Pahoehoe to `a`a transition of Hawaiian lavas: an experimental study
Bull Volcanol (2014) 76:876
DOI 10.1007/s00445-014-0876-9
RESEARCH ARTICLE
Pahoehoe to `a`a transition of Hawaiian lavas: an experimental study
A. Sehlke & A. Whittington & B. Robert & A. Harris &
L. Gurioli & E. Médard
Received: 16 June 2014 / Accepted: 26 September 2014
#
Springer-Verlag Berlin Heidelberg 2014
Abstract Basaltic lavas collected at the Muliwai a Pele lava channel, built during 1974 as part of Mauna Ulu ’ s eruption on
Kilauea
’ s east rift zone, have been studied to investigate the effect of cooling and crystallization on the rheological properties of the lava. We have quantified the viscosity-strain-rate dependence of lava during cooling and crystallization, using concentric cylinder viscometry. We measured the viscosity of the crystal-free liquid between 1600 and 1230 °C, where we observed a deviation from the expected viscosity trend, marking the liquidus. We then made rheology measurements at subliquidus temperatures of 1207, 1203, 1183, 1176, and
1169 °C, varying the applied strain rates at each temperature.
While the crystal-free liquid behaved as a Newtonian fluid, crystallization changed the rheological response to pseudoplastic behavior, even at the lowest crystal volume fraction of
0.025. Pseudo-plastic behavior was observed down to a temperature of 1183 °C, with a crystal fraction of 0.15. Between
1183 and 1176 °C, the two-phase suspension transitioned from a power-law fluid to a Herschel-Bulkley fluid. At temperatures of 1176 and 1169 °C, with crystal fractions of 0.33
and 0.42, respectively, we observed lobate surface textures on the experimental samples, which remained preserved until the end of the experiments. Measurements at these temperatures
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A. Sehlke (
*
)
:
A. Whittington
Department of Geological Sciences, University of Missouri,
Columbia, MO 65211-1380, USA e-mail: asehlke@mail.missouri.edu
B. Robert
:
A. Harris
:
L. Gurioli
:
E. Médard
Laboratoire Magmas et Volcans, Université Blaise Pascal - CNRS -
IRD, OPGC, 63038 Clermont Ferrand, France indicated yield strengths of 82±16 and 238±18 Pa, respectively. The yield strength resulted from the development of an interconnected crystal network of diopside and enstatite by
1176 °C. By 1169 °C, diopside and plagioclase microcrystals had also appeared, and the effective viscosity was between
2000 and 5000 Pa s, depending on the strain rate. Further cooling to 1164 °C resulted in a rapid viscosity increase, to an effective viscosity in excess of 10
5
Pa s that exceeded the measurement range of our apparatus. The yield strength varies with crystallinity in an exponential fashion, with yield strength in Pa given by
σ y
=1.25e
12.93
Φ c
, where
Φ c is the crystal volume fraction. The physical effect of crystals on the relative viscosity of magma was assessed by removing the effects of changing residual liquid viscosity, due to changing composition and temperature. To do this, we analyzed, synthesized, and measured the most evolved residual liquid from the subliquidus experiments. The effect of crystals was best captured by the
Einstein-Roscoe equation for polydisperse spherical inclusions. We also measured the viscosity of the same crystalliquid mixtures at low temperatures and strain rates using parallel-plate viscometry. The effect of crystals on magma viscosity was slightly greater at low strain rates, in agreement with theoretical models, although no single model reproduced these results well. In our experiments, the transition from pahoehoe to `a`a occurred between 1200 and 1170 °C, at viscosities between 100 and 1000 Pa s, depending on strain rate.
Keywords Viscosity . Suspension . Rheology . Lava flow .
Yield strength . Pahoehoe . `a`a
Introduction
Subaerial lava flow surface morphologies of basaltic composition can fall between two main end-member types, pahoehoe
876, Page 2 of 20 Bull Volcanol (2014) 76:876 and `a`a (Dutton
). Pahoehoe can be described as a smooth, billowy, or ropy surface. In contrast, `a`a lava flows are characterized by a rough, jagged, spinose, and clinkery surface. The differences between these types extend beyond the surface morphology to their internal structure and the mechanism of flow emplacement (Macdonald
Peterson and Tilling (
1980 ) observed that nearly all Hawaiian
basaltic lavas erupt as pahoehoe, and that some lava flows change to `a`a during cooling. Peterson and Tilling (
related this transition to factors such as viscosity (
η
) and the rate of shear strain
γ
. They concluded that lavas with lower viscosity need to experience higher strain rates in order to begin the transition to `a`a. Conversely, a high viscosity lava transitions to `a`a at lower strain rates. This led to the formulation of the concept of a transition threshold zone (TTZ) by
Peterson and Tilling (
). Quantitative values for strain rate and viscosity were, however, missing (Fig.
).
Rowland and Walker (
) showed an effusion rate dependence of surface morphology for lava flows at Kilauea and
Mauna Loa. Here, the formation of rough `a`a surfaces was favored at high effusion rates of greater than 5 to 10 m
3
/s corresponding to higher flow velocities and strain rates.
Below this critical value, pahoehoe was found to form in
open channels. Cashman et al. ( 1999 ) studied samples collect-
ed from an active lava channel on Kilauea volcano during
May 1997 and confirmed the observation made by Kilburn
( 1987 ) that `a`a formed along the channel margins due to
disruption and tearing flow surfaces in the lateral shear zones. This led to the proposition that `a`a formation resulted from high strain rates and the development of a yield strength due to increasing ground mass crystallinity, mainly attributed to plagioclase microcrystals (e.g., Soule and
Cashman
). Similar observations were made by Sato
( 1995 ) on pahoehoe and `a`a lavas of Izu-Oshima volcano
(Japan), where the groundmass of `a`a lava had a higher proportion of plagioclase crystals than pahoehoe lavas.
The transition from pahoehoe to `a`a can be also reversed
(Calvari and Pinkerton
). Hon et al. (
) showed that decreasing strain rate, for example due to a decrease in slope or increase in channel width, can cause an `a`a flow to revert to pahoehoe morphology.
Robert et al. ( 2014 ) collected overflow samples down the
channelized section of the Muliwai a Pele lava flow at Mauna
Ulu (Kilauea), erupted in 1974. The samples were investigated to determine the down-flow evolution in physical and rheological properties that led to a transition from pahoehoe to `a`a at around 4.5 km from the vent. Lava density, microcrystal content, viscosity, and yield strength all increased down the channel, whereas vesicle content and lava temperature (determined by MgO content of the glass matrix) decreased. Comparing these physical characteristics with the surface morphology allowed the conditions of the TTZ to be quantified.
The aim of this study was to experimentally determine the key rheological properties of the Muliwai a Pele lava flow, these being viscosity and yield strength (
σ y
). Both properties depend on temperature ( T ), composition ( X ), crystal fraction
( Φ c
), and vesicularity ( Φ b
). Our measurements replicated T -
X -
Φ c conditions of open channel flow during cooling and measured the rheological response to crystallization. We defined the pahoehoe to `a`a transition, and its dependence on the applied strain rate
ð Þ and measured apparent viscosity
(
η app
), for two-phase suspensions. We compared our experimentally derived results to the field observations at Muliwai a
Pele as reported in Robert et al. (
) and found they are in broad agreement.
