Journal of Volcanology and Geothermal Research 258 (2013) 24–30
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Journal of Volcanology and Geothermal Research
journal homepage: www.elsevier.com/locate/jvolgeores
Effects of thermal quenching on mechanical properties of pyroclasts
Ameeta Patel a,⁎, Michael Manga a, Rebecca J. Carey b, Wim Degruyter c
a
b
c
Department of Earth and Planetary Science, University of California, Berkeley, Berkeley, CA 94720, United States
CODES ARC Centre of Excellence in Ore Deposits, University of Tasmania, Hobart, TAS, Australia
School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA, United States
a r t i c l e
i n f o
Article history:
Received 14 December 2012
Accepted 2 April 2013
Available online 11 April 2013
Keywords:
Pumice
Quenching
Abrasion
Comminution
Pyroclasts
a b s t r a c t
Contact with water can promote magma fragmentation. Obsidian chips and glass spheres typically crack
when quenched. Vesicular pyroclasts are made of glass, so thermal quenching by water may damage them.
If water enters eruption columns, or if pyroclastic density currents interact with water, hot pumice can be
quenched. We performed a set of experiments on air fall pumice from Medicine Lake, California. We made
quenched samples by heating natural clasts to 600 °C, quenching them in water at 21 °C, drying them at
105 °C, and then cooling them to room temperature. We compare these samples with untreated air fall pumice from the same deposit, hereafter referred to as regular pumice. We tested whether quenched pumice
would 1) shatter more easily in collisions and 2) abrade faster. We also tested whether individual clasts
lose mass upon quenching, and whether they increase in effective wet density, two measurements which
may help characterize the magnitude of clast damage during quenching. We also compare pre-quenching
and post-quenching textures using X-ray microtomography (μXRT) images. Results from collision experiments show no clear difference between quenched pumice and regular pumice. Quenched pumice abraded
faster than regular pumice. On average 0.3% of mass may have been lost during quenching. Effective wet density increased 1.5% on average, as measured after 5 minutes of immersion in water. Overall, we find modest
differences between quenched pumice and regular pumice in experiments and measurements. The experimental results imply that quenching may damage small parts of a clast but tends not to cause cracks that
propagate easily through the clast. Post-quenching μXRT imaging shows no obvious change in clast texture.
This is in stark contrast to non-vesicular glass that develops large cracks on quenching. We present four
factors that explain why pumice is resistant to damage from thermal quenching: thin glass films experience
lower transient thermal stresses, many internal surfaces are initially vapor cooled, vesicles can arrest cracks,
and cracks from thermal quenching may not occur in the locations most susceptible to fracture in later
collisions.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
Comminution of volcanic clasts occurs through a combination of
fragmentation and abrasion. Rapid quenching of clasts by water generates thermal stresses that may create cracks. Any cracks produced
may reduce the strength of clasts, promoting fragmentation and
enhancing abrasion. Interaction of hot clasts with water may occur
in volcanic conduits, or when pyroclastic density currents encounter
bodies of water, rain or wet surfaces.
A layer of cooling glass that is constrained to prevent contraction in
the directions parallel to the surface experiences extensional stresses of
σx ¼
EαΔT
;
1−ν
⁎ Corresponding author. Tel.: +1 510 643 8532.
E-mail address: ameeta.patel@outlook.com (A. Patel).
0377-0273/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.jvolgeores.2013.04.001
ð1Þ
where σx is the extensional stress in a direction parallel to the surface, ΔT
is the change in temperature, E is the Young's modulus, α is the coefficient
of thermal expansion, and v is the Poisson's ratio (e.g., Turcotte and
Schubert, 2002). For typical values of E = 70 GPa (Meister et al., 1980),
v = 0.25 (Meister et al., 1980), ΔT = 500 °C, and α = 5 × 10−5/°C
(Spera, 2000), these stresses will be 2.3 GPa. This is greater than the
tensile strength of volcanic glasses, which is about 0.1 GPa (Webb and
Dingwell, 1990). Indeed, Fig. 1b shows many cracks throughout a glass
sphere and some cracks in a piece of obsidian caused by quenching
from 600 °C into water at room temperature of 21 °C. Similar textures
are seen on dense clasts that interacted with water (e.g., Büttner et al.,
1999; Dellino et al., 2001).
