Experimental constraints on the rheology, eruption, and emplacement dynamics of analog lavas comparable to Mercury's northern volcanic plains: Emplacement and Dynamics of Mercury Lava

Abstract

We present new viscosity measurements of a synthetic silicate system considered an analogue for the lava erupted on the surface of Mercury. In particular, we focus on the northern volcanic plains (NVP), which correspond to the largest lava flows on Mercury and possibly in the Solar System. High-temperature viscosity measurements were performed at both superliquidus (up to 1736 K) and subliquidus conditions (1569–1502 K) to constrain the viscosity variations as a function of crystallinity (from 0 to 28%) and shear rate (from 0.1 to 5 s-1). Melt viscosity shows moderate variations (4 –16 Pa s) in the temperature range 1736–1600 K. Experiments performed below the liquidus temperature show an increase in viscosity as shear rate increases from 0.1 to 5 s-1, resulting in a shear thinning behaviour, with a decrease in viscosity of ca. 1 log unit. The low viscosity of the studied composition may explain the ability of NVP lavas to cover long distances, on the order of hundreds of kilometres in a turbulent flow regime. Using our experimental data we estimate that lava flows with thickness of 1, 5 and 10 m are likely to have velocities of 4.8, 6.5 and 7.2 m/s respectively, on a 5° ground slope. Numerical modelling incorporating both the heat loss of the lavas and its possible crystallization during emplacement allows us to infer that high effusion rates (> 10000 m3/s) are necessary to cover the large distances indicated by satellite data from the MESSENGER spacecraft.

Full text

Experimental constraints on the rheology, eruption and
emplacement dynamics of analog lavas comparable to Mercury’s
northern volcanic plains
F. Vetere1, S. Rossi1, O. Namur2,3, D. Morgavi1, V. Misiti4, P. Mancinelli1, M. Petrelli1, C.
Pauselli1, D. Perugini1
1 Department of Physics and Geology, University of Perugia, Perugia, Italy.
2 Institut fu!r Mineralogie, Leibniz Universita!t Hannover, Hannover, Germany.
3 Department of Earth and Environmental Sciences, KU Leuven, Leuven, Belgium
4 Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy.
Corresponding author: Francesco Vetere (francesco.vetere@unipg.it)
Key Points:
• New viscosity data for Mercury northern volcanic plains lavas are presented.
• Mercury lavas show shear thinning behaviour with a decrease of viscosity of ca. 1 log
unit as shear rate (!) varies from 0.1 to 5.0 s-1.
• Heat loss during lava flow and emplacement implies that high effusion rates, >10000
m3/s, are required to cover large distances as observed by MESSENGER (NASA).

Abstract
We present new viscosity measurements of a synthetic silicate system considered an analogue
for the lava erupted on the surface of Mercury. In particular, we focus on the northern volcanic
plains (NVP), which correspond to the largest lava flows on Mercury and possibly in the Solar
System. High-temperature viscosity measurements were performed at both superliquidus (up to
1736 K) and subliquidus conditions (1569–1502 K) to constrain the viscosity variations as a
function of crystallinity (from 0 to 28%) and shear rate (from 0.1 to 5 s-1). Melt viscosity shows
moderate variations (4 –16 Pa s) in the temperature range 1736–1600 K. Experiments performed
below the liquidus temperature show a decreases in viscosity as shear rate increases from 0.1 to 5
s-1, resulting in a shear thinning behaviour, with a decrease in viscosity of ca. 1 log unit. The low
viscosity of the studied composition may explain the ability of NVP lavas to cover long
distances, on the order of hundreds of kilometres in a turbulent flow regime. Using our
experimental data we estimate that lava flows with thickness of 1, 5 and 10 m are likely to have
velocities of 4.8, 6.5 and 7.2 m/s respectively, on a 5° ground slope. Numerical modelling
incorporating both the heat loss of the lavas and its possible crystallization during emplacement
allows us to infer that high effusion rates (> 10000 m3/s) are necessary to cover the large
distances indicated by satellite data from the MESSENGER spacecraft.

1 Introduction
The eccentricity of the orbit of Mercury, in combination with the planet’s vicinity to the
Sun, is responsible for its very long days (~ 59 terrestrial daytimes) and, locally, extremely high
surface temperatures. The daylight temperature at perihelion, estimated on the surface at the
equator, is ~700 K, whereas it decreases to ~350 K at 85°N. During the night, the lack of a
shielding atmosphere produces a high loss of thermal energy due to radiation and temperature
decreases to ~100 K [Paige et al., 1992; Vasavada et al., 1999].
The surface of Mercury is dominated by a secondary volcanic crust, the majority of
which formed between 4.2 and 3.5 Ga [Head et al., 2011; Weider et al., 2012; Denevi et al.,
2013; Byrne et al., 2016], with minor explosive volcanic activity until ~ 1.0 Ga [Thomas et al.,
2014]. Geochemical mapping using the X-Ray Spectrometer (XRS) and Gamma-Ray
Spectrometer (GRS) of the MErcury Surface, Space ENvironment, GEochemistry, and Ranging
(MESSENGER) spacecraft [Solomon et al., 2001] revealed that the volcanic crust is Mg-rich and
Al- and Ca-poor in comparison with terrestrial and lunar crustal material [Nittler et al., 2011;
Weider et al., 2012, 2015; Peplowski et al., 2015]. Mercury’s crust is also strongly depleted in Fe
[Izenberg et al., 2014; Weider et al., 2015]. This is most likely due to extreme partitioning of
iron into the core [Hauck et al., 2013] during early differentiation of the planets under highly
reducing conditions (IW-3 to IW-7 with IW being the iron- wüstite oxygen fugacity buffer)
[Malavergne et al., 2010; McCubbin et al., 2012; Zolotov et al., 2013; Namur et al., 2016a]. The
extremely high sulfur contents measured by MESSENGER (1–3 wt.%; [Weider et al., 2015]) can
also be explained by differentiation under reducing conditions [Namur et al., 2016a], as sulfur
solubility in silicate melts increases with progressively reduced oxygen fugacity conditions

[McCoy et al., 1999; Berthet et al., 2009; Zolotov et al., 2013; Cartier et al., 2014; Namur et al.,
2016a].
The largest effusive events on Mercury occurred at the highest latitudes of the northern
hemisphere and are represented by lavas with the highest SiO2- and Al2O3-contents and the
lowest MgO-contents detected on the planet [Weider et al., 2015; Namur et al., 2016b]. These
lavas belong to a single smooth plain deposit referred to as the northern volcanic plains (NVP)
[Weider et al., 2012; Denevi et al., 2013], which was dominantly formed between 3.7 and 3.5 Ga
2011; [Head et al., 2011; Weider et al., 2012; Ostrach et al., 2015; Byrne et al., 2016] and covers
~ 6% of the surface of the planet [Denevi et al., 2013]. A notable characteristic of this geological
sector of Mercury is that it contains well-preserved lava flows with a low crater density. Some of
these flows can be followed for distances exceeding 100 km [Byrne et al., 2013; Hurwitz et al.,
2013], making them extremely useful to gain a better understanding of the dynamics of magma
emplacement on planetary surfaces in general, and on Mercury in particular. Another distinct
feature of these lava flows is their very high Na2O (up to 8 wt.%) [Peplowski et al., 2014, 2015],
which have been explained by 15–30 % melting of a plagioclase-bearing lherzolitic mantle
source [Namur et al., 2016b; Vander Kaaden and McCubbin, 2016] and low Al2O3 contents,
responsible for the low viscosity of the lavas [Charlier et al., 2013; Sehlke and Whittington,
2015].
Several authors have investigated the nature of lavas constituting the NVP through
morphological and compositional analyses [Head et al., 2011; Ostrach et al., 2015; Weider et al.,
2015], mineralogical analysis [Namur and Charlier, 2017; Vander Kaaden et al., 2017], flow
modelling [Byrne et al., 2013] and rheological measurements of analog lavas [Sehlke and
Whittington, 2015]. The origin of such large lava flows and their lateral extent are controversial

and may be due to the low-viscosity of the lava [Stockstill-Cahill et al., 2012] and/or very high
effusion rates [Head et al., 2011; Ostrach et al., 2015; Sehlke and Whittington, 2015; Namur and
Charlier, 2017]. However, to the best of our knowledge, there is presently no work that takes
into consideration the possible variation of heat loss of the lava and its relationship with effusion
rates.
In order to better understand the mechanisms of lava emplacement in the NVP, we
provide new viscosity measurements using synthetic material with a composition that has been
estimated using the most recent XRS and GRS data from MESSENGER [Weider et al. 2015;
Peplowski et al. 2015; Table 1]. Viscosity measurements were performed at both superliquidus
and subliquidus temperatures, at varied shear rates, and are combined with numerical models in
order to propose a hypothesis for the rheological behaviour, eruption and emplacement dynamics
of NVP lavas. We propose that the formation of very large lava flows may adequately be
explained by a combination of low viscosity (10-20 Pa s) and high effusion rate (> 10000 m3/s).
In particular, we show that the effusion rates necessary to produce NVP lava flows are
comparable to those observed in large igneous provinces (LIPs) on Earth, which could be
consistent with formation of NVP lavas by adiabatic decompression of the mantle source [Namur
et al., 2016b]. Our work also shows the critical effect of low Al2O3 and high Na2O contents on
lava rheology and we believe that accurately measuring these elements and their variability
across the planet should be a priority target of the BepiColombo mission [Benkhoff et al., 2010].
2 Starting materials and experimental techniques
The elemental compositions of NVP lavas were obtained from XRS (normalized to Si)
and GRS measurements and presented by Nittler et al. [2011], Weider et al. [2012; 2015] and