Methods
The rheological behavior of a shearing material can be defined as the relation between the deforming shear stress (
σ
) and the resulting strain rate γ . The simplest form of this relation is for a Newtonian fluid:
σ ¼ η γ ˙ ð
1
Þ
Fig. 1 Viscosity-strain-rate diagram illustrating the transformation of pahoehoe to `a`a in the transition threshold zone ( TTZ ). Modified from
) where
η is the viscosity of the liquid. The presence of solid particles and/or vesicles may cause a deviation from this linear relationship, which can be described by:
σ ¼ σ y
þ
K
γ n ð
2
Þ
Bull Volcanol (2014) 76:876 where
σ y is the yield strength that needs to be overcome to initiate deformation, K the consistency (for a strain rate of
1 s
− 1
), and n is the flow index. The flow index describes the deviation from Newtonian behavior ( n =1) of the fluid, with n being greater than one for shear-thickening and less than one for shear-thinning behavior.
The viscosity of the melt was measured using a sample of a roof that formed over the channel during the final phase of flow (Harris et al.
). The sample was collected at a distance of around 4 km from the vent (Robert et al.
2014 ). The actual sample used is of
little importance because all the samples have identical bulk chemistry (Robert et al.
bubbles were removed during remelting. This tube roof sample was fine-grained crushed and placed in a high form Pt90-Rh10 crucible that had previously been saturated with iron. It was then melted for 2 h at 1600 °C, in air. The melt was quenched by pouring on to a copper plate. In order to ensure chemical homogenization of the sample, the resulting glass was then crushed and remelted under the same conditions for 1 h, and quenched again. This sample will be referred as Mauna
Ulu remelt in the manuscript.
Concentric cylinder viscometry
Superliquidus experiments were performed using a Theta
Industries Rheotronic II Rotating viscometer with a Brookfield DV3TRV Rheometer with a calibrated spring torque (
τ
) of 7.187×10
−
4
Nm, capable of measuring viscosities from 0.1
to 1000 Pa s. This instrument was calibrated against Brookfield standard viscosity oils in the range of 10 to 100 Pa s.
Measurements at subliquidus temperatures and higher viscosities require a stronger spring and were performed using a
Brookfield HBDV-III Ultra measuring head with a calibrated full-range spring torque (
τ
) of 57,496×10
−
7
N m. The viscometer was checked against National Institute of Standards and Technology (NIST) standard glasses, which indicated an accuracy of better than 0.06 log units (Getson and Whittington
Samples were placed in an iron-saturated Pt90-Rh10 crucible with a depth of 65 mm and an inner radius ( R c
) of
15.075 mm. The crucible was held stationary using three alumina rods. The assembly is then lowered into the furnace.
An iron-saturated Pt90-Rh10 sleeve with a hemispherical tip covered an alumina spindle. The spindle had a length of
65 mm and an outer radius ( R b
) of 3.75 mm. To calculate viscosity, we measured the torque required to maintain a defined angular velocity (
ω
), so that the shear stress can be defined by:
σ ¼
τ
2
π
R
2 b
L
ð
3
Þ with L being the immersion depth of the spindle, which is controlled by a micrometer. The actual immersion depth was determined by measuring the level of residual melt covering the spindle after each experiment. The assemblage has a widegap geometry with a R c
/ R b of 4.02. This allows alignment of solid phases with large aspect ratios (such as plagioclase which has R >4). We calculated the strain rate from the experimental geometry, the measured angular velocity ω , and the flow index n (Stein and Spera
):
γ ¼
2
ω n 1
− ð
R b
=
R c
Þ 2 = n
ð
4
Þ
The flow index was obtained by calculating the slope of the measured ln(
τ
) against ln(
ω
). With both viscometers, the viscosity can be measured in a range between 0.1 and 10
5
Pa s.
Temperature during the experiment was measured using an
S-type thermocouple with an alumina sheath, positioned at the bottom of the crucible. Previous tests showed that no temperature gradient existed within the crucible, and the accuracy of the temperature measurement is ±3 °C, typical for S-type thermocouples. Once a stable sample temperature condition is reached (±2 °C), viscosity measurements are performed for at least 30 min at stable torque readings (±0.1 %), at three different angular velocities corresponding to strain rates between 55.5 and 35.5 s
− 1 to check for non-Newtonian behavior of the liquid. Viscosity measurements were performed at
25 °C increments toward lower temperatures, until the liquidus was detected. To check for any instrumental drift over the duration of the entire experiment, one final viscosity measurement close to the initial temperature, usually around
1550 °C, is performed.
Subliquidus measurements
Page 3 of 20, 876
Subliquidus measurements were performed in a similar fashion as for liquid viscosities. Measurements always began at
1550 °C to ensure complete melting of all crystalline phases in the sample, followed by a second measurement at 1450 °C to check the liquid viscosity. We kept the measurement duration to no more than 1 h, to minimize loss of volatile alkali elements at these high temperatures. We then cooled the sample at 10 °C/min, while maintaining a constant angular velocity of the spindle. Once the target temperature was reached, the sample temperature and spindle speed were held constant for 12 to 16 h. Equilibrium conditions were assumed to have been reached when no further torque increase was observed over a period of a few hours. Upon reaching equilibrium conditions, we varied the angular velocity in a stepwise manner beginning with the highest torque (80
–
100 % of the spring capacity) and ending with the lowest possible
876, Page 4 of 20 torque (
∼
1 %). Measurements were performed at controlled strain rates between 20 and 0.2 s
−
1
. The duration of each individual measurement at a given strain rate was at least
10 min of stable torque reading (±0.1 %). To check the time dependence of viscosity and instrumental drift, we gradually increased the strain rate for a few steps. A. Sehlke was present during all rheological measurements, observing the viscometer in order to detect any deviations from ideal measurements such as stick
– slip. No such behavior was observed.
On completion of rheology measurements, the crucible was quickly removed from the furnace and quenched by dipping in a water bath to avoid further sample crystallization. The cooling front migrated quickly from the crucible wall to the sample center, resulting in cooling from red hot to hand hot within 2 min. The thin film of residual melt attached to the spindle is immediately quenched in air during removal from the melt and exposure to ambient temperatures. Samples from both the crucible and the spindle were observed at high magnification using scanning electron microscopy, and no differences in crystallinity were observed.
Parallel plate viscometry
Several cylindrical cores of 6.6 mm diameter were drilled from the quenched glass. Viscosity of the supercooled liquid was measured under uniaxial compression in a Theta Industries Rheotronic III parallel-plate viscometer with a 1500 g load. This instrument is capable of measuring viscosities in the range 10
8 to 10
12
Pa s. The sample length was measured to
0.1
μ m using a transducer and recorded at set time intervals.
The longitudinal strain rate
ð ∂ ε = ∂ t
Þ gives the viscosity via the relationship (Dingwell
):
η ¼
σ
3
ð ∂ ε = ∂ t
Þ
ð
5
Þ
10
Strain rates during the measurements ranged between 1.5×
−
8 s
−
1 and 1.5×10
−
4 s
−
1
. The viscometer was checked against NIST standard glasses, indicating an accuracy of better than 0.06 log units (Whittington et al.
). The duration of each experiment was around 4 h, and viscosity data were collected at alternating higher and lower temperatures, which allows for easy detection of anomalous viscosity readings caused by crystallization.
Density measurements
The density of each sample was measured both before and after experiments. Measurement used the well-known Archimedean method whereby the sample is first weighed in air, and then immersed in ethanol. Each sample was measured five times, giving a standard deviation of 2 kg/m
3
.
Bull Volcanol (2014) 76:876
Chemical analysis
Compositions of glasses and crystals were analyzed at Washington University in St. Louis on a JEOL JXA-8200 electron microprobe equipped with five wavelength-dispersive spectrometers (WDS) and a JEOL (e2v / Gresham) silicon-drift energy-dispersive spectrometer (EDS). Operating conditions were a 15-kV accelerating potential and 25-nA probe current with a 5-
μ m beam diameter. Oxide and silicate standards were used for calibration, and data were corrected using CITZAF
). For each sample, both the core drilled from the crucible and material attached to the Ptspindle were analyzed. A minimum of six individual analyses were completed for the glasses, and at least three individual analyses were made of each crystal phase (olivine, pyroxene, and plagioclase) in each sample.
