Introduction

Motivation and scope of this study

Lava flows are the most common volcanic features on Earth and cover the majority of the surfaces of other terrestrial planets (90% of Venus, 50% of Mars, at least 20% of the Moon and some 70% of the Earth) (Sigurdsson 1999). The flow of lava is dominantly governed by its viscosity, the lava effusion rate and the underlying topography (Cashman et al. 2013; Dragoni et al. 1986; Hallworth et al. 1987; Harris and Rowland 2001; Pinkerton 1987). Low viscosity lava flows have been recognized as significant volcanic hazards and are the cause of considerable economic damage worldwide (Behncke et al. 2005; Favalli et al. 2012; Kauahikaua et al. 2003). Mitigating the hazards posed by lava flows that threaten settlements has only shown moderate success to date (Barberi et al. 2003). This is largely due to an incomplete understanding of how lava flows, when it stops and a lack of methods to provide rapidly updated topographic surface models (Cashman et al. 2013; Farquharson et al. 2015; Favalli et al. 2010; James and Robson 2014; Kolzenburg et al. 2016a). These shortfalls reduce our ability to predict lava flow behaviour.

One of the more challenging aspects to predicting the flow dynamics of lavas is that the rheological properties of lava flows evolve during eruption and emplacement. The transient nature of the rheological properties is caused by changes in the composition, texture and temperature of the lava resulting from gas loss, crystallization and cooling. This produces strongly heterogeneous flow conditions, lava textures and lava-morphologies (Sigurdsson et al. 2015) that evolve both in space and time. The evolution of the lava’s rheology determines, for instance, whether lava advances as sheet- or channel-like flows. The rheology also dictates the lava’s surface morphology (i.e. the transition from pāhoehoe to ʻAʻā and blocky lava flows), which in turn has great influence on, for example, heat loss from the flow. Some flows have been observed to develop well-insulated plumbing systems like lava tunnels, allowing them to reach extremely high velocities and to flow long distances (Calvari and Pinkerton 1998; Greeley and Hyde 1972; Peterson et al. 1994).

A detailed understanding of the rheological evolution of crystallizing magmas/lavas requires direct measurement of the flow properties at emplacement conditions. To date, few direct measurements of the rheology of lavas/magmas under natural conditions have been reported (Pinkerton and Norton 1995; Pinkerton and Sparks 1978; Shaw et al. 1968). These are crucial measurements for benchmarking of experimental data but are insufficient to support a systematic study on the evolution of lava flow properties in temperature or shear rate space.

This study presents a new, integrated approach using non-isothermal experimentation, fieldwork and remote sensing data to reconstruct the thermal and deformation history as well as the rheological evolution of the Holuhraun lava flow field during emplacement. We then discuss the results and analyses with regards to the flow field emplacement and lava flow modelling in general.

The 2014–2015 eruption at Holuhraun: general overview and summary of the activity and erupted products from the 17th to 22nd of November 2014

The eruption took place in the tectonic fissure swarm between the Bárðarbunga-Veiðivötn and the Askja volcanic systems. It lasted about 6 months (31 August 2014–27 February 2015) and produced ca. 1.2 ± 0.3 km3 of basaltic lava (Pedersen et al. 2017; Thordarson 2015). Lava effusion rates during the eruption period range from 320 to 10 m3/s. Averaged values are ∼250, 100 and 50 m3/s during the initial (August–September 2014), intermediate (October–December 2014) and final phase (December 2014 to February 2015), respectively (Pedersen et al. 2017; Coppola 2017; Thordarson 2015). The lava was emplaced on the sandur planes (glacial outwash sediment planes) north of the Vatnajökull/Dyngjujökull glacier, partially covering the previous two Holuhraun lava flow fields south of the Askja caldera (Hartley and Thordarson 2013). The area is gently sloping (average inclination <0.5%; i.e. ∼0.3°) to the east-northeast. The shallow gradient resulted in low topographic forcing of the flow and, therefore, rather slow lava flow advance. Lava advancement rates are generally below ∼0.0167 m/s during the initial eruption phase (Pedersen et al. 2017; Thordarson 2015) and drop to ∼0.017 m/s during our field campaign, making the eruption an ideal target for monitoring and sampling. Figure 1 shows an IR satellite image of the active zones of lava emplacement on the 20th of November 2014 (EO-1 ALI image from NASA and USGS from 20 November 2014 21:00 GMT).

All samples and field data used in this study were collected during a field campaign led by the Institute of Earth Sciences at the University of Iceland during the 17th to 22nd of November 2014. During this period, eruptive activity was continuous and concentrated within the Baugur crater (see Fig. 1). A lava lake had formed in Baugur, which was surrounded by spatter built ramparts of ∼60 m height. This lake drained into a secondary lava pond east of the central vent via a narrow opening on the north-east (Fig. 1). From this secondary lava pond, the lava proceeded to flow eastwards through an open channel system and was emplaced initially as rubbly to spiny pāhoehoe, sometimes transitioning downstream into ´a’a (Keszthelyi et al. 2000; Macdonald 1953; Pedersen et al. 2017) toes ca. 4.3 ± 0.3 km downstream of the vent (Fig. 2).