Peplowski et al. [2014, 2015]. They were recalculated by Namur et al. [2016b] on an oxide basis.
These authors combined individual maps of Mg/Si, Ca/Si, Al/Si and S/Si and only calculated
chemical compositions for pixels for which those four ratios were available assuming that the
sum of major oxides is 100 wt.%. The main advantage of this method is that Si contents do not
need to be arbitrarily fixed [Vander Kaaden and McCubbin, 2016]. According to Peplowski et al.
[2014, 2015], Na2O is high in NVP lavas. Consequently, Namur et al. [2016b] used a Na/Si ratio
of 0.20, similar to the average Na/Si ratio of NVP lavas presented by Peplowski et al. [2014].
This procedure resulted in the acquisition of a large compositional range for NVP lavas spanning
from 55 to 66 wt.% SiO2, 8 to 20 wt.% MgO, 3 to 9 wt.% CaO and 9 to 16 wt.% Al2O3
[Peplowski et al. 2015; Weider et al. 2015; Namur et al., 2016b].
As reported by Nittler et al. [2011] and Weider et al. [2015], Mercury’s surface contains
high abundances of sulfur (1–3 wt.%). Sulfur solubility in silicate melts increases with
decreasing oxygen fugacity [Berthet et al., 2009; Cartier et al., 2014; McCoy et al, 1999; Namur
et al., 2016a]. Oxygen fugacity during mantle melting and volcanic eruptions on Mercury is
traditionally considered as being between IW-2 and IW-7 [McCubbin et al., 2012; Zolotov et al.,
2013] although new models show that most lavas were formed at IW-5.4±0.4 [Namur et al.,
2016a]. Therefore, the potential effect of sulfur on the rheology of Mercurian lavas might need to
be considered. However, it was demonstrated that S has a very minor effect on the
polymerization of silicate melts and, hence, on their rheology [Morizet et al., 2015]. In addition,
NVP lavas contain the lowest S contents among Mercurian magmas (0.5 to 2.7 wt.% S with a
median value of 1.64 wt.% Namur et al., [2016a]). Therefore, in this study we consider that
sulfur plays a minor role in modulating the physical properties of NVP lavas.

According to the above considerations, for this experimental study, we prepared a S-free
representative composition of NVP lavas (Table 1). We concentrated on lava compositions from
the northernmost regions of NVP (> 70˚ North), which have the lowest Al2O3-contents [Weider
et al., 2015] but also the highest Na2O contents [Peplowski et al., 2014] and which have not yet
been experimentally investigated for viscosity characterization. The synthetic composition was
prepared at the Petro-Volcanology Research Group laboratories of the University of Perugia
(hereafter PVRG labs). Our composition has a ratio of non-bridging oxygen to tetrahedrally
coordinated cations equal to 0.89 reflecting its high degree of depolymerisation. This
corresponds well with compositions reported by Stockstill-Cahill et al. [2012] and Vander
Kaaden and McCubbin [2016]. When plotted in a total alkali versus silica (TAS) diagram, our
experimental composition lies between trachy-andesite and trachy-dacite fields, similar to the
compositions investigated by Sehlke and Whittington [2015] and Vander Kaaden and McCubbin,
[2016].
Five hundred grams of glass were prepared by melting a mixture of oxides and
carbonates at 1873 K for 4 hours in a Pt80Rh20 crucible in air. Melting was performed in a
Nabertherm HT 04/17 MoSi2-heated box furnace (Nabertherm GmbH, Lilienthal, Germany). The
melt was poured on to a brass plate to quench. To ensure homogeneity, the quenched melt (glass)
was crushed, re-melted and quenched again using the same technique. This technique ensures
compositional homogeneity of the glass [Vetere et al., 2015]. Qualitatively, high fluidity was
observed during quenching suggesting a low viscosity of the melt.
Viscosity measurements have been performed in a Gero HTRV 70-250/18 high-
temperature tube furnace with MoSi2 heating elements (Gero GmbH, Neuhausen, Germany)
operating up to 2073 K at room pressure. Thermal ramps can be precisely controlled via

computer using the Eurotherm iTools v. 9.57.11 software (Eurotherm, Worthing, West Sussex,
UK). Viscosity measurements were performed with a rotational Anton Paar RheolabQC
viscometer head at the PVRG labs. This instrument consists of a sample-filled crucible and a
rotating measuring spindle that is immersed into the sample. The crucible hosting the silicate
melt is made of Pt80-Rh20 with an inner diameter of 37 mm (outer diameter 40 mm) and height of
70 mm. The spindle is made of Al2O3 with a circular section of 12.2 mm in diameter and is fixed
with a standard collet chuck to the head of the viscometer. The lower end of the Al2O3 rod is
sheathed by a tight-fitting Pt80-Rh20 foil (0.2 mm thick) in order to prevent any contamination of
the silicate melts during the experimental runs. The rotational viscometer allows measurements
under controlled shear rate (!). This allows us to investigate possible shear thinning (an increase
of viscosity with decreasing !) or shear thickening (a decrease of viscosity with decreasing !)
effects. Methods and procedures described by Dingwell [1986] and Ishibashi [2009] were
applied in order to determine melt and melt + crystals viscosities. With this equipment, viscosity
can be measured in the range from 0.1 to 105 Pa s [Hess et al., 1996]. The viscometer was
calibrated against NIST 717a standard glass, for which the temperature-viscosity relationship is
accurately known (https://www.nist.gov). Reproducibility of measurements on the standard glass
is on the order of ± 0.03 log units. Since NVP melt viscosity was expected to be low, before
running experiments we calibrated the viscometer using a Wacker silicone standard having
viscosity of 10 Pa s [Spina et al., 2016a, 2016b]. One hundred measurements were performed and
the results showed good reproducibility, with average values of 9.7 ± 0.3 (standard deviation) Pa
s.
The furnace hosting the experimental charge is equipped with aluminium cooling heads.
These are positioned on the top and the bottom openings of the furnace tube in order to prevent

overheating of the viscometer head. Cooling is achieved by a continuous flux of cold water (20°
C). The furnace can move vertically using two pneumatic cylinders (details in Morgavi et al.
[2015]). This has two major advantages as it allows us to: (1) carefully prepare the experimental
geometry by precisely positioning the outer and inner cylinders outside the furnace; (2) bring the
furnace directly to the experimental temperature while the sample is still outside the furnace,
preventing the sample from undergoing the entire thermal ramp.
Two cross-mounted Thorlabs single-axis translation stages with a standard micrometer
allow the correct positioning of the spindle and the crucible. An alumina (Al2O3) rod (length=600
mm; FRIATEC Aktiengesellschaft, Mannheim, Germany) is fixed to the lower part of the
structure holding the outer cylinder. Temperature was monitored using an in-house built S-type
thermocouple (Pt10Rh90 vs. Pt) within an Al2O3 sheath, positioned at the bottom of the crucible.
As the rotation of the viscometer prevents the use of thermocouples directly wired to a controller,
OMEGA wireless thermocouple transmitters UWTC-Series were employed (OMEGA
Engineering, INC., Stamford, Connecticut, USA). Uncertainty on temperature measurements is
on the order of 0.5 K.
Prior to viscosity measurements, ca. 70 g of melt was stirred at 1773 K for 2 hours at
strain rates (!) of 5–10 s-1. This allowed for the complete removal of possible gas bubbles and
the attainment of a compositionally homogeneous melt [Dowty, 1980; Lofgren, 1983; Davis and
Ihinger, 1998; Armienti, 2008; Iezzi et al., 2008, 2011; Pupier et al., 2008; Vetere et al., 2013a,
2015]. Samples used in the subliquidus temperature experiments were first melted at
superliquidus conditions. The temperature was then decreased continuously to the required
subliquidus value at a rate of 5 K/min. At the end of the experiments, samples were quenched by