Iron-redox determination
The long experiment durations of the subliquidus concentric cylinder viscosity measurements at atmospheric conditions may result in sample oxidization, which can lead to a slight increase in melt viscosity (Dingwell and Virgo
). We measured the bulk iron oxidation state of all samples using
the method described by Wilson ( 1960
) and Schuessler et al.
( 2008 ), which uses a combination of wet chemistry and
ultraviolet/visible (UV/Vis) photo-spectrometry. We dissolved
10 to 20 mg samples in a mixture of ammonium vanadate and hydrofluoric acid. All ferrous iron present in the sample was oxidized during decomposition, so the solution was then neutralized with boric acid, which restored the original ferrous iron content of the sample. The sample solution was then added to an ammonium acetate buffered solution containing
2,2
′
-bipyridine that causes a reaction to a red-colored complex containing only ferrous iron.
Absorbance spectra in the range of 420 to 720 nm were collected with a Thermoscientific Nanodrop 1000 UV/Vis photo-spectrometer and a path length of 1 mm. The background absorbance at 700 nm was subtracted from the characteristic absorbance peak of the organic Fe
2+ complex at
523 nm. A calibration curve was constructed from standard solutions of known iron concentration in the range of 0 to
56 ppm. The iron concentration of the sample solution was calculated using the Beer-Lambert law. The amount of ferrous iron originally present was denoted as original Fe
2+
. In order to measure the remaining ferric iron in the solution (which has not partaken in the redox-reaction between ferrous iron and vanadium), a reducing agent was added to an aliquot of the sample solution and 5
μ l of this solution was analyzed in the same way as before. This new measurement, of the total iron concentration in the sample, was denoted
Σ
Fe
2+
. The difference between total
Σ
Fe
2+ and original Fe
2+ reflected iron present in the original sample as ferric iron. For each sample,
Bull Volcanol (2014) 76:876 two individual analysis solutions were prepared, and the original and total ferrous iron concentrations of each solution were measured three times. The accuracy of the procedure was checked with one blank measurement and two measurements of original and total Fe
2+ for USGS standards BIR-1a (basalt) and W-2a (diabase) with each batch of seven unknown samples. The Fe
2+ and Fe
3+ contents of the USGS standards were typically reproduced with an uncertainty of 0.15 wt.% (2
σ
).
Evaluation of crystal volume fraction and crystal aspect ratios
Several backscattered electron images (BSE) were acquired for each sample at magnifications of ×40, ×200, and ×600.
The gray-scale images were then processed with Adobe
Photoshop® in order to enhance the crystal boundaries and contrast within the glassy matrix. The enhanced images were then further processed in order to only show single phases present in the sample (e.g., individual pictures showing only glass, spinel, olivine, pyroxenes, and plagioclase). Using the histogram function, the number of pixels for each phase was determined. Processing images at different magnifications for the same samples yielded a standard deviation of 2 vol% for the reported crystal fractions.
Aspect ratios of crystalline phases were evaluated with
ImageJ, by applying its automatic ellipse fitting procedure to the previously outlined grain boundaries for each phase. A manual quality check of the fitting ellipses was done afterwards to check for possible errors during auto-fitting. In the case of fitting failure, which is common at higher crystal fractions where crystals are in contact, aspect ratios were measured manually. Mean aspect ratios are reported as
R
¼
X
R i ϕ i ϕ c
ð
6
Þ where R i is the mean aspect ratio for each phase and crystal fraction.
Φ c the
Results
Sample texture and mineral assemblages
Figure
shows backscattered electron (BSE) images with tabulated values of mineralogy, crystal fractions, and aspect ratios in Table
for every subliquidus experiment. The first measurement below the liquidus was at 1207 °C, where we observed iron- and titanium-rich chromium spinel as well as a few forsterite-rich olivine crystals as liquidus phases. The total
Page 5 of 20, 876 crystal fraction
Φ c
∼
2.2 (Fig.
).
was
∼
0.03 with a mean aspect ratio R of
At 1203 °C, we observed enstatite (containing up to
6 mol% iron and about 2 mol% calcium) and spinel again, but no olivine. The crystal fraction had increased to
∼
0.06
with a slight decrease in the mean aspect ratio to ∼ 2.1 due to increasing spinel content. An experiment at 1194 °C yielded spinel and forsteritic olivine, with diopside in place of enstatite. The crystal fraction was
∼
0.09 and the mean aspect ratio dropped to
∼
1.9. The presence of olivine in the 1994 °C sample is probably due to its unusually high Fe
2+
/
Σ
Fe
2 ratio of 0.32 (Table
). In most of our experiments, the oxidizing environment promotes the crystallization of oxides and suppresses olivine. At 1183 °C, the mineral assemblage had reverted to spinel and enstatite, but with a higher crystal fraction of 0.15 and mean aspect ratio of
∼
2.1.
In the experiment at 1176 °C, we identified an irontitanium spinel (almost chromium free), enstatite, and diopside. The crystal fraction had increased markedly to a value of
0.33 and R increased slightly to 2.24, due to the appearance of acicular diopside crystals. Moreover, due to the higher crystallinity, an interconnected network of enstatite and diopside crystals started to develop at this temperature.
At our lowest measured temperature of 1169 °C, spinel, enstatite, and diopside were still present and anorthite-rich plagioclase now appeared. The crystal fraction continued to increase rapidly, to ∼ 0.42, with an increase in the mean aspect ratio to
∼
2.6 due to tabular plagioclase. Enstatite appeared as larger phenocrysts embedded within a network of diopside and plagioclase microcrystals (Fig.
). In summary, we noticed a steady increase in mean crystal aspect ratio with greater crystal fractions, whereas the mode of the aspect ratio is only slightly varying between 1.40 and 1.60.
Melt chemistry evolution
At successively lower temperatures, crystal fraction increased, melt fraction decreased, and the melt evolved toward more silicic and less magnesian compositions (Fig.
the melt composition are given in Table
decreased, we observed a steady increase in SiO
2
, Al
2
O
3
, and alkalis, whereas the total FeO and MgO contents decreased monotonically. CaO contents increased to a maximum at
1183 °C, then decreased due to the appearance of diopside at
1176 °C and anorthite-rich plagioclase at 1169 °C. Titanium content also peaked at 1183 °C, due to concentration of Ti into spinel at lower temperatures.
Liquid viscosity
Viscosity data for crystal-free liquids are given in Table
and plotted on an Arrhenian diagram in Fig.
876, Page 6 of 20 Bull Volcanol (2014) 76:876
Fig. 2 Backscattered electron images of all six subliquidus experiment temperatures at 1207, 1203, 1194, 1183, 1176, and 1169 °C. The identified mineral assemblages are given below each image. Note that image ( a ) through ( d ) are taken in ×40 magnification and ( e ) and ( f ) in ×200 magnification sample (Mauna Ulu remelt) and the most evolved interstitial glass composition (Mauna Ulu evolved) show a distinctly non-Arrhenian temperature dependence of viscosity. The evolved composition is between 0.5 and 1 log unit more
Bull Volcanol (2014) 76:876 Page 7 of 20, 876 viscous than the bulk remelt over the full temperature range of measurement. The evolved composition is more polymerized, with a theoretical ratio of non-bridging oxygens to tetrahedral cations (NBO/T) of
∼
0.60 compared with the tube roof with a
NBO/T of
∼
0.92, considering all iron as FeO only (see Table
). In fact, the melt was always partially oxidized, so that
NBO/T actually decreased from
∼
0.60 to
∼
0.35 as the crystal fraction increased (Fig.