Because vesicular pumice clasts are fragile (Dellino et al., 2012;
Dufek et al., 2012) and their elastic moduli and compressive strength
are less than dense glass (e.g., Orenstein and Green, 1992), pumice
might be expected to break or abrade more easily than dense glass
fragments after quenching.
A. Patel et al. / Journal of Volcanology and Geothermal Research 258 (2013) 24–30
25
a) Pre-quenching
1 cm
b) Post-quenching
many cracks
some cracks
ambiguous
Fig. 1. (a) Glass marble, piece of obsidian, and pumice clast. (b) Objects from (a) after being heated to 600 °C and then quenched in water at 21 °C.
Thermal quenching may play a role in phreatomagmatic eruptions,
an end-member of explosive volcanic activity, associated with the interaction of ascending magma or lava with water. Such eruptions are notable for producing a large fraction of fine ash (Walker, 1973; Heiken and
Wohletz, 1985). Increased ash production in phreatomagmatic eruptions
is usually attributed to thermal quenching by water (e.g., Wohletz,
1983). Fragments typically have a blocky shape (e.g., Büttner et al.,
1999) and high density (Houghton et al., 2004), consistent with the
textures generated experimentally by quenching analogue melts
(e.g., Büttner et al., 2002, 2006).
Here we report a set of experiments and measurements that we
use to assess whether pumice clasts break, or become more susceptible to breakage and abrasion, upon thermal quenching. We find that
quenching from 600 °C to room temperature has little effect on the
breakage and mechanical properties of pumice. We show that these
observations can be explained by the nature of the heat transfer
involved and the geometrical structure of pumice.
2. Methods
We performed a set of experiments on rhyolitic air fall pumice
from Medicine Lake, California. Mean density is 900 kg/m 3 and crystal volume fraction is less than 1% (Manga et al., 2011). An image of
typical textures is shown in Manga et al. (2011). We chose this
pumice because a variety of related or complementary thermal and
mechanical properties have been measured, including breakup during collisions (Dufek and Manga, 2008; Dufek et al., 2012), mass
loss by abrasion (Cagnoli and Manga, 2005; Manga et al., 2011),
momentum loss during collision (Cagnoli and Manga, 2003; Dufek
et al., 2009) and steam generation during quenching in water
(Dufek et al., 2007).
2.1. Experiments comparing quenched samples with regular samples
We made “quenched” samples by heating clasts to 600 °C, quenching
them in water at 21 °C, drying them for 24 h at 105 °C, and then cooling
them to room temperature. The quenched samples were kept in the
furnace at 600 °C for 1–2 h. Using measured heat transfer coefficients
for similar size pumice from the same deposit (Stroberg et al., 2010),
the time scale to heat these clasts is less than 10 min. In quenching, we
dropped clasts from their hot crucibles into room temperature water 2
to 3 s after removing them from the furnace. We compare these samples
with untreated pumice from the same deposit, hereafter referred to as
“regular” pumice.
Pyroclastic density currents will have temperatures from a few
hundred degrees up to eruption temperatures, depending on the
amount of air they entrain and the distance they travel. In order to
be consistent with the measurements and interpretations, we use
pyroclasts heated to 600 °C as representative of hot pyroclastic currents. This is similar to the upper end of emplacement temperature
at Montserrat, for example (Scott and Glasspool, 2005), and maximum measured temperatures of block and ash deposits (Cole et al.,
2002).
2.1.1. Collision experiments
We used compressed air to propel 8–9.5 mm sieve size pumice
clasts vertically downward at a container filled with regular pumice.
In order to easily identify fragments from the propelled clast, we
first colored quenched and regular samples using a 1:50 solution of
water-based food coloring in water, and then let the clasts dry at
room temperature for one week. This treatment did not increase
clast mass by a measurable amount, given scale readability of
0.001 g. We removed the colored fragments from the container
after impact. We measured initial mass of the clast, its velocity prior
to impact, and the mass of the largest fragment remaining after impact. Additional details of the experimental setup are described in
Dufek et al. (2012). These experiments test whether quenching in
water makes pumice break into fragments more easily.