Fig. 1
figure 1

Reconstruction of the lava field activity during the week of the 17th to 22nd of November 2014. a Overview map of Iceland, showing the two main rift branches and some iconic volcanic centres for orientation. The eruptive centre of Holuhraun is located just south of the Askja caldera and highlighted by the box; modified after Thordarson and Höskuldsson (2008). b Enlargement of the box in a showing an EO-1 ALI image from NASA & USGS from the 20 November 2014 21:00 GMT with an outline of the extent of the lava field on that day. Hot colours indicate active parts of the lava field emitting radiation. Note the two incandescent parts of the flow field highlighted as “dead branches”. Analysis of the infrared bands of the MIROVA satellite (sampling frequency ca. 8 h) during the days of fieldwork confirmed these not to be active (Coppola and Laiolo, personal communication). c Schematic of the active part of the flow field during the days of sampling and field measurement

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Fig. 2
figure 2

Emplacement situation at the flow front. a, b Examples of the flow emplacement situation, showing the spiny pāhoehoe to ´a’a texture. The thickness of the individual flow toes varies between ∼1 and 6 m. c Breakout of the higher temperature/lower viscosity core of the lava from a flow section after inflation. Note that the previously emplaced part of the same flow lobe acted as a buttress until the lava managed to breach. d Direct measurement of the lava emplacement temperature using thermocouples mounted on steel poles deeply inserted into freshly exposed parts of the lava

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The activity at the eruptive centre during the week of fieldwork consisted of periods of ca. 2–5 min of intense bubbling above the central vents (southern and central part of the lava lake in Baugur) that was accompanied by a pulse of increased drainage from the Baugur lava lake and intermittent periods of ca. 10–15 min of lower effusive activity without bubble bursting.

Although the eruptive activity at the central vent was pulsating, flow in the channel downstream of the secondary lava pond appeared steady and the flow front did not show pulsating behaviour. This indicates that a hydrostatic equilibrium was reached within the secondary lava pond, soon after the lava was expelled from the Baugur lava lake. Flow advance was, therefore, primarily governed by the hydrostatic head and the evolving thermorheological properties of the melt.

At the flow front, the lava was emplaced as ca. 70–100 m wide and 1 to 3 m high toes of rubbly/spiny pāhoehoe and ´a’a. These toes advanced at rates of about 0.0017 m/s, locally reaching up to 0.0083 m/s at smaller secondary breakouts from the flow core. Individual lobes occasionally halted and transitioned from steady advance to inflation. The inflation lasted until it reached a point where the crust was thinned or the internal pressure increased sufficiently for the core of the lava flow to breach the crust. Breaching occurred mostly at the base of the flow, as it is typical for a pāhoehoe and transitional lava emplacement style (Fig. 2d). Occasionally, breaching also occurred from within the flow front (see Fig. 2c).

Solidified lava samples (i.e. parts of the forming crust) were collected at the active flow front (Fig. 1) for petrographic and rheological investigations. The erupted lava is variably vesicular microcrystalline basalt (see Fig. 3). The vesicularity ranges from ca. 8 to over 45% with vesicle sizes ranging from sub-millimetre to centimetre scale averaging around 4–6 mm. The dominant fraction of bubbles is sub-circular. Intense bubble deformation is only present near the outer crust of the lava flow with 2D aspect ratios (measured in hand samples) as high as 7. Shear is more intense in the crust as a result of pāhoehoe flow style, where flow of lava beneath a solidifying crust creates shear zones and fresh outbreaks commonly occur from the base of these lobes. As the surface is solidifying, it is unable to deform viscously and acts as a surface against which the lava flowing beneath it is deformed. The vesicles near this surface, consequently, experience higher deformation rates than those at the centre of the flow. The matrix (see Fig. 3) is made up of microcrystals of plagioclase, pyroxenes, opaque Fe-oxides and glass (glass content increasing from 0 to ∼25% vol. towards the outer few cm of the crust). The total range of reported phenocryst contents of the eruption lies between 2 and 6% (Gíslason et al. 2015; Guðfinnsson and Jakobsson 2014; Lavallée et al. 2015). The phenocryst assembly comprises dominantly plagioclase crystals with a maximum dimension from below 1 to ∼6 mm and subordinate olivine and pyroxene crystals below 2 mm (Fig. 3).

Fig. 3
figure 3

Photomicrographs of lava samples taken at the flow front on 19th and 20th of November 2014. The dominant phases in the lava samples are plagioclase (pl), pyroxene (px) and olivine (ol). The matrix is made up of plagioclase and pyroxene microlites with small amounts of glass. a Overview photograph of a thin section from the lava crust. Note the high vesicularity and bubble shapes that are generally sub-rounded and coalesced in places. b, d Close-up of thin section in a in transmitted light; c, e close-up of thin section in a in cross-polarized light. Note that the microlites in the matrix do not show a preferred orientation. f Overview photograph of a thin section from the lava interior. Note the lower vesicularity and smaller bubble size. Also, microphenocrysts dispersed in the matrix are somewhat smaller in size. Bubble shapes are more contorted than in a. g, i Close-up of thin section in f in transmitted light; h, j close-up of thin section in f in cross-polarized light

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Rheology of crystallizing magmas