). The significant increase in viscosity that accompanies this increase in polymerization means that the interstitial liquid viscosity at each subliquidus temperature should be measured individually in order to accurately determine the influence of suspended crystals on magma viscosity. For both liquids, the viscosity data measured from
1600 °C to the glass transition were fitted with a Vogel-
Fulcher-Tammann (VFT) equation in the form of log
η
(Pa s)= A + B /( T
−
C) (Vogel
), where A , B , and C are adjustable parameters for measured viscosity and T is the temperature in kelvin. The best-fit parameters obtained by least-squares regression are reported in Table
for both liquids.
At temperatures between 1250 and 1230 °C, we observed a disproportional increase in measured viscosity of the remelted tube roof, as well as much longer stabilization times for torque readings. We inferred that the liquidus was crossed in this temperature interval, and that subliquidus rheology measurements should be carried out at temperatures below 1230 °C.
Rheological properties of two-phase suspensions
The flow index ( n ) was determined for each individual temperature from the slope on a diagram of ln(
τ
) against ln(
ω
)
(Fig.
7a ). The uncertainty of the flow index has been derived
by the error on the slope of the linear regression and are reported as a 2
σ
. At temperatures above the liquidus, the basaltic liquid behaved as a Newtonian fluid ( n =0.98±0.02).
Once the liquidus has been crossed and crystals appear (here first detected at 1207 °C), the flow index decreases, reaching
0.96±0.01 at 1207 °C, and the two-phase suspension develops a pronounced non-Newtonian or pseudo-plastic behavior. Further cooling and increasing crystal fraction enhances the shear-thinning character of the two-phase suspension
(Fig.
), with the flow index decreasing to 0.49±0.03 at
1169 °C and a crystal fraction of 0.42 (Table
determined the flow index for each temperature, the strain rate for non-Newtonian fluids was adjusted by Eq. (
), allowing flow curves for each temperature to be constructed (Fig.
The non-Newtonian (power-law) behavior of the suspension is quite evident (Table
).
Petrographic observations (Fig.
) indicated a crystal framework of enstatite and diopside developed by 1176 °C and more distinctly by 1169 °C between diopside and plagioclases. In order to disrupt this crystal network, a minimum stress may be required to initiate flow indicating the
876, Page 8 of 20
Fig. 3 Frequency of measured aspect ratios (length/width) in 0.2
increments of crystals for each temperature, n =is the number of analyzed crystals and R corresponds to the calculated mean aspect ratio
Bull Volcanol (2014) 76:876 development of a yield strength (
σ y
), which should result in a non-zero intercept of the flow curve on the stress axis (Kerr and Lister
). The development of a yield strength in our experiments at 1176 and 1169 °C is supported by the observation of surface textures of the lava (Fig.
9 ), preserved after quenching immediately
following the highest strain-rate measurement. Smooth lobate flow structures about 3 – 5 mm wide and 1 – 2 mm tall formed in these experiments but were not observed in experiments at temperatures above 1176 °C.
Because measurements at zero strain rate are infinitely time-consuming, this always requires estimation by extrapolation of an assumed flow law. One approach is to linearly extrapolate the two measurements made at the lowest strain rate, which then provides a maximum estimate of the yield strength (Avard and Whittington
2012 ). When applied to our data, we obtained
σ y of
42 Pa at 1183 °C, increasing to 112 Pa at 1176 °C, and
636 Pa at 1169 °C. These are unrealistically high estimates because the lowest strain rates we could measure at were 0.04 s
− 1
, and the linear extrapolation remains higher than a power-law extrapolation to lower strain rates. So, we adopted an alternative approach, whereby we estimated
σ y by using the power-law fits to calculate the stress required for deformation at a lower strain rate of 0.01 s
−
1
. The resulting estimated yield strengths were
16 ± 2 Pa at 1183 °C and 82 ±16 Pa at 1176 °C, increasing to 238 ± 18 Pa at 1169 °C. We would like to point
Bull Volcanol (2014) 76:876 Page 9 of 20, 876
Table 2 Major oxide chemistry of quenched glass equilibrated at subliquidus temperatures compared with the crystal-free starting composition remelted
(1268 °C) and a synthetic composition (MU evo) reflecting melt equilibrated at 1169 °C
Temperature (°C) 1268 1207 1203 1194 1183 1176 1169 MU evo wt.% ± wt.% ± wt.% ± wt.% ± wt.% ± wt.% ± wt.% ± wt.% ±
SiO
2
TiO
2
Al
2
O
3
Cr
2
O
3
FeO a
MnO
MgO
CaO
Na
2
O
K
2
O
P
2
O
5
Σ
Fe
2+
/
Σ
Fe
2+
FeO
Σ
FeO
Fe
2
O
3
NBO/T a
NBO/T b
NBO/T c
49.70
0.20
50.34
0.38
51.38
0.23
51.03
0.27
51.52
0.10
53.06
0.43
55.04
0.32
54.68
0.52
2.22
0.02
2.26
0.03
2.32
0.04
2.34
0.04
2.41
0.04
2.25
0.07
2.20
0.04
2.27
0.04
12.26
0.03
12.64
0.07
12.86
0.13
13.04
0.10
13.28
0.07
14.26
0.24
13.65
0.06
14.45
0.04
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.03
0.03
10.13
0.09
10.57
0.26
9.15
0.17
9.67
0.13
8.83
0.09
7.67
0.10
7.37
0.17
6.47
0.05
0.17
0.01
0.17
0.03
0.16
0.02
0.17
0.03
0.16
0.03
0.17
0.03
0.18
0.01
0.15
0.02
10.35
0.60
0.30
0.08
9.64
0.56
0.28
0.09
9.28
0.47
0.26
0.13
8.56
0.50
0.24
0.17
8.70
0.45
0.25
0.07
7.52
0.38
0.20
0.10
6.88
0.34
0.17
0.13
6.78
0.42
0.33
0.05
10.27
0.08
10.36
0.16
10.86
0.15
10.66
0.15
10.89
0.15
10.31
0.13
9.58
0.13
9.89
0.05
2.11
0.03
2.04
0.05
2.16
0.03
2.21
0.04
2.24
0.02
2.79
0.04
2.85
0.04
2.90
0.03
0.42
0.01
0.42
0.04
0.44
0.02
0.43
0.03
0.43
0.03
0.57
0.05
0.70
0.06
0.81
0.01
0.21
0.02
0.24
0.05
0.24
0.03
0.23
0.05
0.21
0.05
0.33
0.04
0.38
0.06
0.45
0.01
97.84
0.41
98.70
0.48
98.85
0.48
98.35
0.44
98.67
0.28
98.95
0.19
98.84
0.20
98.88
0.54
0.32
0.02
0.33
0.01
0.163
0.01
0.316
0.01
0.17
0.02
0.18
0.01
0.17
0.02
0.39
0.03
3.64
0.20
3.39
0.11
1.82
0.13
3.67
0.16
1.83
0.22
1.88
0.12
1.85
0.11
2.34
0.08
11.22
0.35
10.39
0.26
11.19
0.30
11.61
0.30
10.78
0.33
10.46
0.28
10.68
0.28
6.24
0.21
8.31
0.21
7.78
0.20
10.40
0.28
8.82
0.23
9.94
0.30
9.53
0.25
9.80
0.25
4.33
0.15
0.92
0.87
0.82
0.80
0.78
0.66
0.60
0.57
All iron accounted as (a) FeO, (b) FeO and Fe
2
O
3
, and (c) Fe
2
O
3 only
“
±
” standard deviation of six individual glass analysis per sample,
Σ the total of the micro probe glass analysis by electron microprobe in wt.%, Fe
2+
Σ
Fe the ratio of absolute Fe
2+ over
Σ
Fe in the bulk sample determined by wet chemistry (A value of one sample being fully reduced (0 fully oxidized)),
/
NBO/T the ratio of non-bridging oxygen (NBO) over tetrahedrally coordinated cations (T) a
All iron expressed as FeO by electron microprobe out that the error estimate for the yield strength is only valid for the strain rate of 0.01 s
− 1
. We have selected this strain rate of 0.01 s
−
1 to represent a very slowly migrating lava flow, which is effectively about to stop moving.