moving them into the cooled head of the furnace. The quench rate was of the order of 100 K/min
which was sufficient to avoid the formation of quench crystals.
3 Analytical methods
Experimental samples were cored out from the outer cylinder after quenching, mounted
in epoxy, ground flat and progressively polished using diamond paste for textural and chemical
analysis. The composition of phases, i.e. the starting glass (for superliquidus experiments), the
glass matrix and crystalline phases of run-products (for subliquidus experiments) were analyzed
using a CAMECA SX100 electron microprobe analyser (EMPA) at the University of Hannover
(Germany). Analyses were performed with an accelerating voltage of 15 kV. For glasses, we
used a beam current of 8 nA and a defocused beam of 10 µm. Mineral analyses were performed
with a beam current of 15 nA and a focused beam (1 µm). Counting time on peak was 15–20 s
(7.5–10 s for background) for each element. For glasses and minerals, we used the following
standards for Kα X-ray line calibration: albite for Na, orthoclase for K, wollastonite for Si and
Ca, Al2O3 for Al, TiO2 for Ti, MgO for Mg. Raw data were corrected with the CATZAF software
and results are reported in Table 1 and Table S1-S2 (supplementary information). A high-
resolution scanning electron microscope with field-emission gun (FE-SEM LEO 1525 - ZEISS),
installed at the Department of Physics and Geology (University of Perugia), was used to collect
back-scattered electron (BSE) images of the experimental charges. Additional details about the
analytical conditions of FE-SEM and EPMA, as well as data reduction procedures, are reported
in Vetere et al. [2015] and Namur et al. [2016a].
Abundance and distribution of mineral phases in each experimental charge were
determined on BSE images using the Image-ProPlus 6.0 software. This software was also used to
calculate length-width aspect ratios (AS) of the crystals by applying an automatic ellipse fitting

procedure. When crystals were in contact, aspect ratios were measured manually. Details on the
analytical protocol for image analysis are given in previous works [Iezzi et al., 2008, 2011;
Lanzafame et al., 2013]. Representative BSE images are reported in Figure 1. In particular, the
estimation of mineral phase proportions (in area %) was made by linking grey-level values of
BSE images with compositions. No stereological correction was applied [Iezzi et al., 2008;
Vetere et al., 2010 and 2013a-b]. Magnification used in image acquisition ranged from 150× to
1600× depending on the size, shape and amount of crystalline phases. For each sample, five to
ten BSE images, cut perpendicularly to the rotational axis, were collected and analyzed on
different parts of the polished section to ensure that results were statistically significant.
4. Results
4.1 Mercury’s superliquidus melt viscosity and modelling
The liquidus temperature (TL) of our NVP composition was estimated using the alpha-
MELTS software package [Asimow, et al., 2004; Smith and Asimow, 2005] providing a value for
TL = 1581 K. Experimental data are in good agreement with this estimate; indeed, the experiment
performed at 1569 K contained only 2.1 area % of crystals indicating that the liquidus
temperature is slightly higher. This is confirmed by the experiment at T=1600 K in which no
crystals were detected.
Twenty-seven superliquidus experiments in the temperature range between 1600 and
1736 K were performed in order to determine the dependence of melt viscosity on temperature
(Table 2 and Figure 2). In these experiments, melt viscosity ranges from 4.0 Pa s and 16.3 Pa s.
Each of the viscosity values presented in Table 2 is an average of 100 to 500 measurements,
collected on timescales from 120 to 240 minutes, with torque values measured continuously. The
majority of the experiments were performed at a shear rate of 5 s-1. We selected this value

because of the very low viscosity of the investigated composition. At lower shear rate the
instrument’s torque limit is reached and measurements are not feasible. Experiments at 1736 K
(M3a-b), 1711 K (M7a-b) and 1691 K (M10a-b) were repeated twice and show a high
reproducibility (Table 2). The dependence of viscosity upon shear rate (!) was investigated with
a series of 7 experiments performed at 1672 K with ! from 5 to 10 s-1 (samples M16a-g in Table
2). Larger strain rates were not applied in order to prevent the melt to spill out from the crucible
due to its high fluidity. No measurable effect of shear rate on viscosity was detected at
superliquidus temperature (Table 2).
The obtained viscosity dataset was used to develop an empirical model of viscosity as a
function of temperature. The model is based on the Vogel-Fulcher-Tammann (VFT) equation
[Vogel, 1921]:
log η (Pa s) = A + B/(T – T0) (1)
where T is the temperature in Kelvin and A, B, and T0 are fitting parameters, representing the
pre-exponential term, the pseudo-activation energy (related to the barrier of potential energy
obstructing the structural rearrangement of the liquid), and the VFT temperature, respectively.
The VFT approach accounts for the non-Arrhenian temperature dependence of melt viscosity.
Data were fitted using a non-linear least-square regression providing the following parameters: A
= - 4.30 (Pa s), B = 6244.9 (K) and T0 = 471.2 (K). This relationship reproduces our
experimental data with a r2 value of 0.99 (Figure 2). Note that the fitting parameters reported
above are only valid for high-temperature viscosity data. In fact, when comparing our VTF
parameters with those presented in Sehlke and Whittington [2015] for melts considered similar to
those erupted on Mercury, we observe a general agreement with terms A and B, but a

disagreement with the T0 parameter. This reflects the inability of the above model to reproduce
data below the liquidus temperature.
The comparison of viscosity data presented here to those recently published by Sehlke
and Whittington [2015] shows a maximum difference of 5.0 Pa s log (η) (Table 1 and Figure 3)
mainly due to the different chemical composition of the silicate melt used in the experiments. In
this respect, an important feature of our composition is the high Na2O (8.85 wt.%) and low Al2O3
(8.95 wt.%) contents, in agreement with MESSENGER data for the most evolved lavas of the
NVP [Peplowski et al., 2014, 2015]. These compositional characteristics are responsible for the
low viscosity of our silicate melt. Previous experimental data (e.g. Le Losq and Neuville, 2013;
Vetere et al., 2014; Stabile et al., 2016) are in agreement with the lower melt viscosity described
here.
4.2 Mercury’s subliquidus viscosity
The viscous behaviour of the melt below TL was investigated using 15 experiments in the
temperature range of 1569–1502 K at three different shear rates: 0.1, 1.0 and 5.0 s-1. Prior to
cooling the melt was kept at 1673 K for 2 h in order to erase possible crystal nuclei. The final
dwell temperature was reached using a cooling ramp rate of 20 K/min. Experiments were run for
up to 24,000 s. In this temperature range, crystals nucleated and grew, increasing from 2 to 28
area %, as temperature decreased (Table 3 and Figure 4a-b).
The relative abundance of mineral phases, crystal sizes, and shapes do not vary
significantly at different shear rates. Olivine (pure forsterite) is the liquidus phase in all
experiments. Clinopyroxene appears at a temperature of 1520 K and remains stable in the system
down to 1502 K. Clinopyroxene does not show significant compositional evolution, varying

from Wo39En61 at 1520 K to Wo37En62 at 1502 K, although a slight increase of sodium content is
observed (from 0.25 to 0.95 wt.%) with decreasing temperature (Table S2, supplementary
materials). Image analysis estimates of crystal fractions and those obtained by mass balance
calculations agree well and are reported in Table 3 and in Figure 5.
The compositional evolution of the melt during crystallization is shown in Figure 6 (see
also electronic supplementary material). SiO2 increases from 62.35 to 65.95 wt.% as temperature
decreases from liquidus (TL) to 1502 K. Similar trends are observed for Al2O3, TiO2, and K2O,
whereas CaO and MgO decrease. Na2O shows a more scattered behaviour, presumably due to the
combined effect of devolatilization of this element at high temperature and its incorporation into
clinopyroxene crystals.
Viscosity vs. time at constant temperature shows a typical S-shape curve, as reported in
Figure 7a-c-e. On the right panels of the figure, representative BSE images of experimental
samples are also shown for three selected samples (M34, M35 and M36; table 3) at 1510, 1520
and 1533 K at shear rate (!) of 5.0 s-1 (Figure 7b-d-f).
As shown in Table 3 and Figures 4 and 7, viscosity at ! = 0.1 s-1 varies between 2.72–
4.01 Pa s [log (η)] for temperatures ranging from 1533 to 1502 K. As ! values increase to 1.0
and 5.0 s-1, viscosity [log (η)] varies between 1.93–3.04 Pa s (at 1545 K) and 2.25–3.36 Pa s (at
1502 K), i.e. viscosity decreases as shear rate increases. This points to a shear thinning behaviour
of the partly crystallized melt. From the curves displayed in Figure 7, the time for crystal
nucleation and growth can be evaluated at different temperatures [Vona et al., 2011]. Crystal
growth appears to be inversely correlated to the shear rate indicating that the higher the applied
shear rate, the lower the time needed for crystals to nucleate and grow. For example, at 1510 K
the time to reach a constant viscosity value (plateaux in Figure 7a) at ! = 0.1 s-1 is slightly longer