2.1.2. Abrasion experiments
We performed abrasion experiments on clasts of 12.5 + mm sieve
size using a rock tumbler. We started with one quenched sample of
40 clasts and one regular sample of 40 clasts. Regular clasts were
washed by submerging them in room temperature water and then
drying them completely. Both samples had roughly the same initial
total mass, and each sample filled about half the tumbler.
We measured sample mass as a function of time by periodically removing the clasts from the rotating tumbler and weighing them. We
A. Patel et al. / Journal of Volcanology and Geothermal Research 258 (2013) 24–30
removed the ash from the tumbler prior to each mass measurement.
We measured mass at the same short time intervals for each sample.
We did not put the ash back in the tumbler, so that both samples
would have similarly small amounts of ash in the tumbler at any
given tumbling time. Our abrasion experimental apparatus is described
in more detail in Manga et al. (2011). These experiments test whether
quenching makes pumice produce ash by abrasion more quickly.
2.2. Comparing post-quenching with pre-quenching
We examine how quenching affects individual clasts. We compare
properties of each clast post-quenching with that same clast prequenching. This allows us to isolate actual effects of quenching from
natural differences between different pyroclasts.
2.2.1. Measurements of effective wet density and mass loss
Effective wet density is defined as underwater density of a clast
when water occupies part of the pore space (Whitham and Sparks,
1986). Effective wet density, measured as a function of time after
immersion, characterizes the volume of air in pores that is replaced
by water. An increase in effective wet density implies that vesicle
walls were damaged during quenching, allowing water to infiltrate
the pore space faster. Effective wet density is defined as
!
Mg
ρp
¼ ;
V g þ V a ðt Þ
ρf
3. Results
3.1. Collision experiments
Fig. 2a shows the relationship between mass lost as a fraction of
initial mass and pre-collision velocity (see electronic supplement for
tabulated data). Filled squares indicate quenched pumice and open
squares indicate regular pumice. We define mass lost as the difference between initial mass of the clast and mass of the largest fragment remaining after each experiment. Therefore, a large fraction of
mass lost indicates that the clast broke into small pieces. More mass
a)
0.9
ð2Þ
where Mg is the mass of the solid (glass and crystals) parts of the
clast, Vg is the volume of the solid parts of the clast, Va is the volume
of air in the clast, (t) indicates that Va is a function of time, ρp is the
mean density of the clast, ρf is the density of water. In calculating
ρp, the mass of air in the clast is negligible. We compare λ measurements taken at 5 min after gentle immersion of room temperature
clasts in room temperature water. At one minute intervals we remove
bubbles attached to the apparatus and rotate the clast to release bubbles stuck on the underside. We used 20 clasts of 12.5 + mm sieve
size. For each clast, we took the pre-quenching λ measurement,
dried the clast at 105 °C for 24 h, cooled it to room temperature,
and then recorded the pre-quenching dry mass. Then, we kept the
clast in a furnace at 600 °C for 2 h, quenched it in water at 21 °C,
dried it for 24 h at 105 °C, cooled it to room temperature, and then
recorded the post-quenching dry mass. Then, we took the postquenching λ measurement. Δλ helps characterize the magnitude of
clast damage during quenching.
Total mass loss may be due to a combination of clast damage during quenching and escape of water such as hydrated volatiles while
the clast is hot. To quantify an average mass loss from heating, we
recorded the mass of a 20 clast sample of regular pumice, kept it in
a furnace at 600 °C for 2 h, slowly cooled it to room temperature,
and then recorded the mass left. Here we used a sample of 20 clasts
in order to improve relative scale accuracy, and then repeated the
experiment using 50 clasts. We compare average mass loss due to escape of water in this pumice with total mass loss in quenched pumice.
The difference may help characterize the magnitude of clast damage
during quenching.