Several attempts were made to carry out one additional measurement at a lower equilibration temperature, between 1160 and 1165 °C, but the exerted stresses on the spindle were too high for our apparatus even at the lowest possible strain rates. We infer that the deformation of the crystal mush at a temperature of 1160 °C and below requires much higher stresses, correlating to effective viscosities greater than 10
5
Pa s. In summary, the Hawaiian basalt transitioned from a Newtonian liquid to a power-law suspension almost immediately upon crossing the liquidus, with shear-thinning clearly detectable at a crystal fraction of 0.025. In addition to the shear-thinning character, the suspension developed a detectable yield strength at a crystal fraction of
∼
0.15, beyond which the suspension can be classified as a
Herschel-Bulkley material.
Discussion
Magma flow laws and yield strength
The measured apparent viscosities at various strain rates are plotted as a function of crystal fraction in Fig.
unequivocally pseudo-plastic behavior ( n <0.95) becomes evident in the range between
Φ c
=0.06 and
Φ c
=0.15. The suspensions clearly exhibit shear-thinning behavior, with higher strain rates resulting in lower apparent viscosities. The term
“ apparent viscosity
” is used to indicate that the result depends on the particular strain rate at which it was measured. The shear-thinning effect is modest at the lowest crystal fractions but increases with crystallinity. At
Φ c
=0.42, an increase in strain rate by a factor of ∼ 500 results in a decrease in apparent viscosity by a factor of
∼
24.
These are similar to the results of previous experimental studies using concentric cylinder viscometry at similar strain rates. Ishibashi and Sato (
2007 ) detected pseudo-plastic be-
havior in an alkali olivine basalt at
Φ c of only 0.05 (olivine, plagioclase, and spinel). Ishibashi (
) detected pseudo-
876, Page 10 of 20
Fig. 4 Evolution of the melt/ glass composition in mol% for the major oxides with decreasing melt fraction. Appearance of crystal phases are indicated with spinel present in all samples (see also Table
)
Bull Volcanol (2014) 76:876
Bull Volcanol (2014) 76:876 Page 11 of 20, 876
Table 3 Liquid viscosities at high and low temperatures for remelted tube roof and evolved composition
High-temperature viscosity measurements from concentric cylinder viscometry
Low-temperature viscosity measurements from parallel plate viscometry
Remelted tube
Temperature (°C)
1574
1547
1522
1496
1471
1445
1420
1394
1369
1344
1318
1293
1268
1242
1217
VFT-fit parameters
A =
−
5.08
B =6140.5
C =558.8
Evolved composition
Temperature (°C)
1577
1541
1517
1492
1466
1440
1413
1389
1363
1338
1313
1286
1260
1228
1207
1181
1170
1140
VFT-fit parameters
A =
−
3.64
B =4950.2
C =633.4
10,000/T (K
−
1
)
5.41
5.49
5.57
5.65
5.73
5.82
5.91
6.00
6.09
6.18
6.28
6.38
6.49
6.60
6.71
RMSD=0.12 log Pa s
10,000/T (K
5.40
5.51
5.58
5.67
5.75
5.84
5.93
6.02
6.11
6.21
6.30
6.41
6.52
6.66
6.76
6.87
6.93
7.08
−
1
)
RMSD=0.08 log Pa s
Log
η
(Pa s)
−
0.15
−
0.08
0.00
0.08
0.16
0.26
0.35
0.46
0.55
0.68
0.80
0.93
1.07
1.23
1.47
Log
η
(Pa s)
0.47
0.56
0.69
0.78
0.88
0.98
1.09
1.20
1.31
1.43
1.55
1.70
1.84
2.01
2.16
2.33
2.40
2.61
Temperature (°C) 10,000/T (K
−
1
) Core 1 Log
η and core 2 (Pa s)
742.1
9.85
8.52
742.0
733.9
729.9
724.3
712.7
712.7
697.9
691.8
680.3
674.7
666.0
658.9
647.2
691.3
702.2
711.3
721.0
730.6
740.2
9.85
9.93
9.97
10.03
10.14
10.14
10.30
10.36
10.49
10.55
10.65
10.73
10.87
10.37
10.25
10.16
10.06
9.96
9.87
8.51
8.67
–
9.01
9.53
–
–
–
–
–
11.43
–
11.70
Temperature (°C) 10,000/T (K
−
1
) Log
η
(Pa s)
681.3
10.48
11.68
11.35
10.65
10.44
10.21
9.90
9.53
–
–
–
8.58
–
–
9.18
9.73
10.00
10.39
10.69
–
11.34
–
876, Page 12 of 20 Bull Volcanol (2014) 76:876
Fig. 5 Measured liquid viscosity of remelted tube roof ( black dots ) and evolved composition (based on residual melt composition of crystallization experiment at 1169 °C) between 1594 and 1140 °C measured by concentric cylinder viscometry and 742 and 647 °C by parallel plate viscometry. Measured data are fitted by a VFT equation ( solid lines ) and thickness representing the uncertainty. The temperature range of crystallization for the remelt detected by viscometry is shaded in gray , and the glass transition ( Tg ) at a viscosity of 10 12 Pa s is given for both compositions plastic behavior in a basalt from Mt. Fuji at
Φ c as low as 0.06
to 0.13 due to suspended plagioclase crystals. Vona et al.
) observed shear thinning behavior in lavas from
Stromboli and Etna at
Φ c greater than 0.15. Ryerson et al.
) detected pseudo-plastic behavior in picritic magma at
Φ c exceeding 0.25 (olivine and spinel). Variations in the crystal fraction at which the onset of pseudo-plastic behavior is detected can arise from different behavior of different magmas, with different crystal assemblages, and also from the range of strain rates used and the sensitivity of the apparatus.
The simplest form of non-Newtonian behavior is Bingham rheology, where stress vs. strain rate is linear but has a positive intercept on the y -axis that equates to the yield strength.
) reinterpreted the data of Ishibashi
) using a Bingham fluid model, yielding a slightly better fit to their data, and calculated
σ suspensions with Φ c y of 19.5±4.6 Pa for their of 0.25. However, we find a great reduction in the flow index at crystal fractions above 0.15 (Fig.
and prefer the model pseudo-plastic rheology model. Using the previous defined approach, we calculated σ y
Φ c of 0.15 (1183 °C), 82±16 Pa at increasing to 238±19 Pa at
Φ c
Φ c of 16±2 Pa at of 0.33 (1176 °C), of 0.42 (1169 °C). Ryerson
) adopted a quadratic relationship between stress and strain rate for the purposes of calculating the yield strength in their experiments in picrites. They found
σ at Φ c
∼ of ∼ 0.25, increasing rapidly to ∼ 300 – y of
∼
47
–
311 Pa
700 Pa at
0.31, and fitted a power-law relationship between
σ y
Φ c and
Φ of c
.
Compiling all these results demonstrates the sensitivity of yield strength estimates to the method used, and suggests that an exponential relationship may be more appropriate (Fig.