Lava flows are spatially restricted and directed by the increasing strength of a continuously growing rheological contrast zone or “crust” that is cooled to a point where the viscosity is relatively high and crystallization is rapid (Calvari and Pinkerton 1998; Cashman and Mangan 2014; Hon et al. 2003; Kauahikaua et al. 1998; Kolzenburg et al. 2016b). The influence of the rapidly changing rheology of lava on its emplacement style becomes especially apparent in the late stages of flow, where its resistance to flow is increasing. As the lava’s crust becomes stronger, it increasingly hinders lava advancement and is subjected to folding and/or fracturing. Rheological gradients resulting from the differential cooling of a lava’s surface versus its interior play a significant role in the generation of flow-directing features like levees and tubes as well as transitions in eruption style, as shown by Giordano et al. (2007), Giordano et al. (2010), Gregg et al. (1998), Griffiths (2000), Griffiths et al. (2003), Lipman and Banks (1987) and Sparks et al. (1976).

Isothermal sub-liquidus experimentation has been carried out on natural silicate melts of a variety of compositions, dominantly basaltic and andesitic. This is because they provide favourable crystallization kinetics, resulting in a manageable time frame of experimentation (Chevrel et al. 2015; Giordano et al. 2007; Ishibashi 2009; Ishibashi and Sato 2007; Sato 2005; Shaw et al. 1968; Vona et al. 2011, 2013). Evaluating the influence of the evolving flow properties of lavas on their emplacement dynamics, however, requires characterization of the rheological properties of lavas at non-isothermal and non-equilibrium conditions. In such conditions, the lava undergoes transient increases in viscosity, reaching increasing degrees of undercooling until a “rheological cutoff temperature” (T cutoff) (Giordano et al. 2007; Kolzenburg et al. 2016b) is reached, where the effective lava viscosity rises steeply, terminating its capacity to flow. This transient rheological gradient, that is present in all natural emplacement situations, governs the lavas’ emplacement style. Surprisingly, studies capturing the transient rheological evolution of lavas at natural emplacement conditions, where lavas undergo permanent heat loss, are few (Giordano et al. 2007; Kolzenburg et al. 2016b).

Below, we reconstruct the thermal and shear conditions of lava flow emplacement at Holuhraun and present a series of data from concentric cylinder rotational viscometry (CC) experiments mimicking these conditions. We describe the rheological evolution of lava as a function of cooling and strain rate and discuss these data in the context of what we know of the natural environment.

Reconstruction of lava flow emplacement dynamics for the 2014–2015 lava at Holuhraun

Temperature measurements of the lava during emplacement

Emplacement temperatures were determined by (1) in situ measurement of the lava temperature at the flow front using thermocouples, (2) indirect measurement of the surface temperature of freshly exposed parts of the lava using a FLIR T650 camera and (3) petrologic model estimations using MELTS (Gualda and Ghiorso 2015) as a geo-thermometer.

Direct measurements of the lava temperature were performed on the 19th and 20th of November 2014 using K-type thermocouples mounted on 2-m-long steel poles that were inserted between 10 and 50 cm deep into the lava at active lava toe breakouts (see Fig. 2d). The temperature data was logged digitally at a sampling rate of 1 Hz. After insertion of the thermocouple into the lava, thermal equilibrium (i.e. a constant temperature reading) was achieved after ∼1–3 min. Measured lava temperatures at the flow fronts range from 1082 to 1128 °C with an average temperature of 1095 °C (calculated from 14 measurements). Measurements were made at a distance of ∼4.3 ± 0.3 km downstream of the vent (Fig. 1). Simultaneous FLIR T650 IR-Camera measurements for freshly exposed patches of lava are in good agreement with the direct thermocouple measurements (1080 to 1125 °C).

Eruption temperatures of the lava at the primary vent, measured using infrared spectroscopy, range from 1200 to 1147 °C (Icelandic-Meteorological-Office 2015). The higher temperatures are probably the best estimate of the actual eruptive temperature, with the lower ones representing measurements of partially cooled lava.

The pre-eruptive phenocryst content of 2–6% (crystals >∼0.5 mm, determined via microscopy) is assumed to have grown under magma storage conditions as supported by the microporphyritic texture (see Fig. 3 and also Gíslason et al. 2015; Guðfinnsson and Jakobsson 2014; Lavallée et al. 2015). Petrographic model estimates of the magma’s pre-eruptive temperature using MELTS software (Gualda and Ghiorso 2015) return a range of 1191–1181 °C for a dry melt at atmospheric pressure and fO2 at the NNO buffer. These values are in reasonable agreement with field estimates of the IR spectroscopy eruption temperature measured at the vent, as reported by the Icelandic Meteorological Office (2015). Using the above data, we calculate 91 ± 5 K as the average heat loss of the lava during flow from the vent to the flow front.

Reconstruction of the lava flow path during emplacement

Reconstruction of the large-scale flow field dynamics between the 18th of November 2014 and 6th of December 2014 from MIROVA-IR satellite images (Coppola et al. 2015, 2017) shows that the vast majority of the active flow front shifted from an eastward to a southward advancement on the 19th of November and only returned to the east on the 1st of December (Coppola and Laiolo, personal communication and Pedersen et al. 2017). For the reconstruction of the lava’s flow velocity, we therefore assume that the bulk of the erupted lava volume followed the flow path reconstructed in Fig. 1.

