Shear-induced bubble coalescence in rhyolitic melts with low vesicularity



[1] We have experimentally demonstrated for the first time, shear-induced development of bubble size and shape in a rhyolitic melt. The deformation experiments have been performed by using an externally heated, piston-cylinder type apparatus with a rotational piston. At 975°C, the vesiculated rhyolitic melts having cylindrical shape were twisted at rotational speeds of 0.3, 0.5 and 1.0 rpm. The number, size and shape of bubbles were then measured by using the X-ray computed tomography. The experimental results show that coalescence of bubbles occur even at low vesicularity (20 vol.%) and the degree of coalescence is enhanced with the shear rate. Because the shear-induced deformation seems to be produced for magmas ascending in a volcanic conduit, we propose the possibility of the vesiculated magma undergoing bubble coalescence at a significant depth (low vesicularity), resulting in the formation of permeable magmas, at least near the conduit wall.

1. Introduction

[2] Vesiculation of hydrous magmas controls the dynamics of conduit flow in volcanic eruptions. The vesiculation decreases magma density, and hence accelerates magma to the earth's surface. The development of size and shape of bubbles (bubble structure) is also important for the flow dynamics, because they influence the viscosity [Stein and Spera, 1992; Manga et al., 1998; Pal, 2003] and the permeability [Blower, 2001] of the vesiculated magma. There are geological observations, indicating that bubble structure may be changed by shear in flowing magmas [Stasiuk et al., 1996]. It is therefore necessary to study the development of bubble structure during the ascent of the magma.

[3] The development of bubble structure has been experimentally investigated in mostly isostatic magmas [Gardner et al., 1999; Mangan and Sisson, 2000; Burgisser and Gardner, 2005]. In these studies, the dependence of bubble structure on the rate and magnitude of magma decompression was investigated extensively. On the other hand, the effect of the shear on bubble structure has been examined by experimental and theoretical studies in other fields of engineering and science, and those studies showed that the shear controlled the deformation of bubble and the coalescence rate of bubbles [e.g., Sheth and Pozrikidis, 1995; Lyu et al., 2002; Rust and Manga, 2002]. However, there are surprisingly few experimental studies dealing with the influence of shear on the bubble structure in actual magmas [Stein and Spera, 2002].

[4] This study aims to investigate how the bubble structure develops in flowing magmas. For this purpose, we have performed high temperature deformation experiments on bubbly rhyolitic melt and analyzed the bubble structure in the experimental products using micro X-ray computed tomography (CT). Consequently, we show that the bubble coalescence is enhanced with increasing shear rate.

2. High Temperature Deformation Experiments

[5] The experiments were carried out using an externally heated piston-cylinder type apparatus that consists of a stationary upper piston and a rotational lower piston (Figure 1a). The basic design of the pressure vessel other than the piston assembly is similar to that of Nowak et al. [1996]. The rotation of the piston is controlled by a motor with a gear head (VSD560ICU-GVH and GVH5G30, ORIENTAL MOTOR CO. LTD).

Figure 1.

(a) A schematic view of the cell assemblage, (b) CT image (gray scale in 8-bit), (c) binary image for extracting bubbles and (d) typical 3D structure of coalesced bubbles in the 1.0 rpm experiment. The arrows represent the direction of rotation. The gravity center of the coalesced bubbles in Figure 1d is located in 2.4 mm from the sample center and 3.0 mm from the upper surface of the sample.

[6] This study used natural obsidian (0.5 wt% water) from Wadatouge, Japan [Okumura and Nakashima, 2005] as starting material. Cylindrical samples with ca. 4.7 mm in diameter and 5 mm in length were cored from the obsidian. The sample was then placed into a graphite container (ca. 5 and 9 mm in inner and outer diameters, respectively, and 5 mm in length) and sandwiched between the pistons (Figure 1a).