The best fit to our data is given by:
σ y
¼
1
:
25e
12
:
93
Φ c
ð
7
Þ
Fig. 6 Calculated degree of polymerization expressed as non-bridging oxygen (NBO) tetrahedrally coordinated cations (T) (NBO/T) of the residual melt with decreasing melt fraction considering the melt containing only FeO, FeO+Fe expressed as Fe
2
O
3
2 only
O
3
(determined by wet chemistry), and all iron which is also consistent with the results of Ishibashi (2010).
The results of Ryerson et al. (
) are underestimated by
), but the rheological meaning of their quadratic flow law used to estimate the yield strength is not clear. Their picrites crystallized early olivine and chrome spinel, followed by clinopyroxene and plagioclase, so the differences between their results and ours are unlikely to be due to differences in aspect ratio. We also compared our
results to those of Hoover et al. ( 2001 ) done on analog
materials. Their findings of prismatic particles on yield
strength are similar to our results. We recommend Eq. ( 7 ) be
used in modeling Hawaiian basaltic lavas and similar compositions.
Effect of crystals on magma rheology
Our subliquidus measurements reflect the combined effects of increasing crystal content and changing residual melt viscosity, which in turn is affected both by decreasing temperature
Bull Volcanol (2014) 76:876 Page 13 of 20, 876
Fig. 7 a Measured torque (
τ
) against angular velocity (
Ω
) on a double logarithmic plot to evaluate the slope (flow index ( n )) of each temperature curve. Accuracy of individual measurement is smaller than symbol size.
b and changing residual melt composition (Getson and
Whittington
). Estimating the residual liquid composition is particularly important when it comes to calculating and s modeling the relative viscosity (
η r
), which is defined as
η r
/
η l
, with
η s and
η l
=
η
as the viscosity of the suspension and liquid, respectively. There exists a large volume of literature on the subject of suspension rheology, but mostly it deals with the addition of crystals to a liquid of constant composition and temperature. In order to extract the effect of crystals on magma rheology, the interstitial melt viscosity must be known,
Determined n against the crystal fraction shows a transition from Newtonian fluid ( n =1) for crystal-free lava to a pseudo-plastic fluid ( n <1) with increasing crystal fraction (
Φ c
) either through time-consuming direct measurement or by calculation. We compared the reliability of these two approaches.
First, we calculated the viscosity of the residual liquid in each experiment, from the analyzed glass composition and known experimental temperature, using the viscosity model
for magmatic liquids provided by Giordano et al. ( 2008 ). For
the crystal-free liquid viscosity at 1230 °C, we measured a viscosity of 27 Pa s and the Giordano et al. (
) model predicts 17 Pa s. For subliquidus conditions, the Giordano
Fig. 8 a Constructed flow curves of subliquidus rheology experiments for each temperature. Collected data points ( black dots ) are well fitted by a power-law relationship. The determined flow index ( n ) is given and decreases with decreasing temperature, indicating a more pseudo-plastic behavior ( n <1) at lower temperatures.
b Close-up of the flow curves up to a strain rate of 0.25 s
−
1 to illustrate an apparent yield (
σ y can be extrapolated at 0.01 s
−
1
) strength, which in the order of 82 to 238 Pa, respectively, classifying the two-phase suspensions at those temperatures as Herschel-
Bulkley fluids.
Open circles cutting the 1203 °C curve represents an experiment at 1194 °C, which is inconsistent with the general trend (see
“
”
); 2
σ error envelopes are shaded in gray , derived by the standard deviation ( s y
) of the shear stress of our data to the linear regression of ln(
τ
) vs. ln(
ω
)
876, Page 14 of 20 Bull Volcanol (2014) 76:876
Table 4 Measured torque (
τ
) values (±0.1 %) given in
μ
Nm for each RPM and immersion depth ( L ) at each temperature
1268 °C 1207 °C 1203 °C 1194 °C 1183 °C 1176 °C 1169 °C
RPM
τ
(
μ
Nm) RPM
τ
(
μ
Nm) RPM
τ
(
μ
Nm) RPM
τ
(
μ
Nm) RPM
τ
(
μ
Nm) RPM
τ
(
μ
Nm) RPM
τ
(
μ
Nm)
150
120
100
L
684
547
460
=20 mm
87.1
64.0
47.5
38.3
38.0
33.1
21.8
16.0
L
3068
2290
1720
1391
1351
1220
815
606
=32 mm
50.0
40.0
40.0
30.0
20.0
11.0
6.0
L
4386
3670
3552
2870
1992
1215
780
=25 mm
30.0
25.0
20.0
16.5
10.5
9.1
7.8
7.1
936
871
4.1
629
L =24 mm
2173
2005
1726
1481
1095
1027
20.0
11.0
8.2
5.9
1.7
1.4
0.4
L
4136
2479
2041
1654
630
653
277
=28 mm
15.0
10.0
8.0
3.0
1.0
0.5
0.1
L
5393
3967
3954
1995
1059
776
385
=23 mm
3.0
2.0
1.0
0.5
L
3984
3444
2467
1662
=18 mm
) model predicts a substantial increase in melt viscosity from 58 Pa s at 1207 °C to 689 Pa s at 1169 °C.
We synthesized the composition of the interstitial melt at
1169 °C and measured its viscosity over a wide temperature range. At 1169 °C, its viscosity is only 305 Pa s, indicating that the Giordano et al. (
) model substantially overestimates the increase in residual melt viscosity during crystallization (Fig.
).
Rather than synthesize and measure the viscosity of the interstitial melt from every experiment, we note that a previous study of residual melt viscosity in several synthetic systems, including An-Di-Fo, found that the evolving viscosity along the liquid line of descent typically follows a linear trend between the highest and lowest temperatures (Getson and
Whittington
2007 ). We made the same assumption and calcu-
lated the viscosity at intermediate temperatures by linear interpolation between the bulk remelt measured at 1230 °C
(approximately the liquidus), to the evolved composition at
1169 °C (Fig.
).
Using this interpolated interstitial liquid viscosity, we calculated the increase in relative viscosity due only to the physical effect of the crystal fraction, and compared our results to existing models (Fig.
although the data from this study are broadly consistent with the predictions of several previous models, they cannot be reproduced accurately by any other model. Aside from the noticeable initial increase in relative viscosity as crystal fraction increases between 0 and 0.1, our data plot on the relative viscosity predicted by the Einstein-Roscoe equation for polydisperse spheres (Roscoe
1952 ) up to our highest measured
crystal fraction of 0.42. At higher crystal fractions, relative viscosity could continue to follow this model or follow any of the models of Costa et al. (
Fig. 9 Subliquidus rheology surface texture preserved during the experiment at 1176 °C ( left ) and 1169 °C ( right ). Lobe structures about 3 to
6 mm wide and 1 to 2 mm high are observed around the central hole where the spindle was immersed
Fig. 10 Measured apparent viscosity at different strain rates against crystal fraction showing the strong strain rate dependence of the suspensions with increasing crystal fraction
Bull Volcanol (2014) 76:876 Page 15 of 20, 876
Fig. 11 Calculated yield strength
σ y as a function of crystal fraction
Φ c of this study derived by a power-law model are plotted as solid diamonds , and by the Bingham model as half-filled diamonds , and are compared
with results published by Ryerson et al. ( 1988
) by the quadratic flow law,
) by the Bingham model, and Hoover et al.