The average length of this channel from the vent to the active lava front, where the direct temperature measurements were performed, is 4.3 ± 0.3 km. Its width varies between ∼700 m (the width of the secondary lava pond) and ∼40 m with an average width of ∼110 ± 15 m. Lava thickness during emplacement and prior to inflation (i.e. prior to the time when flow front advancement stopped and lava flux was accommodated by volume increase of the flow core) ranged from 1 to 6 m with an average of ∼4 m (see Fig. 2). Accounting for the chilled base of the lava in contact with the prior land surface, we estimate 3 ± 1 m as a reasonable number for the average depth of the active lava channel. Using these measurements, we have reconstructed the lava channel cross section.

Reconstruction of the thermal evolution and shear rate during emplacement

Based on the min (190 m2) and max (500 m2) estimates for the cross-sectional area of the lava channel, the min (4 km) and max (4.6 km) channel length and the average effusion rate for this eruptive period (∼100 m3/s), the flow velocity along the channel can be estimated to range between 0.2 and 0.53 m/s using the following equation:

$$ V=\frac{Q}{w^{\ast } h} $$
(1)

where V is the flow velocity in metres per second, Q is the effusion rate in cubic metres per second and w and h are the width and depth of the lava flow in metres, respectively. These velocities are reconstructed for flow in the confined lava channel and are, therefore, higher than the velocity of the lava flow front that was unconfined and spreading and expanding onto the sandur plane.

At these velocities, the lava travelled from vent to flow front in 127 to 383 min, and therefore, the heat loss at 91 ± 5 K resulted in a cooling rate of the lava between 0.22 and 0.76 K/min or 18.7 to 24 K/km. These values present the absolute maximum and minimum values for these estimates. The most reasonable estimate for lava cooling rate is ∼0.4 K/min (based on averaged measurements of w = 110 m, h = 3 m, l = 4300 m, delta T = 91 K). These data are in good agreement with the minimum cooling rates estimated for lava flows on Hawaii, which range between a minimum 7 to 24 K/km and a maximum of 25–80 K/km; see for example Flynn and Mouginis-Mark (1992), Soule et al. (2004) and Riker et al. (2009).

Cooling rates of basaltic lavas measured on the surface and interior of active lava channels on a variety of locations (dominantly Hawaii, due to the relatively easy access and the availability of supporting infrastructure) range from 0.01 to 15 K/min with high cooling rates being associated to crustal cooling and low cooling rates to the interior of well-insulated flows (Cashman et al. 1999; Flynn and Mouginis-Mark 1992; Hon et al. 1994; Keszthelyi 1995; Witter and Harris 2007). Cooling rates have also been evaluated through theoretical studies on the flow geometry and crystal structures for komatiites at 1–21 K/min (Huppert et al. 1984).

Narrow and shallow dikes may undergo cooling rates from few degrees per hour to more than 50 K/min, where magma is introduced into a fracture (see Giordano et al. (2007) for the case of the 2002 eruption of Nyiragongo). Cooling rates then decrease as a function of the size of the dike and time. After the initial transient stages, magma in narrow dikes cools at rates of the order of ca. 5 K/min or less.

The thermal history reconstructed for the 2014–2015 lava at Holuhraun lies at the lower end of the average cooling rates estimated for other basaltic lavas. This is most likely a result of the low topographic gradient of the emplacement surface. The resulting low flow rates produce more insulating flow geometries, i.e. with little exposed incandescent surface, which reduces radiative heat loss (Coppola et al. 2013, 2017; Dragoni 1989; Dragoni et al. 1995; Harris and Rowland 2009).

Assuming a simple shear within the lava flow channel, the average shear rate (έ) can be calculated as follows:

$$ \acute{\varepsilon} =\frac{V}{h} $$
(2)

Using the above channel geometries and effusion rate Q = 100 m3/s, the shear rate is estimated to be between 0.05 and 0.26 s−1 for channels of h = 4 m; w = 125 m and h = 2 m; w = 95 m, respectively. For a simplified non-linear flow velocity profile, as commonly modelled for lava flow channels (e.g. Piombo and Dragoni 2009), where ∼80% of the flow velocity is reached in the lower half of the flow and the shear rates at the flow base are higher, the estimates vary from about 0.01 to 0.52 s−1 for the same flow channel geometries. These are calculated as follows:

$$ {V}_{\mathrm{surf}}={\left({\acute{\upvarepsilon}}^{\ast }\ 0.8\right)}^{\ast }\ \left({h}^{\ast }\ 0.5\right)+{\left({\acute{\upvarepsilon}}^{\ast }\ 0.2\right)}^{\ast }\ \left({h}^{\ast }\ 0.5\right) $$
(3)

Where V surf is the surface velocity, έ the shear rate and h the channel height. These values increase drastically in sections where the flow channel is constricted, such as the initial outlet from Baugur crater lake, where a channel width of 15 m at 4 m depth returns shear rates of 0.4 and 0.6 s−1 for linear and non-linear flow velocity profiles, respectively.