0.8
Fraction of mass lost
1
λ¼
ρf
solid and void. We mounted each clast in the sample holder and
took pre-quenching images at energies of 20 keV: 1440 projections
at 200 millisecond exposure times, rotating the sample. We then
kept the clast in a furnace at 550 °C for a few hours, and then
quenched it in room temperature water. We then remounted and
rescanned the clast. Imaging was done prior to and independently
of our other quenching experiments and measurements, hence the
different furnace temperatures used. We compare post-quenching
and pre-quenching images to identify overall change in texture, the
scale of breakage of bubble walls and changes in clast size.
0.7
0.6
0.5
0.4
0.3
0.2
0
0
10
20
30
40
50
Velocity (m/s)
60
70
30
40
50
Velocity (m/s)
60
70
b)
1
0.9
Quenched
Regular
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2.2.2. Imaging
We also compare pre-quenching and post-quenching textures
using X-ray microtomography (μXRT), using the 8.3.2 beamline at
the Advanced Light Source at the Lawrence Berkeley National Laboratories. We used Medicine Lake pumice with diameters between 12.5
and 16 mm and average density of 900 kg/m 3. Within samples,
modal densities of pumice clasts vary by 400 kg/m 3. The threedimensional textures permit us to capture changes in clast size and
breakage of bubble walls. μXRT reconstructions identify two phases:
Quenched
Regular
0.1
Breakup
26
10
20
Fig. 2. (a) Fraction of initial mass lost as a function of pre-collision velocity. Symbols
indicate the largest fragment remaining after each experiment. Horizontal error bars
show measurement accuracy of ±2%. Vertical error bars show absolute uncertainty
given scale accuracy of ±0.002 g. (b) Fraction of experiments that caused breakup as
a function of bin averaged pre-collision velocity. Data presented in Fig. 2a are averaged
in bins of 10 m/s. Horizontal error bars show 1 standard deviation. Vertical error bars
show 1 standard error. Solid curves are the best fit of Eq. (3) to the data and dashed
curves are 95% confidence bounds. In both (a) and (b), filled squares indicate quenched
pumice and open squares indicate regular pumice.
A. Patel et al. / Journal of Volcanology and Geothermal Research 258 (2013) 24–30
2
f ¼ cu ;
a)
70
50
40
30
20
10
0
0
ð3Þ
3.2. Abrasion experiments
Fig. 3a shows the total mass of quenched pumice clasts and regular pumice clasts as a function of time in the rotating tumbler. Each
data series indicates one set of clasts that were abraded together.
The fine ash was not recovered, so we did not analyze the ash.
Fig. 3b shows the rate of mass loss normalized by initial mass,
−M1 ΔM
Δt , as a function of time in the rotating tumbler. The inset
shows the same data, with the time axis on a log scale. Filled squares
indicate quenched pumice and open squares indicate regular pumice.
For both types of pumice, abrasion rate declined as particles lost
mass while becoming more rounded, as noted in previous studies
(e.g. Manga et al., 2011; Kueppers et al., 2012). Quenched pumice
lost mass faster in initial stages of abrasion, but both quenched pumice
and regular pumice lost mass at similar rates later in the experiment.
−3
Quenched pumice average −M1 ΔM
min−1 prior to
Δt was 1.5 × 10
−3
−1
losing 10% of initial mass and 1.0 × 10
min after. Regular pumice
−3
average −M1 ΔM
min−1 prior to losing 10% of initial mass
Δt was 1.1 × 10
and 0.9 × 10−3 min−1 after. This implies that the exterior of the
quenched clasts abraded more easily than the exterior of regular clasts,
but the interior of quenched clasts abraded at similar rates to regular
clasts. There was no major change at 10% mass loss; the curves are generally smooth. Jumps or steps in the overall trend of decreasing rate of
mass loss occur when small chips break off clasts. The quenched pumice
lost more small chips than the regular pumice.