) for analog materials for spheres, flow based ( fb ), and texture based
( tb ) prisms
Fig. 13 Comparison of historic and recent relative viscosity models with experimental data ( black solid and dotted lines ). Einstein (
) for polydisperse particles B =2.5, Roscoe (
b =1.35, Guth and
B =2.5, and B
1 with B =2.5 and
Φ m
δ
=8, and
ξ
=10
−
4
=14.1, Krieger and Dougherty ( 1959
)
=0.67 and Costa (2009) with B =2.5,
Φ
*
=0.6,
α
=5,
). However, the Einstein-Roscoe
(Marsh
; Roscoe
), as well as the Einstein ( 1911 ) and Guth and Gold ( 1938 ) models are of limited use when
Fig. 12 Illustration of measured liquid viscosities fitted by VFT equations for Mauna Ulu remelt ( gray line ) and evolved Mauna Ulu remelt
( blue line ) in the temperature range of 1150 to 1240 °C. The linear interpolated viscosities are plotted as black/blue diamonds and are compared with the modeled viscosities by the model of Giordano et al. (
The measured apparent viscosities are plotted as solid circles with crystal fraction given in parentheses rheology is clearly non-Newtonian, because relative viscosity then depends on strain rate. This is clearly demonstrated in our samples (Fig.
), and therefore we place more emphasis on models that include strain-rate dependence, such as Costa
In order to estimate which of these models would be most realistic for our two-phase suspensions, we estimated an additional datum. At a temperature of
∼
1164 °C, the instrumental viscosity limit of 10
5
Pa s had been reached and represents a minimum estimate of the effective viscosity of the suspension. This sample had to be reheated before the spindle could be extracted, so the actual crystal content at 1164 °C is not known. However, it can be estimated by extrapolating the observed T -
Φ c trend (Fig.
14 ), resulting in an estimated crystal
fraction of 0.66. This point is plotted on Fig.
and could be plotted at a somewhat higher viscosity or lower crystal fraction, but not vice-versa. It therefore implies a rapid increase in relative viscosity as
Φ c increases from
∼
0.4 to
∼
0.6, deviating sharply from the models of Einstein (
) and Guth
and Gold ( 1938 ). The trend of apparent viscosity is broadly
consistent with the models of Roscoe (
), Krieger and
Dougherty (
1959 ), and Costa (2009). Considering the
mean aspect ratio of 2.67, the crystals in the sample are moderately prolate, shifting the relative viscosity to the left of the Einstein-Roscoe curve, as demonstrated by Mueller et al. (
). Additional data are needed to determine which of these models provides the best fit in this intermediate crystallinity range.
876, Page 16 of 20 Bull Volcanol (2014) 76:876
Fig. 14 Observed total crystal fraction as a function of temperature fitted by a power-law relationship ( solid line ) to estimate the crystal fraction at the lowest experimental temperature of 1164 °C ( star symbol ), where experiments failed due to exceeding instrumental capability, translating to
η
>10
5
Pa s. The dashed line represents the theoretical sigmoidal path of
the curve adopted after Marsh ( 1981 )
Fig. 15 Drilled cores from quenched subliquidus experiments measured at low temperatures near the glass transition show the increase in apparent viscosity of only 2 to 3 orders of magnitude for a crystal fraction of 0.33
compared with the liquid viscosity at that temperature
We also applied the model algorithm presented by Mader
), who recommend a variety of calculation approaches depending on crystal fraction ( Φ c
), maximum packing fraction (
Φ max
), crystal aspect ratio, and flow index. We find that this algorithm slightly underestimates the viscosity at crystal fractions below 0.15, mainly due to the use of a semiempirical flow index of 1 (i.e., Newtonian behavior), which contradicts our observations of pseudo-plastic behavior of the suspension even at crystal fractions as low as 0.06. At crystal fractions higher than 0.15, the algorithm by Mader et al.
( 2013 ) strongly overestimates the relative viscosity, as the
crystal fraction begins to approach the maximum packing fraction.
We also measured the viscosity of the crystal-bearing samples, cored from the quenched subliquidus experiments, using the parallel-plate viscometer (Fig.
). At these lower temperatures, viscosity becomes very sensitive to small changes in temperature and melt composition. The curves of the bulk remelt and crystal-bearing glasses are nearly parallel across the measured range of temperature and viscosity, and apparent viscosity of the magma increases with increasing crystal content. The most crystalline sample ( Φ c
=0.42) plots 0.6 log units below the next highest crystal content (
Φ c
=0.33), which may reflect some heterogeneity in crystal distribution within the sample core. The finite strain in the parallel-plate experiment for the sample with
Φ c
=0.42 was about 15 %, and strain would concentrate in the lowest viscosity (lowest crystallinity) regions if the core were heterogeneous.
Interstitial melt viscosities were again calculated by linear interpolation between the measured data for the bulk liquid and the evolved composition. Relative viscosity of the magma to the crystal-free liquid was then calculated at 727 °C for all samples (Fig.
relative viscosity initially increases quite steeply, by a factor of 20 for a crystal fraction of 0.15, in good agreement with the predictions of Mader et al. (
By
Φ c
= 0.33, the increase is only a factor of 58, which falls below the Mader et al. (
matches quite well with the model of Costa (2009).
The latter has been recalculated for the lower strain rates employed in the parallel-plate viscometer, which moves it to the left relative to its position in Fig.
we do not know why the data for the most crystalline sample (
Φ c
= 0.42) are inconsistent with the other samples, we have not plotted it on Fig.
, but it would have a relative viscosity of only
∼
10.
In summary, physical models for the effect of crystals on magma viscosity ignore the effects of changing temperature and residual melt composition, which will affect the rheology of lava flows. Careful experimentation can remove these effects, with some uncertainty, allowing physical models to be tested over a wide range of strain rate. The results suggest that no single model works well over a wide range of crystal fraction and strain rate, although our data are best reproduced by the model of Roscoe (
) at moderate crystal fractions
and high strain rates, and by the model of Mader et al. ( 2013 )
at low strain rate and low crystal fraction. There is a clear need for more rheological data on crystal-bearing magmas, especially at crystal fractions above ∼ 0.3.
Bull Volcanol (2014) 76:876 Page 17 of 20, 876
Fig. 16 Relative viscosity of samples measured at low temperatures by parallel plate in comparison with the model of Costa (2009) and Mader
(2013) at a strain rate of 0.001 s
−
1
.
Dashed lines represent the indicated models at a strain rate of 1 s
−
1 to illustrate the shift in relative viscosity to higher values at lower strain rates
Application to lava flow morphology
In order to quantify the rheological conditions of the pahoehoe-`a`a transition, we superimposed the apparent viscosity (flow) curves obtained for each temperature on the TTZ
diagram of Peterson and Tilling ( 1980 ) (Fig.
). We define the onset of the transition as occurring where the behavior changes from a Newtonian liquid to a distinctly non-
Newtonian (power-law) behavior (Hon et al.
), which occurs between 1207 and 1203 °C. At these temperatures, flow has become non-Newtonian even though there is no detectable yield strength. We did not observe fully developed
`a`a textures in our experimental samples, so the end of the transition must occur at higher strain rates and/or apparent viscosities than we achieved. Our experimentally determined isothermal flow curves show a pronounced curvature to higher apparent viscosity at low strain rates, which was explained by
Kilburn (
) using an assumed Bingham rheology. The same pattern is expected for power-law materials, with or without a yield strength. To accord with observations made by Hon et al. (
), we allow for the isothermal transition from pahoehoe to `a`a by schematically illustrating the TTZ as crossing the isotherms on Fig.
. Although the surface morphology along a lava flow can reverse this transition as surface gradients and strain rates change (Hon et al.
reversible for a single quantum of lava (Kilburn
).
Additional constraints can be placed on the location of the transition from field observations of surface morphology
(Robert et al.
2014 ). Viscosities were calculated from mea-
sured crystallinity and vesicularity of the samples, strain rates were derived from measured channel geometry, and yield strengths were calculated from measurements of ground slope and flow lobe thickness (Robert et al.
of the vesicles ranges up to 2 orders of magnitudes, but is typically much larger than the size of the microlites, we calculated the three-phase mixture viscosities using the formulation appropriate for bubbles larger than crystals. Samples
MU01, MU07, and MU10 are all smooth golden pahoehoe samples, while MU12 shows the first signs of transition
(Fig.