than 4.0 hours. At the same temperature, viscosity reaches a constant value after about 2.0 hours
at ! = 5.0 s-1. As temperature increases to 1533 K, the time taken to reach a constant viscosity in
the partly crystallized system is about 2.0 hours and 1.0 hour, for ! of 0.1s-1 and 5.0 s-1,
respectively (Figure 7e).
4.3 Further rheological considerations
During crystallization, the shear thinning behaviour becomes evident for all experiments,
with viscosity decreasing as the shear rate increases (Figure 4). Noteworthy is the fact that the
shear-thinning behaviour also arises at low crystal fractions (Φc=0.05) and increases at higher
crystal contents (Figure 4a). Following the work from Sehlke and Whittington [2015], Sehlke et
al., [2014] as well as from Vona et al., [2011 and 2013], we calculate the flow index using the
linear regression coefficients derived from our experimental data set (Table 3 and Figure 8 a
and b; see also supporting information files for details).
Flow index values are relatively low compared to those estimated by Sehlke et al. [2014]
for Hawaiian basalts, as well as from Sehlke and Wittington [2015] for Mercury’s analog
compositions (Fig. 8b). This is presumably due to the large aspect ratios of crystals in our study
(up to 14) that can strongly influence flow index values [Mader et al. 2013]. This highlights the
highly non-Newtonian behaviour of our partly crystallized analog composition. As an example,
at a temperature of 1533 K and crystal content of ca. 9.0 area % (sample M36 in Table 3) the
flow index (n) is 0.53. Under these conditions, an increase in shear rate from 0.1 to 5 s-1 results in
a decrease in viscosity by a factor of 6. In a similar way, experiment M33 performed at 1502 K
(crystal content of 28 area % with n = 0.42) shows a decrease in viscosity by a factor of 10 (see
Table 3 and Figures 4 and Figure 8). A comparison between the rheological behaviour of our

composition with data from Sehlke and Wittington [2015] is provided in Figure S1
(supplementary materials), where the change in apparent viscosity with crystal fraction is shown.
Results indicate a good general agreement between literature data and our experimental results.
A slight deviation is observed at the lowest shear rate possibly due to differences in crystal
shapes and distributions.
Flow curves for Mercury lavas superimposed on the pahoehoe to `a`a transition threshold
diagram, derived from Sehlke et al. [2014], are presented in Figure 9. Mercury’s lavas show
similar characteristics, but at slightly lower crystal fractions (0.05) compared to those studied by
Sehlke et al. [2014]. As the melt crosses the liquidus temperature (1581 K), pseudoplasticity
arises (flow index n < 0.7), as shown by the fact that the magma lies in the transition threshold
zone (TTZ) in Figure 9. It is not surprising that pseudoplastic behaviour is found at very low
crystal content. In fact, Ishibashi and Sato [2007] detected pseudoplastic behaviour in alkali
olivine basalt at Φ as low as 0.05 (olivine, plagioclase, and spinel). In addition, Ishibashi [2009]
detected pseudoplastic behaviour in basalt from Mount Fuji between Φ of 0.06 to 0.13 due to
suspended plagioclase crystals. The transition from pahoehoe to `a`a for the analog Mercurian
lava studied here begins at a temperature of ~1533 ± 10 K.
In modelling viscosity vs. crystal content, the relative viscosity (defined as ηr = ηeff/ηm,
where ηeff is the effective viscosity of the suspension with a volume fraction of crystals, and ηm is
the viscosity of the melt; see supplementary materials for details) is one of the most used
parameter. Figure 10 shows the variation of ηr as crystallinity (
Φ
) increases. Our experimental
data can be described by the Einstein-Roscoe equation (see supplementary information) for
relatively high !. Lowering ! to the value 0.1 s-1 results in higher
η
r (reaching values up to ca.
15) matching results reported by Vona et al., [2011] for crystallinity higher than 20 vol.%.

5. Discussion
According to results presented by Byrne et al. [2013] on the lava flows forming the NVP,
some important constraints emerge: i) NVP lavas can flow over very long distances, on the order
of hundreds of kilometres; ii) the channels filled by the lavas appear quite variable in terms of
their width, spanning from a few hundreds meters to tens of kilometres; iii) the morphological
characteristics of lava flows, observed using high-resolution images of the planet surface,
indicate that lavas were emplaced as turbulent flows [Byrne et al., 2013]. These constraints must
be taken into account when attempting to shed new light upon the mechanisms that might have
contributed to the emission and emplacement of lava flows forming the NVP. In the following
discussion, the new experimental data presented in this work are integrated with the above
constraints, in order to refine our understanding of the dynamics of NVP lava flows. Notably, in
conducting both superliquidus and subliquidus experiments, we attempt to constrain the
behaviour of lavas in terms of velocity and distance covered by the flows, as well as the possible
effusion rates.
The initial issue to consider is the slope of the terrains on which the lava was emplaced.
Although it would be preferable to use pre-eruption topographic data to estimate lava flow
velocity, this is not possible at present and we must rely upon present day, post-NVP
emplacement, topography [e.g. Byrne et al., 2013]. Hereafter, we consider average slope values
in between 0.1°–5°; these are of the same order of magnitude as those used in other studies of
lava flows on the surface of Mercury [e.g., Byrne et al., 2013; Hurwitz et al., 2013].
As the emplacement of lavas on Mercury likely occurred in a turbulent regime [Byrne et
al., 2013] we can use the approach proposed by Williams et al. [2001], which is valid for high
Reynolds numbers (Re>>2000), to infer the possible velocity of lava flows. This method allows

for the estimation of lava flow velocity u (m/s), considering the ground slope
θ
(°) and the lava
friction coefficient
λ
:
!=!!!!"#(!)
! (2)
where g (m/s2) and h (m) are the acceleration due to gravity and the lava flow thickness,
respectively. The acceleration due to gravity on Mercury is g=3.61 m/s2 (i.e. almost 1/3 of that of
the Earth; Mazarico et al. 2014).
λ
can be calculated as follows:
!=!
!.!" !" !" !!.!" ! (3)
where Re is the Reynolds numbers defined as:
!" =!!"!
! (4)
ρ is the bulk lava density (2450 kg/m3 for the melt considered here, calculated following Ochs
and Lange [1999]) and
η
is the lava viscosity (Pa s).
With regard to the thickness of the flows to be used in the above equations, the total
thickness of NVP lavas has been estimated to be ~ 0.7–1.8 km [Ostrach et al., 2015; Head et al.,
2011; Klimczak et al., 2012; Byrne et al., 2013]. However, this thickness is likely to be the result
of the superimposition of different lava flows, whose individual thicknesses are presently
unknown. Some constraints can be derived from terrestrial analogous lavas. Among them,
Hawaiian lavas with rheological behaviours similar to the silicate melt considered here typically
show individual flow thicknesses ranging from 1 to 5 m [Griffiths, 2000]; furthermore,
komatiites, also commonly considered similar to Mercurian lavas [Weider et al., 2012], show
flows with a slightly greater thickness of about 10 m [Williams et al., 2001]. Accordingly, values
of h from 1 to 10 m are used in equations 2 and 4.

