nal tangential surfaces, which represent the planes of
maximum shear strain [Paterson and Olgaard, 2000]
(Supplementary Figure S2a). One of the two sections
was placed in epoxy, polished, and carbon coated for
two-dimensional (2D) observations using a scanning
electron microscope (SEM; Merlin Compact Zeiss at
ISTO) (Supplementary Figure S2b).
The sample polished sections being about 5–
10 mm long by 10–15 mm wide and often show-
ing microtextural heterogeneities, the sample anal-
ysis was performed by processing 5 to 10 thumb-
nail images that covered the whole section. The
SEM images were segmented using the SPO2003
image-processing software [Launeau and Robin,
1996, Launeau and Cruden, 1998], in order to de-
termine the average 2D bubble and crystal contents
(accuracy of ±3 area% determined on repeated mea-
surements), bubble and crystal sizes, shapes, and
orientations (following the method of intercepts;
[Launeau and Robin, 1996], and bubble and crystal
number densities, as follows:
• Crystal-free bubble content: Φb_melt_2D =
(bubble area)/(bubble area + glass area) ×
100;
• 2D-bulk porosity: Φb_bulk_2D = (bubble
area)/(bubble area + glass area + crystal
area) × 100;
• 2D-bubble-free crystal content: Φc_melt_2D =
(crystal area)/(crystal area + glass area) ×
100;
• 2D-bulk crystal content: Φc_bulk_2D = (crys-
tal area)/(bubble area + glass area + crystal
area) × 100;
• 2D-bulk glass content: Φg_bulk_2D = glass
area/(bubble area + glass area + crystal area)
× 100;
• Crystal-free areal bubble number density:
BND = (number of bubbles)/(glass area).
• Bubble-free areal crystal number density:
CND = (number of crystals)/(glass area).
• Bubble long and short axes; bubble eccen-
tricity: R = (long axis)/(short axis); the radius
(a) equivalent to the bubble surface; bubble
orientation to the horizontal (θb).
1.2.2. X-ray Computed Tomography (XCT)
After the removal of the two longitudinal tangen-
tial sections for the 2D analysis, the sample rest was
bored perpendicularly to the shear plane (0 strain
4 Camille Daffos et al.
in centre; Supplementary Figure S2c) in order to get
an oriented 3-mm core sample for three-dimensional
(3D) analysis using XCT (Phoenix NanoTOM at ISTO).
The XCT images were reconstructed using a Phoenix
3D software with a voxel resolution of 1.4-µm side.
A qualitative analysis of the whole core sample was
performed in order to segment the glass+crystal ma-
trix, the isolated bubbles, and the bubbles connected
to the outside of the core sample, using the com-
mercial software VGStudio Max. Smaller sample vol-
umes (cubes of 600 and 1400-µm side) were defined
to qualify bubble size and spatial distribution, as well
as to quantify the 3D bulk porosity (Φb_bulk_3D) and
the volume content of bubbles connected to the sam-
ple border (Φb_connect_3D), using the commercial soft-
ware Blob3D. The porosity measurements,Φb_bulk_3D
and Φb_connect_3D, were determined with an accu-
racy of ±3 vol%. Because the small size of the ex-
perimental samples precludes porosity 3D measure-
ment iterations, the assumption made here is that
the volumes on which the measurements have been
made are representative of the whole experimental
sample.
1.2.3. Glass H2O contents
The H2O contents of the starting hydrated glasses
were checked using an elemental analyser (Ther-
moFlash2000 at ISTO), given with a precision of
±0.15 wt%. The results confirmed the H2O solubil-
ity data from [Newman and Lowenstern, 2002], i.e.
H2O contents of 9 to 10 wt% for the 400-MPa hydra-
tions and ∼5 wt% for the 170-MPa hydrations. As the
elemental analyser is a destructive method (sample
pyrolyze), the H2O contents of the residual glasses
from the run products were analysed using an elec-
tron microprobe (EMP; Cameca SX Five at ISTO) fol-
lowing the “by-difference” method of Devine et al.