18 ). Overbank spatter sample MU21sp and overflow
unit MU21 exhibit rough pahoehoe surface textures, defining the approximate end of the TTZ. Here, MU21sp plots close to our experimental 1169 °C isotherm and sample MU21 to the right (toward higher apparent viscosities). This is the
Fig. 17 Flow curves of apparent viscosity ( black dots ) against strain rate for liquid-crystal suspensions, fitted by power-law.
Star symbols correspond to surface morphology observed at the
Mauna Ulu lava flow described in
the work of Robert et al. ( 2014
).
The change from pahoehoe to `a`a surface texture occurs in a temperature interval between 1200 and 1160 °C based on the chosen strain rate. The question mark emphasizes the approximate location of the end of the TTZ
876, Page 18 of 20 Bull Volcanol (2014) 76:876 temperature at which we observe lobate surface structures in our experiments. Measurements only a few degrees below that temperature failed due to a rapid increase in viscosity, suggesting that this point may be close to the onset of `a`a flow.
Moreover, the yield strength of
∼
238 Pa determined experimentally at this temperature is very close to the calculated yield strengths of field samples near the transition, which cluster around 250 to 600 Pa (Robert et al.
). The ground-
mass crystallinity derived by Robert et al. ( 2014
) for transitional samples (10 to 30 vol%) is also in agreement with our observations, although we here extend the transition zone to crystal fractions of up to 40 vol%, and probably greater.
Figure
divides the Muliwai a Pele lava channel into three main zones based on surface morphology, beginning with pahoehoe near the vent, moving to transitional samples between 3.5 and 5.5 km and becoming `a`a dominated thereafter.
The pahoehoe to `a`a transition has been experimentally determined before, using analog materials (Soule and
Cashman
). They were able to measure higher viscosities, for a mixture of rice and corn syrup, and observed additional processes such as shear zone formation. Their location of the
TTZ in viscosity-strain-rate space is consistent with Hon et al.
( 2003 ), and with our results. However, the temperature range
at which the transition occurs in our experimental study is about 30 to 50 °C higher than proposed by Hon et al. (
but at very similar viscosity-strain-rate conditions. Our temperature range is also between 40 and 30 °C higher that that derived by MgO thermometry for glass by Robert et al.
( 2014 ). Robert et al. ( 2014
) used the original calibration by
Helz and Thornber (
1987 ), but using the revised calibration by
Putirka ( 2008 ) reduces the discrepancy to 10
– 20 °C. Moreover, our experimental glasses have in average 1 to 2 wt.% higher MgO contents (becoming smaller with greater crystal fractions), leading to higher temperatures in our experimental results.
There are two reasons why our experimentally determined viscosities may be higher than those of the lava flowing in the
Muliwai a Pele lava channel. First, our experimental melts were more oxidized (Fe collected in the field (Fe
2+
2+
/
∑
Fe=0.16 to 0.33) than samples
/
∑
Fe=0.72). Dingwell and Virgo
( 1988 ) noted an increase in viscosity by 0.6 log units between
Fe
2+
/
∑
Fe=0 and 0.5 for a synthetic basaltic melt containing
33.3 wt.% total Fe
2
O
3 at 1200 °C. However, our melts contain much less iron (
∼
10 wt.% total Fe
2
O
3
), and we estimate that the difference in oxidation state should account for less than
0.2 log unit variation in our experiments. Secondly our samples are two-phase mixtures, whereas real lava is a three-phase mixture of liquid, crystals, and vesicles (Harris and Allen
2008 ). The transitional to `a`a samples collected at the channel
contain mostly sheared vesicles, which may lower the mixture viscosity (Mader et al.
; Rust and Manga
Keszthelyi and Self
). Consequently, the rheological map in Fig.
can only be used to estimate the temperature
Fig. 18 Outlined Muliwai a Pele lava flow erupted in 1974 at Mauna Ulu
(Kilauea). Locations of collected samples along the channel as described in Robert et al. (
white circles with highlighted samples
( red ) allowing for classification of channel morphology into pahoehoe
( orange ), transition zone ( green ), and `a`a ( blue ). Map shows topographic lines to illustrate break in slope, modified from Robert et al. (
of lava in the field, if a
∼
20 °C correction is applied to account for the effect of vesicles. This correction will vary depending on the actual vesicularity of the lava.
Bull Volcanol (2014) 76:876
Conclusions
We experimentally determined the rheological response of
Hawaiian basaltic lavas to cooling and crystallization. We observed that the onset of non-Newtonian behavior started at low crystal fractions (between 0.06 and 0.15), in line with previous studies on basalts (Ishibashi and Sato
Vona et al.
2011 ; Ishibashi 2009 ) but somewhat lower
than for picritic lavas from Kilauea Iki (Ryerson et al.
). We estimated the yield strength of the lavas and fitted an exponential curve as a function of crystal fraction that should be useful in modeling Hawaiian and similar basaltic lavas.
The physical effect of crystals on the relative viscosity of magma was assessed by removing the effects of changing residual liquid viscosity, due to changing composition and temperature. To do this we analyzed, synthesized, and measured the most evolved residual liquid from the subliquidus experiments. At moderate crystallinity ( ∼ 0.1 to ∼ 0.4), the effect of crystals was best captured by the Einstein-Roscoe equation for polydisperse spherical inclusions (Roscoe
).
We also measured the viscosity of the same crystal-liquid mixtures at low temperatures and strain rates using parallelplate viscometry. The effect of crystals on magma viscosity was slightly greater at low strain rates, in agreement with theoretical models (e.g., Costa 2009), and the data at low strain rate were best reproduced by the model of Mader et al. (
2013 ). No single model reproduced our results well
over wide ranges of crystallinity and strain rate.
The experimental data were combined with rheological constraints from field measurements, and observations of flow surface morphology (Robert et al.
to `a`a surface morphology in viscosity-strain-rate space. Our results are consistent with previous estimates based on field observations (Hon et al.
2003 ) and analog experiments (Soule
and Cashman
2005 ). For the Hawaiian basalt studied here, the
transition (zone) from pahoehoe to `a`a surface textures begins at a crystallinity of
∼
10 %. The `a`a end of the transition zone corresponds to crystal fractions exceeding 40 %, where crystals form an interconnected network. We provide a temperature calibration for the rheological map, which can be especially useful for remote sensing of active or extinct lava flow fields on Earth and other planets and moons with a similar composition. Sehlke is currently working on a series of publications for Mercury and Io, as well as Lunar and Martian lavas, performing identical measurements to constrain the rheological evolution of planetary basalts during cooling and crystallization. For example, once the effect of T X -
Φ c on
(apparent) viscosity for a particular composition are known, superimposing the experimental data on to the Pahoehoe to
`a`a transition diagram (Fig.
) may allow to infer temperature, crystallinity, viscosity, and yield strength for lava flow morphologies observed by remote sensing techniques.
Page 19 of 20, 876
Acknowledgments This work was supported by NSF award EAR-
1220051 and NASA grant NNX12AO44G to AW. Travel funding to
AS for field work was granted by AGU (via NSF) and the University of
Missouri-Graduate Student Association (GSA) and Graduate Professional Council (GPC), as well as the Department of Geological Sciences. We thank Hawai
’ i Volcanoes National Park for a research permit and Paul
Carpenter for assistance with microprobe analyses. BR, AH, LG and EM was financed by the French Government Laboratory of Excellence initiative n°ANR-10-LABX-0006, the Région Auvergne and the European
Regional Development Fund. This is Laboratory of Excellence ClerVolc contribution number 124.
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