The values of viscosity to be used in the above equations depend upon the eruptive
temperature. Possible eruption temperatures for Mercurian lavas are estimated to be around 1623
K [Charlier et al., 2013; Namur et al., 2016b]. As the estimated liquidus temperature for the melt
used in the experiments is similar (1600 K) to the suggested eruptive temperature, we started our
modelling considering 1623 K as a representative eruptive temperature of the lava that is initially
erupted. Changing the eruptive temperature to 1600 K does not affects the outcomes of the
model presented below. According to our experimental data and modelling (Figure 2), at 1623 K
the viscosity of the silicate melt is ca. 13 Pa s. Assuming constant effusion rates, calculated
velocities for lava thicknesses of 1, 5 and 10 m, considering varying ground slopes (from 0.1 to
5°) are shown in Figure 11. As expected, results show that lava flows with larger thickness
consistently have larger velocities (see also Table S3 in the supporting materials). In addition, in
order to maintain the turbulent regime (Re larger than 2000) for lava emplacement (Byrne et al.,
2013), minimum velocities must be larger than ca. 1.2 m/s (on a slope of 0.3°), and ca. 0.7 m/s
(on a slope of 0.1°) for lava thicknesses of 5 and 10 m, respectively. Note that for lava
thicknesses on the order of 1.0 m, the turbulent regime is only possible for slopes larger than 10°,
a value which appears unlikely on the basis of recent studies in this sector of the planet’s surface
[e.g., Byrne et al., 2013; Hurwitz et al., 2013]. As the slope increases, the lava flow velocity can
increase up to values of the order of 6.5 and 7.2 m/s, when flowing on a 5° ground slope, for
thicknesses of 5 and 10 m, respectively.
In order to incorporate the possible effects of heat loss during the lava flow in our model,
we performed thermal balance calculations using the FLOWGO model [Harris and Rowland,
2001]. In the model we consider that lavas can flow in channels with variable widths from 100,
1000 and 30000 m, as observed for the NVP on Mercury [Byrne et al., 2013]. In addition, we

consider, as minimum and maximum velocities of the lava, the values obtained above for a lava
flow of thickness h=10 m flowing on a slope of 0.1° (u=0.7 m/s) and for a lava flow of the same
thickness flowing on a slope of 5° (u=7.2 m/s). Note that, according to the above discussion,
these end-member values of u include all possible values of velocity for a lava flowing down a
slope at an angle between 0.1 and 5°, with a thicknesses ranging from 5–10 m. A further
constraint to be considered in the model is the emissivity value of the lava. According to Harris
[2013] this parameter shows little variability, even among very different magmatic compositions.
In particular, it ranges from ca. 0.8 to ca. 0.9 from basalt to trachyte; accordingly, in the model,
we used an emissivity value of 0.85. The differences produced when this parameter is changed
are negligible. The FLOWGO model accounts for the formation of a crust developing on the
outer part of the lava acting as a thermal insulation boundary and limiting the heat loss. In
addition, turbulence cannot be directly included in FLOWGO. However, the large velocity
values used in the model can be considered as a proxy for turbulence implying that larger
velocities produce larger covered areas by the lava and, hence, larger heat losses. Parameters
used in the model are reported in Table S4 (supplementary materials); details about the
FLOWGO model can be found in Harris and Rowland [2001].
Figure 12 shows the variation of heat loss (in K/km) of the lava as a function of effusion
rate (in m3/s). The plot displays six curves corresponding to lava flows with the above-
considered velocities (0.7 and 7.2 m/s) flowing in channels with widths of 100, 1000 and 30000
m. The graph shows that the curves have a similar behaviour and tend to saturate towards
constant values of heat loss at high effusion rates (of the order of 104, 105 and 107 for channels
having width of 100, 1000 and 30000 m, respectively). At lower effusion rates the heat loss
dramatically increases (Figure 12). The curves corresponding to the lava flowing with a velocity

of 0.7 m/s indicate that, at the same value of effusion rate, the heat loss is always lower in
comparison to the lava flowing with a velocity of 7.2 m/s. From Figure 12, it also emerges that
the channel width plays a major role in modulating heat loss. In fact, to maintain a similar
amount of heat loss, strongly increasing effusion rates are required as the width of the channel
increases.
As stressed above, a fundamental constraint to be satisfied is that a turbulent regime
likely characterized the emplacements of the lava for distances on the order of 100 km [Byrne et
al., 2013]. According to the above discussion, Reynolds numbers larger than 2000 are possible
considering the eruptive temperature T=1623 K (and relative value of viscosity,
η
=13 Pa s), and
lava velocities larger than 0.7 m/s, according to the slope values and lava thicknesses reported
above (see supporting information, Table S3). Keeping lava velocity constant in the limits
imposed above (i.e. 0.7 and 7.2 m/s), we can use the results shown in Figure 12 to evaluate how
heat loss impacts lava rheology and the consequent dynamic regime of lava emplacement. As the
lava cools down during its flow, its viscosity is expected to increase leading to a decrease of the
Reynolds number and resulting, eventually, in the suppression of the turbulent regime.
According to our experimental results and modelling (Figure 2), the viscosity of the analogous
melt studied here shows minimal variations (13–20 Pa s) in the temperature range 1623–1581 K
(i.e. from eruptive to liquidus temperature; Figure 3). This implies that the Reynolds number
remains relatively constant during this temperature drop (ΔT=42 K, i.e. 1623–1581 K) allowing
the turbulent regime to remain almost unchanged. Considering that the lava has to cover a
distance on the order of 100 km in turbulent regime [Byrne et al., 2013], this would correspond
to a heat loss of ca. 0.4 K/km. According to the model shown in Figure 12, a heat loss of 0.4
K/km can be obtained at different effusion rates depending on the width of the channel in which

the lava flows. In particular, effusion rates larger than ca. 104, 105 and 106 m3/s are required for
channel widths of 100, 1000 and 30000m, respectively. It is noteworthy that these estimates are
in concurrence with independent results given by Keszthelyi and Self [1998] for the emplacement
of long (on the order of 100 km) basaltic lava flows. In particular, Keszthelyi and Self [1998]
report that in order to cover these large distances, a heat loss equal to or lower than 0.5 K/km is
necessary. Furthermore, these authors suggest that effusion rates larger than 103–104 m3/s, and
velocities on the order of 4–12 m/s are also required. These values are comparable to those
arising from our model. From this discussion, it is therefore clear that the Mercurian analog melt
studied here is able to flow over the long distances observed for the NVP in turbulent regime,
under the effusion rates given above. Significantly, the required effusion rates (and relative
single lava flow thickness) are comparable to those estimated for some of Earth’s basaltic
eruptions forming the so-called LIPs [e.g. Bryan et al., 2010; Head et al. 2011]. Consequently,
the mechanism of eruption and emplacement of terrestrial flood basalts can be considered, as a
first approximation, as a plausible geologic analogue for the Mercury’s NVP lavas in agreement
with the results reported by Vander Kaaden and McCubbin [2016].
A further issue that might deserve consideration is the possible effect of cooling of the
lavas due to the temperature difference between diurnal and nocturnal times on Mercury. During
a Mercurian day (corresponding to 59 terrestrial days), surface temperature can reach 725 K. At
night, the surface temperature drops to about 90 K [Strom, 1997]. In these conditions, the high
temperature of the planet may limit heat dissipation during daytime eruptions and, consequently,
enhance the emplacement of lava flows. Conversely, during the night, the temperature drop
could act as a limiting factor for the distance the lava is able to flow. However, in modelling lava
flows, the formation of a crust developing on the outer part of the lava must be considered. This

effect is considered in the FLOWGO models presented above. The formation of this crust acts as
thermal insulation for the lava and, therefore, the effect of temperature difference between
Mercurian day and night can be considered negligible.
According to the above discussion, it is apparent that NVP lavas were able to cover large
distances without undergoing strong degrees of crystallization. Accordingly, most of their
solidification history would have occurred when they stopped flowing and emplaced, defining
the present morphology of Mercury’s NVP. The causes why lavas stopped flowing on the
surface of the planet can be variable. One possibility might be that the topography of the planet
played a key role, for example because of the presence of low topographies due to pre-existing
impact craters that allowed the lavas to stagnate, lose heat and solidify.
Further evidence that solidification of the lavas must have occurred mostly after
emplacement is provided by results from crystallization experiments. Lavas can strongly reduce
their ability to flow when approaching the so-called “maximum packing fraction”. The
maximum packing fraction strongly depends on the aspect ratio of crystals [Mader et al., 2013].
Our experiments indicate that crystal aspect ratios range, on average, between 2 and 14.
According to Mader et al. [2013] this corresponds to maximum packing fractions from ca. 52%
to 28%. As here we are evaluating the least favourable conditions under which the lavas can
flow, we considered the lowest maximum packing fraction (i.e. 28%) as the reference crystal
fraction that would strongly reduce (or stop) the ability of the lava to flow. Our experiments
(Figure 4a-b) indicate that temperature needs to drop to 1502 K to reach a crystal content of ca.
28%. The question is whether the lava in these conditions can preserve the turbulent flow
regime, as required by morphological constraints provided by [Byrne et al., 2013]. Our
experimental results presented in Figure 4 and Table 3 show that the rate of increase in viscosity