[7] In the experiments, the temperature was first increased up to 975°C in 50 minutes and held at 975°C for 3 minutes to vesiculate the sample. The sample vesiculation results in the increase of pressure, because sample volume is fixed in the cell. When we assume a closed system, the pressure after the vesiculation is estimated to be a few mega-Pascals. Then, the lower piston was rotated at a rate of 0.3, 0.5 or 1.0 rotation per minute (rpm). Since the rotation angle was 270 degrees in all the experiments, their duration is different because of the different rotational speed. Finally, the rotation of the lower piston was stopped, and the sample was cooled by switching off the heater. The temperature dropped down to less than 935 and 725°C within the first and 9th minutes, respectively, after the heater was turned off. The deformation of the samples was confirmed by the marker incised on the side of cylindrical samples, which means that the samples slipped on the surface of the graphite.

[8] We should note that the shear deformation of bubbles in the samples seems to be unsteady, because the duration of rotation is shorter than the relaxation time [Llewellin et al., 2002]. The characteristic relaxation time τ is estimated from the relation of /σ, where r is the radius of spherical bubble, μ is the melt viscosity, and σ is the surface tension. τ at 975°C was found to be 0.1, 1.4 and 13.7 minutes for bubbles with the radii of 1, 10 and 100 μm, respectively, based on the melt viscosity of 2.2 × 106 Pa·s [Hess and Dingwell, 1996] and the surface tension of 0.265 N/m [Bagdassarov et al., 2000]. Because the duration of rotation is < 2.5 minutes, bubbles with radii larger than several tens of micrometers did not attain steady shapes during the experiments. Actually, we confirmed the bubble shapes to be strain-limited, i.e. unsteady bubble shape, by comparing the bubble shapes that experienced the same shear rate but different strain.

[9] In the present experiments, a potential problem for the investigation of development of bubble structure is that the bubble shape could relax during quenching. At 935 °C, τ is estimated to be 0.3, 3.5 and 34.8 minutes for bubbles of 1, 10 and 100 μm radii, respectively. Therefore, the bubbles of 1 μm radius are probably relaxed during sample cooling, but the relaxation of bubbles with r > 10 μm seems to be negligible. As described in the following sections, this study considers only the bubbles with r > 17 μm.

3. Micro X-Ray Computed Tomography Analysis

[10] The 3D images of samples were obtained by a micro X-ray CT scanner (ELESCAN NX-NCP-C80I(4); Nittetsu Elex Co.) [Tsuchiyama et al., 2002]. The 3D imaging is necessary to evaluate the bubble structure avoiding off-centered sectioning problems, because the bubble shape can change both horizontally and vertically due to the apparatus configuration. Images of transmitted X-ray intensities through the sample were collected at the accelerating voltage of 40 kV and a tube current of 0.1 mA by rotating the sample 180 degrees with the rotation angle increasing at step of 0.2 degrees (900 projections). The 421–625 CT images (2D slice images) were reconstructed from the images of transmitted X-ray intensities and finally a 3D image was obtained by stacking the CT images. The pixel sizes in the 2D images and the slice thickness were 5.8 × 5.8 μm and 9.3 μm for 0.3 and 1.0 rpm experiments, and 6.7 × 6.7 μm and 10.7 μm for the 0.5 rpm experiment. The analyses of the 3D images were carried out using the originally developed software set “SLICE” [Tsuchiyama et al., 2005]. All the CT images were converted to binary format by using the threshold of the CT values, determined manually (Figure 1b and 1c). Then, all the 3D bubbles were numbered in the sample and their volumes were obtained by counting the number of voxels that belongs to each bubble. Each bubble was approximated by a triaxial ellipsoid, where the three principle axes pass through the center of gravity. To avoid the effect of sample relaxation and noise in the CT images, this study deals only with those bubbles with voxel numbers ≥ 100, which corresponds to r > 17 μm in all the experiments.

[11] The spatial resolution of CT images may be insufficient for identifying whether a melt film between two bubbles is ruptured, because the critical film thickness to rupture is less than the order of 1 μm [Klug and Cashman, 1996]. Therefore, we have performed image processing to test the effect of thin melt film on the number and size of bubbles. Namely, two voxel layers were eroded for all the bubbles, which results in the dilation of melt films. Since the dilation of melt films separates a connected bubble into multiple bubbles, their number increases. However, the relationship between bubble structure and rotational speed, which is of interest in this study, showed no qualitative changes in our results. Therefore, we have considered that the effect of thin melt films is qualitatively negligible for the bubble structure and report the result without any image processing in this paper. Here, we note that additional studies by high-spatial-resolution 3D analysis might be necessary to investigate explicitly the effect of thin melt films that are too thin to be observed in the CT images of this study.