[1995], and using HPG8 glass standards with known
H2O contents [samples from Martel et al., 2000]. The
analysed elements were Si, Al, Ca, Na, K, with alka-
lis analysed first, in order to minimize loss under the
electron beam. The EMP conditions were set to an ac-
celeration voltage of 15 kV, a beam current of 6 nA,
peak/background counting times of 10/5 s for all el-
ements, and a defocussed beam of 10× 10 µm size.
The analytical errors on major elements were calcu-
lated at ∼1% (relative) for SiO2, Al2O3 and CaO, and
5% for Na2O and K2O, and ±0.7 wt% on the H2O con-
tent.
Some of the residual glasses were double-checked
by microRaman spectroscopy. The Andor Shamrock
500i spectrometer is coupled with a Nikon ECLIPSE
Ni-U microscope uses a long working distance Nikon
objective (100×, numerical aperture of 0.8), which
allows lateral resolution of 1–2 µm2. A monochro-
matic 532 nm Coherent Genesis MX SLM laser was
used as exciting source (output laser power was set
to 300 mW). The 1200 lines/mm grating was used,
providing two spectral windows spanning 200 to
1500 cm−1 (silicate network) and 2895 to 3800 cm−1
(OH stretching region). For each analysis, the acqui-
sition time was 60 s. In order to determine H2O con-
tent, the HPG8 glass standards were measured in the
same analytical conditions as the samples. The Ra-
man spectra were proceeded following the method of
Behrens et al. [2006].
1.3. Calculations
1.3.1. Gas fraction
The gas fraction equation of Jaupart and Alle-
gre [1991] calculates the gas volume (αmelt) resulting
from degassing of a H2O-saturated melt in closed-
system. The equation writes as follows:
αmelt = 1/{1+ρgas/[(Cwi −Cw f )×ρliq]}×100 (1)
where ρgas is the H2O density at T and final P cal-
culated after Burnham et al. [1969], ρliq is the melt
density taken as 2400 kg/m3, Cwi and Cw f are the
H2O solubilities at initial and final pressures, re-
spectively, calculated after Newman and Lowenstern
[2002]. The uncertainty associated with the αmelt cal-
culation mostly depends on the precision of the melt
H2O contents (Cwi and Cw f ). Assuming an uncer-
tainty of ±0.7 wt% on the EMP “by-difference” H2O
measurements suggests uncertainties of ±3 vol% on
αmelt calculations.
1.3.2. Bulk viscosity
The bulk viscosity (ηbulk) of our samples were
calculated using the Equation (3.2) of Truby et al.
[2015] that gives the relative viscosity (ηr , with ηr =
ηbulk/ηmelt) of a three-phase suspension of bubbles
and crystals in a Newtonian liquid undergoing steady
flow. The model adopts an “effective medium” ap-
proach in which the bubbly liquid is treated as a con-
tinuous medium which suspends the crystals. The
model is valid for a low bubble capillary number (C a)
Camille Daffos et al. 5
regime. C a describes the ratio of the viscous stress
to the restoring stress and writes as follows: C a =
(ηmelt ×γr )/(σ/a), where a is the bubble’s equivalent
spherical radius. For γr of 2×10−4 s−1, bubble radius
of 10 and 100 µm, σ of 0.2 N/m [Bagdassarov et al.,
2000], and ηmelt of 10
6.3 Pa·s (HPG8 liquid with 2.9
wt% H2O at 750 °C; [Hess and Dingwell, 1996], C a is
∼0.02 and 0.2, respectively, which satisfies the low C a
regime (C a < 1) required for the viscosity calculation.
The equation writes:
ηr = (1−Φb_melt_3D/100)−1
×(1−Φc_bulk_3D/Φmax)−2 (2)
where Φmax is the particle maximum packing of
66 vol% [Truby et al., 2015].
Supplementary Figure S3. 3D bubble size distributions.
6 Camille Daffos et al.
Supplementary Figure S4. Crystal breakage. The red squares highlight crystal breakage in the unde-
formed (γ = 0) sample containing 50 vol% crystals (bottom left) and associated crystal size histogram
showing a large population of 0–20 µm diameter crystals (bottom right), in contrast to non-broken crys-
tals in the undeformed sample containing 10 vol% crystals (upper left; same scale bar) associated to a
lower frequency of 0–20 µm crystals (upper right).
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Behrens, H., Roux, J., Neuville, D. R., and Siemann, M.
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