Experimental materials and methods

Sample preparation, composition and rheologic measurements

The experimental material was sampled from active lava flow fronts on the southern extent of the lava field on the 20th of November. These rock samples were crushed and powdered, then melted and homogenized at 1300 °C and finally quenched on a steel plate (see Supplementary materials for details on the methods). The resultant glasses were melted into Pt80Rh20 cylindrical crucibles of 51 mm height and 26.6 mm diameter for rheological experimentation. All melting and experimentation was done in air.

The bulk chemical composition of the experimental materials was determined by electron microprobe analysis (EMPA) for glasses quenched from the melts before and after the experiments in order to assess any chemical change during experimentation. The sample showed no detectable compositional changes during experimentation. Normalized results of the average of 10 post-experimentation analyses are presented in Table 1; average analytical totals are 99.78%. See Supplementary material for details on the analysis method.

Table 1 Chemical analysis: measured after all experiments; normalized to 100%
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The super liquidus melt viscosity was measured at temperatures between 1444 and 1248 °C in temperature steps of ∼21° (see Supplementary material for details). Non-isothermal experimentation was performed using methods similar to those described in Giordano et al. (2007) and Kolzenburg et al. (2016b), where constant cooling was induced in a sample located in a Deltech box furnace while measuring its viscosity (see Supplementary materials for details). A series of experiments were run at constant cooling rates of 0.5, 1, 3 and 5 K/min and initial shear rates of 0.766, 1.532 and 3.064 s−1 (corresponding to 2.5, 5 and 10 rpm, respectively). Experiments at lower initial shear rates were not possible (see Supplementary materials for details). Experiments were continued until the torque limit for the lowest rotation rate was reached. The experimental temperatures at this point are reported in the grey boxes in Tables 3 and 4. Between consecutive dynamic cooling experiments, the sample was re-heated to 1346 °C for a minimum of 2 h and homogenized by stirring at a shear rate of 12.255 s−1 (40 rpm) in order to ensure complete melting of all crystalline phases formed during previous experimentation. The sample used for all the dynamic cooling experiments was re-melted and quenched to a glass after the end of the last cycle.

Suspension rheology and the effect of changing melt composition

In order to resolve the crystallization-induced rheological deviation from the pure melt viscosity at greater detail than in absolute viscosity space, we calculated the relative viscosity of the melt/suspension during cooling using the following formula:

$$ {\eta}_r=\frac{\eta_{\mathrm{s}}}{\eta_{\mathrm{l}}} $$
(4)

where η r, η s and η l are the relative, suspension (i.e. the measured viscosity of the crystallizing sample) and liquid viscosity, respectively.

The temperature-viscosity evolution of the crystal free liquid was reconstructed by interpolating the super liquidus measurements and low T viscosity estimates from the GRD model (for the composition reported in Table 1) using a Vogel-Fulcher-Tammann (VFT) equation (Tammann and Hesse 1926). The relative viscosity due to the effect of crystallization is obtained by normalizing the apparent viscosity measured during the sub-liquidus experiments to the viscosity of the crystal free liquid. In the following sections, the results are presented as the logarithms of both η s and η r.

The effect of the changing residual melt composition, that results from crystallization, on the melt viscosity is estimated to be within 0.03 log units at 1136 °C (∼50% crystallization) and less at higher temperatures. These results are based on calculations of the residual melt composition, starting from the original sample composition. We used MELTS for estimations of the composition of a dry melt at the NNO buffer and atmospheric pressure at 1161 °C and a crystal fraction of 30.7% as well as for a dry melt at 1136 °C and a crystal fraction of 50.5%, respectively. We then modelled the residual melt viscosity-temperature relationship using Giordano et al. (2008). The difference in viscosity between the original melt and residual melt increases with decreasing temperature. These very conservative model results are in reasonable agreement with estimates by Vona et al. (2011) who estimated difference of 0.06 to 0.18 log units between the original and fractionated melt viscosities for basaltic melts from Stromboli and Etna.

Rheological measurements on the new Holuhraun lava

Liquid viscosity

The results of the high-temperature CC liquid viscosity measurements, the low-temperature liquid viscosity estimates following the method described in the Supplementary material and the VFT fit parameters are summarized in Table 2. See Supplementary materials for details on the reconstruction of the pure liquid viscosity.

Table 2 Summary of liquid viscosity measurements (high temperatures) and model estimates of the low-temperature viscosity of the melt
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The cooling rate dependent rheology of the lava at Holuhraun

The temperature-dependent viscosity of the Holuhraun lava when subjected to varying cooling rates is plotted in Fig. 4 and the data are reported in Tables 3 and 4. The rheological evolution of the lava follows the trend of the pure liquid data (log η r = 0) up until the point where the influence of crystalline phases (via nucleation and growth of crystals) starts to measurably increase the sample’s apparent viscosity. At this deviation, the apparent viscosity of the suspension increases with respect to the theoretical liquid (logη r > 0) as a result of increasing crystal content and changing composition of the residual melt (the latter being <0.03 log units). This increase in relative viscosity accelerates rapidly as temperature decreases. The cooling rate dependence of this departure is striking, where slower imposed cooling rates result in a steeper rheological departure at higher temperature. However, at higher cooling rates, this departure commences at progressively lower temperatures (i.e. higher degrees of undercooling) since crystallization of the melt is delayed. This is in agreement with earlier experiments by Giordano et al. (2007) and Kolzenburg et al. (2016b).