0
0
0
50
150
200
250
300
b)
−2
10
10−2
Quenched
Regular
10−3
10−4 −1
10
10 0
−3
10
10 1
10 2
−4
10
50
100
150
200
250
300
Time in tumbler (minutes)
Fig. 3. (a) Mass as a function of time in the tumbler. Error bars are smaller than the
symbols. (b) Normalized rate of mass loss as a function of time in the tumbler. Vertical
error bars show absolute uncertainty given scale accuracy of ±0.002 g. Horizontal
error bars are smaller than the symbols. The inset shows the same data, with the
horizontal axis on a log scale. In both (a) and (b), filled squares indicate quenched
pumice and open squares indicate regular pumice.
3.4. Imaging
Fig. 4a and b shows pre-quenching and post-quenching textures
respectively, for a Medicine Lake clast. Each image is a slice from
the 3-D volumes. We rotated the 3-D images such that 2-D slices
visually matched. Because the slices are not perfectly parallel, boxes
highlight the overlapping section in Fig. 4a and b, allowing direct
comparison of individual vesicles. We see no obvious differences
created by quenching in this section, or in other pairs of slices. The
more striking observation is that the slice shown in Fig. 4b does not
Table 1
Change in effective wet density and mass.
3.3. Effective wet density and mass loss measurements
Table 1 lists the results from effective wet density and mass loss
measurements. Much of the decrease in mass can be explained by
loss of water while in the furnace, but quenching may also have
broken small chips off the clasts. The small increase in λ suggests
that a relatively small number of vesicle walls may have broken
during quenching.
100
Time in tumbler (minutes)
Normalized rate of mass loss (1/minutes)
The constant of proportionality c is determined by nonlinear
least-squares fitting. The solid curves are the model fit, and the
dashed curves bound 95% confidence intervals. For quenched pumice,
c = (1.86 ± 0.31) × 10 −4 s 2/m 2, with R 2 = 0.92. For regular pumice, c = (1.88 ± 0.14) × 10 −4 s 2/m 2, with R 2 = 0.98. Model fits for
quenched pumice and regular pumice are almost identical, showing
similar probability of breakup at any given velocity. The difference
between coefficients is much smaller than the confidence level of
either. Also, the regular pumice model fit cannot be distinguished
from the quenched pumice model fit to within uncertainty, because
its confidence bounds are within the confidence bounds of the
quenched pumice model fit. We see no significant difference between
quenched pumice and regular pumice in collision experiments.
Quenched
Regular
60
Mass (g)
is lost in higher velocity collisions. Little mass is lost at velocities less
than 20 m/s. In some experiments, clasts gained a small amount of
mass from ash abraded off of the particle it collided with.
The wide range of outcomes at a given velocity as shown in Fig. 2a
reflects variability in contact dynamics and the natural heterogeneity
of pyroclasts. The large scatter is a feature common to other properties
of colliding volcanic clasts, such as kinetic energy loss (e.g., Dufek et al.,
2009) and ash production (Dufek and Manga, 2008). We thus average
data in velocity bins of 10 m/s in order to identify systematic trends.
Fig. 2b shows the relationship between the fraction of experiments
that resulted in breakup f and the bin averaged pre-collision speed u.
We define breakup as collisional mass loss of more than 10% of initial
mass. The fraction of clasts that break is expected to scale with initial
kinetic energy per unit mass (Dufek et al., 2012), so we fit data for
each set of clasts with a function of the form
27
Δλ
Total Δ mass
Δ mass from heatinga
Δ mass from quenchingb
Mean
1 standard deviation
1.5%
−1.5%
−1.2%
−0.3%
1.5%
0.4%
0.07%
N/A
a
One sample of 20 clasts and one sample of 50 clasts, kept in furnace at 600 °C
for 2 h.
b
Difference between mean total Δ mass and expected Δ mass from heating.
28
A. Patel et al. / Journal of Volcanology and Geothermal Research 258 (2013) 24–30
a) Pre-quenching
b) Post-quenching
2 mm
Fig. 4. Grayscale μXRT slices of 3-D imaged volumes from a Medicine Lake pumice clast. (a) Pumice texture pre-quenching. (b) Pumice texture post-quenching. The 2-D slices are
not perfectly parallel; this is reflected in the post-quenching external shape. Boxes highlight an area where slices overlap, so individual vesicle walls can be compared between the
two images. We see no obvious cracks in (b).
appear to be riddled with cracks like the glass marble in Fig. 1b. If
cracks exist, they fall below the spatial resolution of the images
(b3.4 μm). Subtle differences between the images might be due to
loss of chips on the order of 10s of microns in size, but can be due
to slight misalignment of slices. Overall, in imaging we see no obvious
changes as a result of quenching.