due to crystallization is different depending on the applied shear rate, due to a shear thinning
behaviour of the lava. As an example, at T=1520 K (corresponding to a crystal content of ca.
10%; Table 3) viscosity changes from 144 Pa s to 1259 Pa s, as the shear rate decreases from 5 to
0.1 s-1. A similar behavior is observed for lower temperatures, i.e. larger crystal contents, up to
the threshold limit of 28% crystal content (Figure 4).
The Reynolds number (equation 4) can be used to assess whether the lava can emplace in
turbulent flow conditions, i.e. Re larger than 2000. In the following calculations, we consider a
lava flow with thickness of 10 m flowing at velocities from 0.7 to 7.2 m/s (see above) and having
viscosities determined by the amount of crystals formed upon solidification (Figure 4). Note that
for lavas with thicknesses lower than ca. 10 m, considering the viscosities for crystal-bearing
lavas with a crystallinity equal to or larger than 5% (Figure 4 and Table 3) and for any of the
above velocities, Re is always lower than 2000; in these conditions the laminar regime prevails.
For lava thicknesses on the order of 10 m, i.e. maximum thickness considered here, the laminar
fluid dynamic regime governs most of the behavior of the flowing lava. However, according to
our experimental results, there are cases in which the turbulent regime might still persist, even
for partially crystallized systems. In particular, Re can attain values above 2000 if viscosity is
lower than 144 Pa s and flow velocity is larger than 6 m/s. From Figure 4, these viscosity values
correspond to partially crystallized systems with crystal contents up to ca. 10% for shear rates of
5 s-1. Lower shear rates shift Re towards values lower than 2000, driving the system towards
laminar conditions. These considerations highlight that, whilst for some narrow combinations of
parameters (i.e. viscosity, velocity, lava thickness), the lava could potentially flow in turbulent
conditions below the liquidus temperature (TL), in most cases it behaves as a laminar system.
However, this is contrary to morphological features observed from satellite images and

considered to reflect a turbulent emplacement of the lava [Byrne et al., 2013]. These
considerations corroborate the idea proposed above, that crystallization of lavas is a process that
most likely occurred after emplacement.
6. Conclusions
The new experiments and modelling presented in this work allow us to shed new light on
the mechanisms that determined the emplacement of what is believed to be one the largest
volcanic deposits in the Solar System [Byrne et al., 2016]; the northern volcanic province on
planet Mercury. The high Na2O content (~8.8 wt.%) of the experimental starting material plays
an important role in reducing lava viscosity, as confirmed by concentric cylinder high
temperature viscosity measurements.
The viscosity of our Mercury analog silicate melt measured at superliquidus temperature
conditions slightly increases from 4 to 16 Pa s in the temperature range 1736–1600 K. In the
temperature range 1569–1502 K (subliquidus), viscosity increases due to the combined effect of
progressive crystallization (from 2 to 28 area %) and chemical evolution of the melt. Here, a
shear-thinning behavior was observed when varying strain rates from 0.1 and 5 s-1. Lava
viscosity decreases by ca. 1 log unit as shear rate varies from 0.1 and 5 s-1.
These new viscosity measurements were used to model the behaviour of Mercurian lavas
during emplacement. Merging experimental data and numerical modelling leads to the
conclusion that the emplacement of lavas in turbulent conditions, as claimed by previous works
[e.g. Byrne et al., 2013], defines a geologic scenario in which lavas might have travelled long
distances without undergoing strong degrees of crystallization. Therefore, it is possible to infer
that solidification (crystallization) of the lavas mostly occurred after emplacement on the surface

of the planet. Effusion rates were estimated to be in the order of 104–107 m3/s, comparable to
those estimated for some Earth’s basaltic eruptions forming the LIPs.
Acknowledgments
This work was funded by the European Research Council for the Consolidator Grant ERC-2013-
CoG Proposal No. 612776 — CHRONOS to Diego Perugini. Francesco Vetere acknowledges
support from the TESLA FRB-base project from the Department of Physics and Geology,
University of Perugia. Olivier Namur acknowledges support from an Individual Intra-European
Marie Curie Fellowship (SULFURONMERCURY) and from the DFG through the Emmy
Noether Program. Rebecca Astbury is gratefully acknowledged for language corrections. We
also wish to thank Nonna Rita for her wise words “adduvi c’è gustu, un c’è pirdenza” that guided
us through the writing of this work. Data of experiments are reported in Tables 1, 2 and 3, in
Figures 1–12 and in Supporting Information as Tables S1, S2, S3 and S4 and Figure S1.

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Supporting Information for
Experimental constraints on the rheology, eruption and
emplacement dynamics of analog lavas comparable to
Mercury’s northern volcanic plains
F. Vetere1, S. Rossi1, O. Namur2,3, D. Morgavi1, V. Misiti4, P. Mancinelli1, M.
Petrelli1, C. Pauselli1, D. Perugini1
1 Department of Physics and Geology, University of Perugia, Perugia, Italy.
2 Institut fu!r Mineralogie, Leibniz Universita!t Hannover, Hannover, Germany.
3 Department of Earth and Environmental Sciences, KU Leuven, Leuven, Belgium
4 Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy.
Introduction
Here we report detailed description on data presented in the main text. In particular, a
description of the theoretical and experimental approaches on two phase magma
rheology are reported in Text S1. Moreover, details on the a) chemistry for the
residual glasses after crystallization processes, b) the chemistry of the solid phases
produced and for c) the calculation concerning the velocities and relative Reynolds
number used in this study are provided in an Excel file (Tables S1, S2 and S3,
respectively)
Text S1.
In order to quantify the effect of cooling and relative crystals content, size
distributions, and crystal shapes on magma viscosity, abundant theoretical and
experimental studies were reported [Shaw, 1969; Murase and McBirney, 1973;
Murase et al., 1985; Ryerson et al., 1988; Pinkerton and Stevenson, 1992; Lejeune
and Richet, 1995; Pinkerton and Norton, 1995; Sato, 2005; Arbaret et al., 2007;
Caricchi et al., 2007; Ishibashi and Sato, 2007; Costa et al., 2009; Vetere et al., 2010,
2013, Vona et al., 2011, 2013; Sehlke et al., 2014; Sehlke and Whittington, 2015]. As
described by [Ishibashi, 2009], one of the most frequently used equations to evaluate
the relative viscosity of a suspension ηr (ηr = ηeff/ηm), where ηeff is the effective

viscosity of the suspension with a volume fraction of crystals, and ηm is the viscosity
of the melt, is the Krieger–Dougherty (KD) equation (Krieger and Dougherty, 1959):
ηr =(1−Φ/ Φm)-νΦm (1)
where Φ is a volume fraction of suspended particles, Φm is the maximum packing
density, and ν is the so called intrinsic viscosity (a measure of the crystal influence to
the magmatic system viscosity). Assuming that νΦm = 2.5, the effective viscosity of
crystal + melts systems is often estimated with the Einstein-Roscoe equation
(Einstein, 1906; Roscoe, 1952):
ηeff = ηm (1-Φ/ Φm)-2.5 (2)
However, this equation is only valid if the shape of the particles can be approximated
to that of a sphere. The Φm value, according to Marsh [1981], is estimated to be 0.6
and corresponds to the crystal fraction at which a transition of the system to the rigid
solid state occurs. However, it has been demonstrated that this value is not always
adequate for natural magmatic systems [Costa, 2005].
Studies on the viscosity of magmatic suspensions can be done allowing crystals to
nucleate and grow from melts at subliquidus conditions in order to examine the
magma’s rheological evolution [Pinkerton and Norton, 1995; Sato, 2005; Ishibashi
and Sato, 2007; Ishibashi, 2009, Vona et al., 2011, Vetere et al., 2013]. This approach
has the advantage of tracking the sequential variation of both the crystal texture and
rheological properties during cooling of magmas and is adopted here.
A fluid is said to be purely viscous if the shear stress (σ) is a function only of the
shear rate (γ !). For non-Newtonian fluids in simple shear flow a viscosity function
η(γ !) is:
η(!)=τ/! (3)
The viscosity function is also called the apparent viscosity (this term is used to
indicate that the result depends on the particular strain rate at which it was measured).
Rheological parameters of two-phase suspension are usually treated by using classical
approach for pseudoplastic (power law) flow.
By using such approach it is possible to identify parameters such as the flow index n
and consistency K by the following:
σ = K !!n (4)
For a Newtonian liquid, n =1. More details can be found in Moitra and Gonnermann
(2014) for the Herschel-Bulkley model (Herschel and Bulkley, 1926). Then, fitting
can be expressed in ln or log terms for stress or for apparent viscosity:
ln σ = ln k + n ln !! (5)
and/or
log η = log k + (n-1) log !!(6)
References
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0273(92)90073-M.