Fig. 4
figure 4

Cooling rate-dependent rheology of the lava at Holuhraun. Subplots a and b show the measured apparent viscosity of the crystallizing lava and the calculated relative viscosity of the suspension versus temperature, respectively. Max and min temperatures of the lava measured in the field and estimated from IR images and petrologic models are shown in grey. At temperatures above 1200 °C, all experimental data follow the thermorheological evolution of a pure melt (dotted line in subplot a). Departure from the pure melt viscosity only occurs at sub-liquidus temperatures and is highly dependent on the imposed cooling rate. At lower cooling rates of 0.5 K/min (squares), this departure occurs at the highest measured temperatures and migrates to lower temperatures (higher degrees of undercooling) at faster cooling rates. The horizontal lines mark the transition from pāhoehoe to transitional to ‘a‘ā flow textures as defined in apparent viscosity-shear rate space by Hon et al. (2003) for a shear rate of 3.06 s−1

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Table 3 Summary of absolute viscosity measurements for all experiments. For simplicity, interpolated values of the experimental data at equal temperature steps are reported with the exception of the final data point for each experiment (in italics). Temperatures related to those points are reported in the last two rows in Kelvin and Celsius, respectively
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Table 4 Summary of the relative viscosity for all experiments. For simplicity, interpolated values of the experimental data at equal temperature steps are reported with exception of the final data point for each experiment (in italics). Temperatures related to those points are reported in the last two rows in Kelvin and Celsius, respectively
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The shear rate dependent rheology of the lava at Holuhraun

In order to assess the influence of shear rate on the rheological departure from the pure melt viscosity of the samples during cooling, we perform experiments at a constant cooling rate while varying the imposed shear rate. The rheological evolution of the samples under these conditions is plotted in logη s and logη r space in Fig. 5a, b and c, d for cooling rates of 0.5 and 1 K/min, respectively.

Fig. 5
figure 5

Shear rate-dependent rheological cutoff of the lava at Holuhraun. Subplots a, b and c, d show the measured absolute viscosity of the crystallizing lava and the calculated relative viscosity of the suspension versus temperature for varying shear rates at a constant cooling rate of 0.5 and 1 K/min, respectively. At the lower cooling rate of 0.5 K/min, the rheological departure from the viscosity of pure liquid (melt) initiates at higher temperatures for elevated shear rates. As a result, the gradient of the departure increases, in the same temperature interval, with increasing shear rate (see highlights in subplot a). At faster cooling rates, however, this effect is not documented and increasing shear rate does not affect the suspension’s thermorheological path. The horizontal lines mark the transition from pāhoehoe to transitional to ‘a‘ā flow textures as defined in apparent viscosity-shear rate space by Hon et al. (2003) for a shear rate of 3.06 s−1 (solid) and 0.77 s−1 (dashed), respectively

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At the slower cooling rate of 0.5 K/min, there is a clear and drastic influence of shear rate, where an increase in shear rate results in a departure from the pure melt viscosity at higher temperatures (lower degrees of undercooling, see Fig. 5a). The evolution of the relative viscosity, plotted in Fig. 5b, further shows that the intensity of this departure (steepness of the curve) increases with increasing shear rate. At the faster cooling rate of 1 K/min, however, this shear rate dependence is no longer evident within the range of thermal uncertainty (Fig. 5d). For the experiments at 1 K/min, the shear rate does not exert a significant influence on the rheological departure of the sample during crystallization.

Unifying field and laboratory measurements

The data presented here spans a wide range of transport conditions during lava/magma emplacement. The experiments at the lowest imposed cooling rate of 0.5 K/min and the lowest shear rate of 0.77 s−1 represent the bulk volume of the lava transported in the main channel at Holuhraun. This is supported by the reconstruction of the cooling history of the lava, as well as measurements and estimates of cooling rates in basaltic melts from previous authors at other locations (see “Reconstruction of the lava flow path during emplacement” section). Experiments at faster cooling rates, in turn, are pertinent to rapid cooling and development of the lava flow’s crust and the development of “frozen” flow impeding and/or levee forming zones that are often related to a pseudo yield strength of lavas (Chevrel et al. 2013; Hulme 1974). The experiments at faster shear rates provide data applicable to flow in spatially constricted parts of lava channels or rapid ascent through feeder dikes. Magmas migrating within the earth’s crust, however, will experience significantly lower cooling rates. This results in different thermorheological paths than the ones presented here, where the rheological departure is expected to occur at lower degrees of undercooling.

Our field, thermal and petrologic observations show that the lava at Holuhraun erupted very close to its liquidus temperature (∼1195 °C, estimated using MELTS software) and featured average cooling rates in the range of 0.24 to 0.79 K/min. The temperature range between liquidus and lava temperature at the flow front is highlighted in grey in Figs. 4 and 5, where the dark and light areas represent the min and max temperature range, respectively. Unification of the field measurements and the experimental data reveals that the lava spent ∼15% of the reconstructed thermal path (between eruption temperature and ∼1175 °C) in a rheological regime where its effective viscosity is equal or similar to that of the pure melt. The majority of the lava’s thermal path during emplacement was spent in a regime, where the lava undergoes drastic changes in bulk rheological properties (3 orders of magnitude increase in relative viscosity). The temperature measurements conducted in the field show that the flow front was within the thermal regime close to the cutoff temperature and, therefore, likely close to halting.