4. Results and Discussion

[12] The run products have similar vesicularities (19, 20 and 17 vol.% for 0.3, 0.5 and 1.0 rpm experiments). To understand the shear-induced development of the bubble structure, we have first examined the homogeneity of the bubble distribution in the samples. The cumulative vesicularity in radial direction is shown in Figure 2. All the experimental results show the increasing cumulative vesicularities, but are higher than that estimated for homogeneous bubble distribution (Model-1). This deviation can be explained if we consider the low vesicularity at the sample edge which is mainly induced by diffusive water loss during the experiments. In addition, the beam hardening results in high CT value at the sample edge [Tsuchiyama et al., 2005] and the bubble near the edge becomes relatively small. Therefore, the accumulation at the edge from 0.9 to 1 in normalized radius is very small. If the theoretical cumulative vesicularity for the homogeneous bubble distribution is normalized to the vesicularity at a normalized radius of 0.9 (Model-2), then we find that the experimental results are reproduced well (Figure 2). We also confirmed the bubble distribution to be homogeneous in the vertical direction. These indicate that either in the vertical or horizontal direction, the bubbles did not show a pronounced movement during the experiments.

Figure 2.

Cumulative vesicularity normalized by total vesicularity as a function of the normalized radius. The vesicularity calculated by assuming homogeneous bubble distribution [Model-1: α/α0 = (R/R0)2, where α, R, R0 and α0 represent the cumulative vesicularity, radius, sample radius and total vesicularity, respectively] is shown as a dashed curve. The solid curve represents the homogeneous distribution normalized to the vesicularity at a normalized radius of 0.9 (Model-2), which reproduces the experimental results well.

[13] The magnitude of bubble deformation is characterized by D = (lb)/(l + b), where l and b represent the halves of semi-major and minor axes of the ellipsoidal bubble. D for a spherical bubble is zero, and D becomes larger with the deformation. In the steady state, D increases with the capillary number Ca [Rust and Manga, 2002] which is given by rGμ/σ where G is the shear rate. In an unsteady state, D is larger for higher Ca at a given time [Sheth and Pozrikidis, 1995; Chinyoka et al., 2005]. D shown here are obtained for those bubbles for which the ratio of the volume obtained from voxel number (N) to that calculated by using the lengths of principle axes obtained (V = 4/3πbcl, where c is the half length of intermediate axis) is > 0.9. This is because the low value of N/V is mainly due to the irregularity induced by bubble coalescence, and those bubbles are not suitable for describing the magnitude of shear-induced bubble deformation. In Figure 3, we plot the gravity center of the bubbles with D > 0.5 in the sample radius–height space. The bubbles with D > 0.5 are mainly located in the outer and lower/upper regions, and the region with large-D bubbles expands toward the center of samples when the rotational speed increases. The shape of bubbles with D > 0.5 is prolate ellipsoid rather than oblate (the average of b/c and c/l are 0.60–0.71 and 0.39–0.50, respectively). In addition to bubbles with large-D values, those with large values of D divided by spherical bubble radius r in millimeter (D/r > 15 mm−1 which corresponds to G > 0.0018 s−1 with D = Ca) are again located in the outer and lower regions (Figure 3). Because D/r increases with G when μ and σ are the constants, the distribution indicates that the shear rate is higher at the outer and lower regions in the samples.

Figure 3.

Spatial distributions of the bubbles with N > 5×107μm3, D > 0.5 and D/r > 15 mm−1, plotted in normalized sample radius–height space. The large bubbles and deformed bubbles are selectively distributed in the outer and lower regions where the shear rate is high.

[14] Figure 4 shows the size distribution of bubbles in the outer and inner regions of samples. The number of the larger bubbles increases with the rotational speed both in the outer and inner regions, but the smaller bubbles decrease. The largest bubbles (108–109μm3) are found only in the outer region. A typical 3D structure of the large bubble, i.e. coalesced bubbles, is shown in Figure 1d. The increase in number of the larger bubbles and the decrease in the smaller bubbles show bubble coalescence. Therefore, the result of this study means that the bubble coalescence is enhanced with increasing rotational speed and at outer region. Because the shear rate is higher at higher rotational speed and outer region of samples, we conclude that the bubble coalescence is enhanced by increasing the shear rate. This is clearly demonstrated by the good correlation between spatial distributions of bubbles with large D/r value and those with N > 5 × 107μm3 (Figure 3).

