Journal of Volcanology and Geothermal Research 258 (2013) 24–30 Contents lists available at SciVerse ScienceDirect 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: firstname.lastname@example.org (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. 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