4. Discussion
In collision experiments, we find no significant difference between
quenched pumice and regular pumice in their susceptibility to breakup over a range of velocities. In our other experiments and measurements, we find modest differences between quenched pumice and
regular pumice. Imaging shows no obvious loss of vesicle walls, cracks
(>3.4 μm), or other changes in clast texture.
Overall, results suggest that quenching may cause some cracks to
propagate in pumice, but that most vesicle walls experience little or
no damage. Also, the cracks that do propagate must not generally be
in locations where they can easily extend through to the far surfaces
of the clast in a later collision.
We now describe 4 factors that may explain these results. We first
list these factors and then discuss them in order.
1) Thin glass films (e.g., vesicle walls) experience lower maximum
tension than thick pieces of glass (e.g., obsidian clasts) under the
same cold shock conditions.
2) Many of the internal surfaces of pumice quenched in water cool
more slowly than external surfaces, because these internal surfaces
initially lose heat to steam rather than water. This results in more
uniform extensional strain rates, allowing internal vesicle walls to
often remain intact during quenching.
3) Cracks in vesicular pumice can end at vesicles, dispersing stresses. This
can prevent a crack from extending through the entire pumice clast.
4) Cracks produced by thermal quenching of pumice may not be in
locations naturally susceptible to becoming new surfaces of clast
fragments.
Factors 1 and 2 are due to the buildup of thermal stresses in glass.
Factors 3 and 4 depend on the geometrical structure of vesicular
pumice.
When a glass film such as a pumice vesicle wall is quenched, the
maximum transient thermal stresses depend on the rate of heat
transfer to the cooling fluid compared with the rate of conduction
within the glass. The center of the glass film cools more slowly than
its surface. This transient temperature gradient results in a greater
contraction rate near the surface. If heat transfer to the cooling fluid
is fast enough compared with thermal conduction within the glass,
the resulting differences in extensional strain rates across the glass
film create enough tension near the surface to fracture the glass.
Glass fracture from thermal stress can be classified into 2 categories: 1) formation of a new crack caused by buildup of extensional
stress that exceeds the tensile strength of the glass (the case considered in the Introduction), and 2) propagation of a pre-existing
crack. Lu and Fleck (1998) present models for each of these cases.
Theoretical strengths of glasses are generally much higher than the
measured strengths. This is because flaws in glass surfaces concentrate stresses in certain locations (Doremus, 1994). Abrasion can
cause these flaws, which propagate into longer cracks under sufficient
stress. Since air fall pumice has experienced particle–particle interaction after initial fragmentation (Dufek et al., 2012), here we consider
fracture due to propagation of a pre-existing flaw.
Lu and Fleck (1998) solve for the time-evolution of stresses in an idealized infinitely long plate of thickness 2H subjected to thermal shock.
The flow of heat in the plate is governed by the heat conduction equation
∂T
∂2 T
¼ κ z 2 ; jzj≤H
∂t
∂z
ð4Þ
where T is temperature, t is time and κz is the thermal diffusivity of the
solid in the z-direction.