Figure 4.

Size distribution of the bubbles in (a) outer and (b) inner regions of the run products. The data of Figure 4a outer region represent bubbles in the region of R/R0 > 0.5, Z/Z0 < 0.25 or Z/Z0 > 0.75, where Z and Z0 represent the height and sample height, respectively. The bubbles in the regions of R/R0 < 0.5 and 0.25 < Z/Z0 < 0.75 are shown in Figure 4b inner region. The inset in Figure 4a represents the frequency of bubbles of 108–109μm3 which are not found in the inner region.

[15] The classical theory [Smoluchowski, 1917] predicts that the coalescence rate of ballistic drops in a simple shear flow (“Smoluchowski rate”) increases with the shear rate, the number density of drop and the drop size. When the hydrodynamic interaction occurs, Smoluchowski rate is not equal to actual coalescence rate, and the coalescence efficiency is defined as the ratio of the actual coalescence rate to Smoluchowski rate [e.g., Lyu et al., 2002]. Theoretical studies [e.g., Vinckier et al., 1998] predict that the coalescence efficiency decreases with increasing shear rate, and hence the actual coalescence rate may increase or decrease with increasing the shear rate. The theoretical prediction also indicates that the coalescence efficiency becomes insensitive to the shear rate and approaches 1 with decreasing viscosity ratio (μv/μm) between the vapor in bubble (μv) and melt (μm) [e.g., Rother and Davis, 2001]. Therefore, the actual coalescence rate is expected to increase with the shear rate at μv/μm ∼ 0. Because μv/μm is nearly equal to 0 for rhyolitic melts, the result of this study (the increase of coalescence rate with the shear rate) might support the theoretical prediction.

5. Implications for Development of Bubble Structure in a Flowing Magma

[16] The present result points to an important aspect for the development of bubble structures in a flowing magma, which is the occurrence of shear-induced bubble coalescence even at low vesicularity (20 vol.%). Burgisser and Gardner [2005] proposed that the bubble coalescence started at a vesicularity of ∼ 43 vol.% based on the decompression experiments, but this value was determined without the explicit effect of the shear deformation. The maximum shear rate Gmax in our experiments is approximately estimated to be the order of 0.01 s−1 based on the height H and radius R of the sample and the rotational speed S (Gmax ∼ 2πR × S/60/H). This shear rate seems to be easily produced in conduit flow, at least near the conduit wall [Gonnermann and Manga, 2003]. A vesicularity of 20 vol.% for rhyolitic melt corresponds to a depth of ∼1600 m, with an initial water content of 3 wt.%, a magma temperature of 975°C and equilibrium dehydration being assumed. Therefore, we propose the possibility of the vesiculated magma undergoing bubble coalescence in a deep conduit, at least near the conduit wall, and also that the size and shape of bubbles continue to change by shear-induced coalescence during the ascent of the magma. These changes influence the rheology (e.g., viscosity) of magmas, and there might be a potential feedback between bubble structure and rheological behavior of flowing magma.

[17] The continuous shear deformation of vesiculated magmas will produce highly elongated bubbles, because the larger bubbles formed by coalescence easily elongate due to the small contribution from surface tension, even when the shear rate is constant. In the natural magmas, the elongated bubbles can not be easily divided by the shear stress, because μv/μm is very small [e.g., Stein and Spera, 1992]. Therefore, it can be inferred that the bubbles are continuously elongated in the deep conduit, and most plausibly, highly permeable zones are formed near the conduit wall. The development of this permeable zone might control the eruption style, i.e. explosive or effusive. For further understanding the effect of shear on eruption dynamics, experiments with wider ranges of vesicularity and viscosity are necessary.


[18] This study was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists to S.O. and MEXT Grant-In-Aid for Scientific Research to M.N. The authors are grateful to T. Nakano of AIST/GSJ for permitting the use of software “SLICE” for 3D image analysis. Official reviews by Alain Burgisser and an anonymous reviewer significantly improved the manuscript.