Figure 2a, b and d show this final phase of flow, where spiny pāhoehoe to ´a’a textures are present and the flow is slowing down drastically, transforming to an inflation regime. During inflation, the lava flow almost stops and only advances slowly through breaching of its crust after significant inflation. Such a breaching scenario is shown in Fig. 2c, where the core of the lava that remained at elevated temperatures breached after self-insulation of the flow and represents the only part able to continue to advance.

Discussion

Advection facilitated crystallization in basaltic melts

At a cooling rate of 0.5 K/min, the shear rate strongly influences the rheological response of the sample and, consequently, its crystallization behaviour. Higher shear rates result in earlier (in temperature space) and more intense crystallization (see the differences in the onset and steepness of the rheological departure in Fig. 5b). Similar observations were made in constant temperature experiments at sub-liquidus conditions by Kouchi et al. (1986), Vona and Romano (2013) and Chevrel et al. (2015). The increasing slope of the rheological departure at elevated shear rates suggests an increase in crystallization intensity. We suggest that this is a result of advection of “fresh” melt to the individual crystal’s surface, which facilitates the crystal growth. This concept is known from the crystallization of a wide range of materials, such as metallic liquids (Shao et al. 2015) and aqueous protein solutions (Azadani 2007), and has been simulated for magmatic conditions (Petrelli et al. 2016). Another potential explanation may be that increased stirring more effectively creates crystal nuclei, as suggested by, for example Cashman et al. (1999), Emerson (1926) and Vona and Romano (2013).

The data presented here are the first to document the effect of varying internal rate of advection on the rheological properties of natural silicate melts under constant cooling conditions similar to those encountered in nature. Interestingly, the experimental results indicate that, for the composition investigated here, this effect seems to diminish at increasing cooling rates. At a cooling rate of 1 K/min, the thermorheological path of the suspension is affected very little by the shear rate. This is likely because the melt is subject to higher degrees of undercooling at a faster rate. Crystallization in this environment is driven largely by the higher degree of undercooling that facilitates crystal nucleation, whereas slower cooling favours crystal growth, where advection can act more efficiently (Arzilli and Carroll 2013; Cashman 1993; Cashman et al. 1999; Gibb 1974; Hammer 2006; Kouchi et al. 1986; Lange et al. 1994; Lofgren 1980; Shao et al. 2015; Vona and Romano 2013; Walker et al. 1976).

It is important to note here that the melts in the lower cooling rate experiments have significantly more time for crystallization. This is reflected also in the higher temperature of the rheological departure, i.e. lower degree of undercooling. This suggests a change in crystallization kinetics, where at high cooling rates, crystallization of the melt is dominated by the degree of undercooling, whereas at lower undercooling, advection due to stirring is a more significant factor.

Implications for the emplacement of lava toes at Holuhraun

The experimental conditions, starting at super liquidus temperatures and imposing cooling rates between 1 and 5 K/min, represent the rapid to intermediate cooling environments present in the interior of high aspect ratio (i.e. sheet-like) lava flows and in the crust forming the flow carapace (Flynn and Mouginis-Mark 1992; Harris et al. 2005; Keszthelyi 1995). The experimental data for the 0.5-K/min cooling rate is well suited for a discussion of the thermorheological path of the bulk of the lava travelling within the channelized system during lava emplacement at Holuhraun. Experimental reconstruction of the lava’s thermorheological path in combination with the presented field measurements allows us to assign certain parts of the flow curve to the natural environment.

The first part of the transport system (between Baugur and the secondary lava pond; see Fig. 1) features rather narrow channel geometries. The lava undergoes the highest shear rates during the entire emplacement history in this part, due to the spatial constriction. Assuming constant heat loss from the system, this high shear rate portion (∼0.8 km equivalent to ∼15 K cooling) falls within the rheological regime where the lava viscosity remains at or close to the pure liquid behaviour (logη r < 0.1) and shear rate shows little to no influence on the lavas’ rheological evolution.

Further down the transport system, in the secondary lava pond and in the ∼100–150-m wide and ∼2–4-m deep channel beyond (∼0.8–3 km transport distance), the lava had reached hydraulic equilibrium (i.e. no pulsating flow behaviour) and underwent constant, intermediate (∼0.12 to 0.28 s−1) deformation rates, calculated after Piombo and Dragoni (2009). The lava, being in an intermediate thermal regime (cooled by ∼20–60 K since eruption), displays a strong increase in viscosity (logη r increasing exponentially by 0.4 to 1.4, depending on the applied shear rate) and shows a strong shear rate dependence of the rheological departure. The shear rates estimated for the natural environment are, however, lower than what was possible to reproduce experimentally (see Supplementary materials). Therefore, the absolute viscosity of the flow during this stage was likely lower than the data presented here.

Approaching the flow front, the relative viscosity increases until, at the flow front, where our constraints of emplacement temperature are best, the lava enters a rheological regime of exponentially increasing effective viscosity until halting (see Figs. 4 and 5).