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experimental study, J. Geophys. Res. Planets, 120(11), 1924–1955,
doi:10.1002/2015JE004792.
Sehlke, A., A. Whittington, B. Robert, A. Harris, L. Gurioli, E. Médard, (2014), Pahoehoe to
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doi:10.2465/jmps.090402.
Vetere, F., H. Sato, H. Ishibashi, R. De Rosa, and P. Donato (2013), Viscosity changes during
crystallization of a shoshonitic magma: New insights on lava flow emplacement, J.
Mineral. Petrol. Sci., 108(3), doi:10.2465/jmps.120724.
Vona, a., C. Romano, D. B. Dingwell, and D. Giordano (2011), The rheology of crystal-
bearing basaltic magmas from Stromboli and Etna, Geochim. Cosmochim. Acta, 75(11),
3214–3236, doi:10.1016/j.gca.2011.03.031.
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magmas from Monte Nuovo (Campi Flegrei, Italy), Chem. Geol., 346, 213–227,
doi:10.1016/j.chemgeo.2012.10.005.

Tables''
'
Table'1'
'
This'work'
'
SW-2015'
''
wt%'
std'
Enstatite'bas'
NVP'
NVP-Na'
IcP-HCT'
SiO2'
61.48'
0.36'
55.06'
57.10'
55.02'
53.30'
TiO2'
0.36'
0.01'
0.18'
0.96'
0.89'
0.89'
Al2O3'
8.95'
0.11'
13.07'
15.27'
14.88'
12.31'
FeO'
-'
-'
0.29'
3.61'
2.88'
3.31'
MnO'
-'
-'
0.14'
0.25'
0.25'
0.23'
MgO'
14.12'
0.21'
19.72'
16.53'
13.59'
22.53'
CaO'
6.81'
0.09'
12.37'
4.95'
4.29'
6.29'
Na2O'
8.85'
0.21'
0.04'
0.29'
6.25'
0.16'
K2O'
0.21'
0.02'
0.08'
0.31'
0.22'
0.19'
'
'
'
'
'
'
'
Tot'
100.78'
'
100.95'
99.27'
98.27'
99.21'
NBO/T'
0.89'
'
1.00a'
0.64'a'
0.68'a'
1.05'a'
'
'
'
–'
0.50'b'
0.55'b'
0.86'b'
'
'
'
–'
0.41'c'
0.53'c'
0.79'c'
'
Table 1. Electron microprobe analyses of the starting material compared to literature
data. The starting composition represents an average of 50 measurements on the
synthetic starting glass material. SW-2015 refers to literature data presented in Sehlke
and Whittington [2015]. Std refers to the standard deviations. The NBO/T values
(non-bridging oxygens (NBO) per tetrahedrally coordinated cation (T) [Mysen and
Richet, 2005]). NBO/T values for Sehlke and Whittington [2015] chemical
compositions refer to calculation results considering (a) ferrous only, (b) ferrous and
ferric, and (c) ferric only.
'
'
'
'
'
'
'
'
'
'
'
'
'
'
'

Table'2'
'
#'
T'(K)'
η'(Pa's)'
std'
!'
'
'
'
'
'
M29'
1600'
16.3'
0.27'
5'
M28'
1610'
14.9'
0.58'
5'
M32'
1618'
12.6'
0.43'
5'
M27'
1621'
14.1'
0.41'
5'
M26'
1630'
12.9'
0.35'
5'
M31'
1639'
10.3'
0.06'
5'
M15'
1652'
9.7'
0.05'
5'
M14'
1662'
8.7'
0.07'
5'
M13'
1671'
7.9'
0.04'
5'
M12'
1681'
7.2'
0.05'
5'
M17'
1687'
6.7'
0.11'
5'
M10a'
1691'
6.8'
0.05'
5'
M10b'
1691'
6.7'
0.08'
5'
M9'
1701'
6.0'
0.06'
5'
M7a'
1711'
5.5'
0.05'
5'
M7b'
1711'
5.7'
0.03'
5'
M'6'
1720'
5.0'
0.03'
5'
M'5'
1730'
4.6'
0.04'
5'
M'3a'
1736'
4.3'
0.03'
5'
M'3b'
1736'
4.0'
0.04'
5'
M'16a'
1642'
10.7'
0.17'
5'
M'16b'
1642'
11.2'
0.15'
5'
M'16c'
1642'
11.2'
0.26'
6'
M'16d'
1642'
11.3'
0.23'
7'
M16e'
1642'
11.2'
0.25'
8'
M16f'
1642'
11.4'
0.21'
9'
M16g'
1642'
11.2'
0.16'
10'
Table 2. Experimental conditions and results of viscosity measurements (η) using the
concentric cylinder apparatus. γ (in s-1) refers to the applied shear stress; std refers to
standard deviation of viscosity measurements.

Table&3&
&
&
&
&
&
&
&
&
&
&
&
&
&
&
Table 3: Experimental conditions and results of viscosity measurements (η) during crystallization experiments at different shear rate (γ).
Rheological parameters [flow index (n) and consistency (k)] and crystal contents (both area% and vol.%) are also reported.
&
#&
Temperature&
Log&η&&
Pa&s&
Log&η&&
Pa&s&
Log&η&&
Pa&s&
Flow&
index&
K"
Olivine&
Pyroxene&
Crystallinity&
Crystallinity&
&
K&
!=5&s-1&
!=1&s-1&
!=0.1&s-1&
n"
Pa&s&
area&%&
area&%&
area&%&
mass&balance&
vol&%&
&
&
&
&
&
&
&
&
&
&
&
M33&
1502&
3.04&
3.36&
4.01&
0.4201&
1172±&175&
17.6&±&3.0&
9.9&±&1.3&
27.5&±&3.0&
23.7&
M34&
1510&
2.67&
3.18&
3.59&
0.4551&
593±&53&
11.5&±&1.9&
9.9&±&0.8&
21.4&±&2.2&
16.3&
M35&
1520&
2.16&
2.69&
3.10&
0.4568&
207±&30&
9.9&±&0.2&
1.7&±&0.2&
11.8&±&1.2&
10.1&
M36&
1533&
1.99&
2.47&
2.72&
0.5272&
131±&22&
8.8&±&0.9&
-&
8.8&±&0.9&
8.2&
M37&
1545&
1.93&
2.25&
&
0.5333&
61±&5&
5.0&±&0.7&
-&
5.0&±&0.7&
7.3&
M38&
1569&
1.63&
&
&
-&
-&
2.1&±&0.3&
-&
2.1&±&0.3&
3.9&

Table&S1
γ&=&0.1&s-1 1545&K Std 1533&K Std 1520&K Std
SiO2 61.94 0.44 63.03 0.60 62.95 0.43
TiO2 0.40 0.02 0.42 0.03 0.43 0.02
Al2O3 9.74 0.16 9.78 0.12 10.16 0.16
MgO 10.59 0.20 9.98 0.21 9.16 0.16
CaO 7.30 0.09 7.42 0.14 7.02 0.09
Na2O 8.46 0.15 8.66 0.19 8.76 0.20
K2O 0.21 0.02 0.22 0.01 0.21 0.02
98.70
γ&=&1&s-1 1545&K Std 1533&K Std 1520&K Std 1510&K Std 1502&K Std
SiO2 62.85 0.54 63.30 0.32 64.76 0.57 65.05 0.58 65.95 0.37
TiO2 0.39 0.02 0.40 0.02 0.43 0.02 0.44 0.02 0.47 0.02
Al2O3 9.56 0.09 9.63 0.09 10.56 0.11 10.81 0.13 11.58 0.16
MgO 10.54 0.15 10.12 0.19 8.69 0.18 8.14 0.20 7.18 0.17
CaO 7.29 0.12 7.34 0.11 6.56 0.08 6.15 0.08 4.93 0.08
Na2O 9.54 0.19 9.42 0.26 8.75 0.40 8.33 0.43 9.00 0.28
K2O 0.22 0.01 0.22 0.01 0.25 0.01 0.25 0.02 0.27 0.02
γ&=&5&s-1 1569&K Std 1545&K Std 1533&K Std 1520&K Std 1510&K Std 1502&K Std
SiO2 61.68 0.26 62.67 0.24 63.42 0.27 63.24 0.27 64.30 0.34 64.64 0.40
TiO2 0.40 0.04 0.40 0.04 0.44 0.04 0.43 0.02 0.46 0.04 0.49 0.04
Al2O3 8.97 0.12 9.73 0.16 9.43 0.13 9.58 0.15 10.27 0.12 11.11 0.11
MgO 11.89 0.23 10.35 0.32 10.03 0.19 9.33 0.10 8.69 0.23 7.51 0.19
CaO 6.84 0.10 7.12 0.11 7.20 0.12 7.08 0.09 6.21 0.11 4.94 0.09
Na2O 7.99 0.13 8.11 0.13 8.29 0.15 8.38 0.14 9.15 0.13 9.69 0.09
K2O 0.19 0.03 0.20 0.02 0.24 0.03 0.20 0.02 0.25 0.02 0.25 0.03
&&&P2O5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
γ&=&shear&rate
Table S1. Electron microprobe analyses of the residual glasses material provided in Figure 6 after crystallization experiments.
Presented data are averages of 50 measurements on each experimental sample. Std refers to the standard deviations.