In a natural material such as pumice, fracture will likely begin at a
flaw or crack. A stress intensity factor K describes the intensification
of a stress field near the tip of a crack. In a dynamic problem, it is a
function of time as well as stress and material properties. The crack
propagates if and when K equals or exceeds the fracture toughness
KIC of the material. For an idealized plate of thickness 2H with an
edge crack of length a, Lu and Fleck (1998) derive the stress intensity
factor K during a cold shock event. This applies over the full range of
Biot number
Bi≡
hH
k
ð5Þ
A. Patel et al. / Journal of Volcanology and Geothermal Research 258 (2013) 24–30
where h is the heat transfer coefficient of the convective medium and
k is the thermal conductivity of the solid. The Biot number describes
the relative resistance to internal heat flow compared to resistance
to external heat flow. A high Biot number describes high transient
tensile stress near the surface of the plate in cold shock. For a given
Biot number, Kmax is the global maximum value of K, occurring at a
specific time given a crack length that optimizes K. Lu and Fleck
(1998) find that Kmax is well described by
2:12 −1
;
K max ¼ 0:222K 0 1 þ
Bi
ð6Þ
where K0 is a reference stress intensity factor that is a function of the
Young’s modulus, Poisson’s ratio, coefficient of thermal expansion,
initial temperature of the plate, temperature of the convective medium and H.
Fig. 5 shows Kmax as a function of H. Physically, H represents the
volume to surface ratio. We assume a thermal conductivity of
1.6 W m −1 °C −1 a value appropriate for rhyolite glass (Bagdassarov
and Dingwell, 1994), initial temperature difference of 500 °C, v =
0.25 (Meister et al., 1980), E = 70 GPa (Meister et al., 1980), α =
5 × 10 −5 °C −1 (Spera, 2000). Heat transfer coefficients of 2.5 × 10 3
and 1 × 10 5 W m −2 °C −1 bound the yellow region, representing
convection with phase change of boiling (Incropera and DeWitt,
2002). Heat transfer coefficients of 10 2 and 10 3 W m −2 °C −1 bound
the green region, representing fully developed film boiling
(Groeneveld et al., 2003). The gray band shows KIC for volcanic
glass, 1.4 to 3.9 MPa m (Balme et al., 2004; Dorfman, 2008). A
pre-existing flaw is expected to advance if Kmax ≥ KIC. A single value
for KIC describes a sample. For a given heat transfer coefficient, the
value of H determines whether the crack propagates. Fig. 5 shows
that thick glass plates are more susceptible to fracture by thermal
stresses than thin plates, illustrating factor 1. The length scale will
influence quenching of natural materials (e.g. Allen et al., 2008)
even though the actual values plotted reflect idealized geometries.
The samples in Fig. 1 are not plates, but glass thickness influences
their susceptibility to break during quenching. The glass sphere has
a diameter of 13 mm, the thickness of the piece of obsidian ranges
from 2 to 4 mm, and pumice vesicle walls in these samples are
10–100 μm across. Since the pumice clast in Fig. 1 is a foam, its
response to thermal quenching also involves the factors that we
discuss next.
This model can be used to help understand fracture of a single
vesicle wall in a pumice clast by thermal stresses on quenching.
1
2
10
9
°C
5
4
3
1 × 10 2
6
2.5 × 3
10
1 × 10 3
W/m 2
× 10 5
7
h=1
Kmax (MPa m1/2)
8
KIC
2
1
0
10−6
10−5
10−4
10−3
10−2
H (m)
Fig. 5. Kmax as a function of H. The gray band shows KIC for volcanic glass. Numbers on
curves indicate heat transfer coefficients. The yellow region represents convection
with phase change of boiling. The green region represents fully developed film boiling.
29
Factor 2 helps explain why any quenching damage may be largely
confined to external parts of clasts. When a vesicular pumice clast
below its melting point and above the Leidenfrost temperature is
submerged in subcooled water at pressures near atmospheric, water
contacts the clast surface because roughness and porosity prevent
stable vapor films from forming (Kim et al., 2011). The water boils,
removing heat from the clast through conduction, convection and
phase change. This process involves fast heat transfer as represented
by the yellow region in Fig. 5.