Hon et al. (2003) described the transition from pāhoehoe to ‘a‘ā lava in viscosity-shear rate space. We have included the respective textural change-zones on the diagrams in Figs. 4 and 5. It becomes apparent that the lava at Holuhraun very rapidly changed from pāhoehoe to ‘a‘ā which is likely the reason for the transitional spiny pāhoehoe to ‘a‘ā texture. This is also supported by the observation of hindered emplacement, such as the transition from flow lobe advancement to halting and inflation that was witnessed during the field campaign. It is important to note here that the experiments were performed on vesicle free, degassed melts in air; please see the Supplementary materials for a more detailed discussion on the limitations of the experimental method and data.

The above correlation emphasizes that effective flow can only occur in thermal regimes above the rheological cutoff temperature (T cutoff). The lavas’ apparent viscosity below T cutoff, however, is significantly influenced by the cooling rate experienced by the lava. In order to evaluate which thermorheological path is pertinent to a certain eruption or to pick which thermorheological dataset is to be used in emplacement modelling of lava flows, it is, therefore, important to estimate the cooling path of lava during eruption.

Implications for lava flow emplacement modelling in general

Rheological gradients resulting from the cooling of the lava surface and the developing crust impede the free flow of a lava body. The core viscosity combined with the bulk flow density and the topographic gradient determines the maximal potential velocity of unconfined lava flow advancement. Effective flow velocity, therefore, is an interplay between the rate and intensity of crust development and the flow velocity of the lava core.

Our data show that the effective lava viscosity may stay close to that of the crystal free liquid low for high degrees of undercooling before reaching the rheological cutoff temperature. In fact, the rheologic cutoff temperature decreases with increasing cooling rate, meaning that the fast cooling crust zone of a lava flow is able to deform to lower temperatures before solidification than the slow cooling core. This highlights that cooling rate dependent rheology is to be considered when describing or modelling the development of flow-directing features.

Most computational models for lava flow emplacement incorporate lava rheology as a constant value of viscosity and/or assume a yield strength at which the lava advance stops (Castruccio et al. 2014; Costa and Macedonio 2005; Del Negro et al. 2008; Dragoni et al. 1986; Favalli et al. 2006; Harris et al. 2015; Harris and Rowland 2001; Hérault et al. 2011; Ishihara et al. 1990; Miyamoto and Sasaki 1997). Incorporating transient rheology into these models requires an accurate description of the lava’s rheological evolution in temperature and shear rate space. Theoretical and empirical models describing the rheological evolution of lava as crystal-liquid or bubble-liquid suspensions during flow, as reviewed in Mader et al. (2013), are being developed step by step.

Applying these for the use of modelling natural environments relies on verification of the model results through experimentation on natural lavas/magmas. This can be done using results from studies of isothermal sub-liquidus rheology, where a detailed textural characterization of the sample is possible (Campagnola et al. 2016; Chevrel et al. 2015; Ishibashi 2009; Ishibashi and Sato 2007; Sato 2005; Sehlke and Whittington 2015; Soldati et al. 2016; Vona and Romano 2013; Vona et al. 2011, 2013).

Although interesting for magmatic systems at constant (or near constant) temperature, such as slowly convecting magma chambers or the interior of lava lakes, isothermal sub-liquidus experiments are not directly applicable to the dynamic thermal conditions present in lava flows or during magma transport within narrow dykes, where heat loss is significant.

Isothermal experiments return systematically higher viscosities than constant cooling rheology experiments for a given temperature since the crystal volume fraction in non-isothermal experiments lags behind that of isothermal ones as they are in thermal disequilibrium (Arzilli and Carroll 2013; Cashman 1993; Coish and Taylor 1979; Gamble and Taylor 1980). This is also the case when modelling lava rheology based on equilibrium thermodynamics (e.g. using MELTS in combination with two phase rheological models such as reviewed in Mader et al. 2013).

Because of this overestimate in lava viscosity, using isothermal experimental data or equilibrium thermodynamic crystallization models in combination with rheological models as input data for the simulation of lava flows would in any case return shorter lava flow runout distances than if constant cooling rheological data, as presented here, were to be used. Incorporating constant cooling rheological data in lava flow models would, therefore, allow for a more realistic description of the magmas’/lavas’ rheological evolution and, therewith, better ability to forecast their emplacement.

Conclusions

Based on the data presented above and the accompanying analysis and discussion, we draw the following conclusions:

  1. 1.

    Cooling rate exerted a first-order control on the rheology of the lava from the 2014–2015 eruption at Holuhraun,

  2. 2.

    Shear rate exerted a second-order control on the lava rheology and appears to have become relevant only at low cooling rates.

  3. 3.

    The combination of field measurements and experimental data shows that lava spent the majority of its thermal path during emplacement in a regime of drastic rheological change.

  4. 4.

    The data suggest that the crystallization kinetics of the lava is a function of the degree of undercooling and rate of advection within the melt.

  5. 5.

    The presented data can be employed to more accurately constrain the results of physical property-based lava flow emplacement models.

  6. 6.

    Implementation of the dynamic rheological evolution of lavas in computational models for assessment of the rheological evolution of lava flows during their emplacement requires an expanded database of non-isothermal rheology measurements such as presented here.