In contrast, many of the internal surfaces of the clast may be
cooled relatively slowly by steam. We infer that steam permeates
hot pumice clasts when they are quenched in water, from observing
that they sink quickly (Whitham and Sparks, 1986; Dufek et al.,
2007). Initially, steam may coat these internal surfaces and insulate
them from the surrounding water, while boiling continues along the
steam–water boundary (Woodcock et al., 2012). Some air will also remain in the pores (Allen et al., 2008). As the clast cools, some steam
condenses, vapor films become thin, and instabilities cause direct
solid–liquid contact. By this point, the temperature difference between the clast and the water may not be high enough to cause a
crack to propagate. The green region in Fig. 5 represents heat transfer
coefficients of fully developed film boiling. This range of heat transfer
coefficients may encompass the initial cooling regimes of many internal surfaces of pumice clasts. Slow heat transfer may protect these
surfaces from quenching damage. We present values for fully developed film boiling because it describes heat transfer to steam with
phase change of boiling occurring along the steam–water boundary.
Exact boiling regimes inside cooling pumice are unknown, but we
do expect many of the internal surfaces to be initially cooled by
steam. Film boiling will not apply in some situations. For example,
the presence of shock waves such as from explosions can collapse
vapor films (Wohletz, 1986; Zimanowski and Büttner, 2003).
In a quenching experiment carried out near atmospheric pressures, steam temperature will be higher than water temperature, so
ΔT will be different for the two fluids. We compare the same ΔT for
both cases to provide conservative estimates while illustrating the
influence of the cooling fluid.
The geometrical structure of pumice provides resistance to damage by quenching. Factor 3 explains why a single crack from thermal
quenching may damage vesicular pumice much less than a single
crack would damage nonvesicular obsidian. A hole can arrest a
crack, releasing energy (Kobayashi et al., 1972; Gibson et al., 2010).
Therefore, a vesicle in a pumice clast may arrest a crack. This is especially clear in the case of a single broken vesicle wall. Orenstein and
Green (1992) find that structural damage in open-cell ceramic
foams from thermal quenching happens on the level of individual
struts even when temperature varies across multiple cells. In contrast,
Kano et al. (1996) suggest that in large blocks that are quenched, slow
cooling of the interior of the block may cause cracks that extend
through multiple cells, forming polygonal patterns on the exterior
surface. In these large blocks, cracks may also end at vesicles.
Factor 4 states that cracks produced by thermal quenching of pumice
may not be in locations naturally susceptible to becoming new surfaces
of clast fragments. Fracture locations in volcanic glass from hammer impacts may be heavily influenced by pre-stresses (Dürig and Zimanowski,
2012). Strengths of brittle foams scale with a power law of the ratio of
foam density to material density (Gibson et al., 2010), suggesting that
pumice would be locally weaker where the porosity is higher. Quenched
pumice does not break more easily in the collision experiments,
suggesting that any cracks produced by quenching are not preferentially
occurring in parts of clasts that control their macroscopic strength.
5. Conclusion
We find that quenching by a 530–580 °C temperature difference
may have modest effects on mechanical properties of pumice. We
30
A. Patel et al. / Journal of Volcanology and Geothermal Research 258 (2013) 24–30
did not find any significant difference between quenched samples
and regular samples in collisions. Quenched pumice abraded faster
than regular pumice. Pre-quenching and post-quenching measurements of mass and effective wet density show small changes. μXRT
image analysis shows no obvious change to clast texture. Therefore,
interaction with water may have a limited influence on mechanical
properties of clasts in pyroclastic density currents.
Vesicular pumice is resistant to damage from thermal quenching
in water because vesicle walls are thin, interior surfaces may initially
be cooled by contact with steam rather than water, vesicles can arrest
cracks, and quenching damage may occur in locations that have
limited influence on bulk strengths.
Although our experimental results do not apply to magma-water
interaction at conduit temperatures or pressures, length scales will
influence any type of quenching. While water–melt interaction may
promote fragmentation and lead to enhanced ash production, we
expect thin glass films in already vesiculated pumice to develop
smaller thermal stresses than thick dense glass.
Acknowledgments
We thank the National Science Foundation for support and U.
Kueppers for comments and suggestions. The μXRT analyses were
conducted on beamline 8.3.2 at the Advanced Light Source, Lawrence
Berkeley National Lab; we thank A. MacDowell and D. Parkinson for
making the imaging possible.
Appendix A. Supplementary data
Data plotted in Fig. 2a can be found online at http://dx.doi.org/10.
1016/j.jvolgeores.2013.04.001.
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