Table&S2
Ol Ol CPx Ol
γ&=&0.1&s-1 1545$K Std 1533$K Std 1520$K Std 1520$K Std
SiO2 42.54 0.63 42.15 0.85 55.75 0.78 42.42 0.73
TiO2 0.02 0.01 0.01 0.01 0.09 0.01 0.01 0.01
Al2O3 0.02 0.03 0.01 0.01 0.42 0.03 0.02 0.01
MgO 56.40 1.15 57.11 0.71 22.26 0.65 57.19 1.56
CaO 0.32 0.03 0.27 0.07 20.82 0.80 0.30 0.04
Na2O 0.04 0.02 0.01 0.01 0.30 0.04 0.04 0.03
K2O 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.01
Ol Ol CPx Ol CPx Ol CPx Ol
γ =&1&s-1 1545$K Std 1533$K Std 1520$K Std 1520$K Std 1510$K Std 1510$K Std 1502$K Std 1502$K Std
SiO2 42.69 0.39 42.93 0.62 56.37 0.18 42.71 0.40 56.27 0.47 43.17 0.53 56.42 0.34 43.21 0.39
TiO2 0.00 0.01 0.01 0.01 0.10 0.02 0.00 0.01 0.11 0.03 0.00 0.01 0.10 0.01 0.00 0.01
Al2O3 0.01 0.02 0.03 0.04 0.45 0.04 0.02 0.04 0.48 0.07 0.05 0.11 0.49 0.11 0.02 0.02
MgO 57.08 0.39 57.09 0.52 22.68 0.71 57.09 0.57 22.08 0.63 56.93 0.52 23.10 0.82 57.38 0.26
CaO 0.30 0.03 0.32 0.04 20.21 0.80 0.32 0.04 20.85 0.49 0.34 0.07 19.62 0.94 0.31 0.03
Na2O 0.04 0.03 0.07 0.02 0.28 0.04 0.08 0.05 0.28 0.06 0.08 0.08 0.34 0.09 0.08 0.02
K2O 0.02 0.01 0.01 0.01 0.02 0.01 0.02 0.01 0.01 0.01 0.02 0.01 0.02 0.01 0.02 0.01
Ol Ol Ol Cpx Ol Cpx Ol Cpx Ol
γ&=&5&s-1 1569$K Std 1545$K Std 1533$K Std 1520$K Std 1520$K Std 1510$K Std 1510$K Std 1502$K Std 1502$K Std
SiO2 42.26 0.29 41.73 0.36 42.32 0.34 56.22 1.40 42.18 0.17 56.63 0.63 41.23 0.65 56.78 0.60 41.81 0.12
TiO2 0.00 0.00 0.04 0.05 0.04 0.03 0.07 0.00 0.02 0.01 0.12 0.04 0.00 0.00 0.13 0.05 0.01 0.00
Al2O3 0.03 0.02 0.04 0.03 0.03 0.03 0.46 0.06 0.10 0.09 1.20 0.61 0.02 0.03 1.15 0.65 0.09 0.04
MgO 54.39 0.80 56.16 0.57 54.75 0.96 22.92 0.95 55.24 0.61 21.65 1.52 54.03 1.15 21.94 1.58 54.87 0.52
CaO 0.27 0.05 0.31 0.03 0.32 0.04 19.65 0.03 0.35 0.66 18.75 0.61 0.36 0.06 18.47 0.90 0.35 0.04
Na2O 0.02 0.01 0.02 0.01 0.06 0.04 0.25 0.07 0.05 0.03 0.92 0.53 0.11 0.04 0.80 0.43 0.08 0.03
K2O 0.01 0.01 0.02 0.01 0.03 0.04 0.02 0.01 0.01 0.02 0.06 0.03 0.06 0.01 0.02 0.01 0.02 0.00
γ&=&shear&rate
Table S2 Electron microprobe analyses of the crystalline phases, for experiments M33– M37 (Table 3) in temperature range 1569–1502 K. Std refers to the standard deviations.

Table&S3
Data&derived&by&using&equation&2,&3&and&4.&Please&refer&to&text
gravity
m/s2
lava-flow-thickness -(m)
lava-bulk-density
-(Kg/m3)
dynamic-viscosity Pa-s
slope&(°)& velocity&(m/s) Re velocity&(m/s) Re velocity&(m/s) Re
0.1 0.732 2762 0.611 1153 0.353 133
0.2 1.109 4183 0.973 1836 0.590 223
0.3 1.410 5320 1.227 2315 0.786 296
0.4 1.671 6304 1.459 2751 0.955 360
0.5 1.905 7186 1.677 3164 1.111 419
0.6 2.119 7995 1.873 3532 1.254 473
0.7 2.319 8748 2.048 3862 1.388 524
0.8 2.507 9456 2.214 4177 1.515 572
0.9 2.685 10127 2.377 4484 1.636 617
1.0 2.854 10766 2.534 4780 1.751 661
1.1 3.016 11378 2.682 5058 1.862 703
1.2 3.172 11967 2.821 5320 1.970 743
1.3 3.323 12534 2.955 5573 2.073 782
1.4 3.468 13083 3.087 5823 2.174 820
1.5 3.609 13615 3.217 6069 2.271 857
1.6 3.746 14132 3.344 6307 2.366 893
1.7 3.879 14634 3.465 6535 2.459 928
1.8 4.009 15125 3.581 6754 2.549 962
1.9 4.136 15603 3.695 6969 2.638 995
2.0 4.260 16071 3.808 7182 2.724 1028
2.1 4.381 16528 3.920 7394 2.809 1060
2.2 4.500 16976 4.030 7600 2.893 1091
2.3 4.617 17415 4.136 7801 2.974 1122
2.4 4.731 17846 4.238 7994 3.055 1152
2.5 4.843 18269 4.339 8185 3.133 1182
2.6 4.953 18685 4.440 8374 3.211 1211
2.7 5.062 19094 4.540 8562 3.288 1240
2.8 5.168 19496 4.638 8749 3.363 1269
2.9 5.273 19892 4.734 8930 3.437 1297
3.0 5.376 20282 4.828 9106 3.510 1324
3.1 5.478 20666 4.919 9279 3.582 1351
3.2 5.579 21045 5.011 9451 3.654 1378
3.3 5.678 21419 5.102 9624 3.724 1405
3.4 5.776 21787 5.193 9795 3.793 1431
3.5 5.872 22151 5.281 9961 3.862 1457
3.6 5.967 22511 5.367 10123 3.930 1482
3.7 6.061 22866 5.452 10283 3.997 1508
3.8 6.154 23217 5.537 10444 4.063 1533
3.9 6.246 23563 5.623 10606 4.129 1557
4.0 6.337 23906 5.707 10764 4.194 1582
4.1 6.427 24245 5.788 10917 4.258 1606
4.2 6.516 24581 5.868 11067 4.321 1630
4.3 6.604 24913 5.949 11221 4.384 1654
4.4 6.691 25241 6.031 11375 4.447 1677
4.5 6.777 25566 6.109 11522 4.508 1701
4.6 6.863 25888 6.184 11665 4.570 1724
4.7 6.947 26207 6.265 11817 4.630 1747
4.8 7.031 26523 6.340 11958 4.690 1769
4.9 7.114 26836 6.416 12102 4.750 1792
5.0 7.196 27146 6.492 12244 4.809 1814
10 10.647 40163 9.659 18219 7.312 2758
20 15.613 58897 14.236 26852 10.974 4140
Table S3 Variation of lava flow velocity and relative Reynolds number for lavas flows with thickness of 1 m, 5 and 10 m
as-a-function-of-viscosity-(Pa-s),-topographic-slope-(°),-and-density-(Kg/m3).
3.6
1
2452
13
3.6
5
2452
13
3.6
10
2452
13

Table S4
flow velocity Effusion rate Stephan-Boltzmann constant emissivity Thot Tcrust
σ ε temperature of exposed molten lava Temperature of the crust
m s-1 m3 s-1 W m-2 K-4 K K
0.7 100 5.67E-08 0.85 1623 700
7.2 1000
30000
fcrust viscosity thickness lava density latent heat cryst
Pa s m
Kg m-3 J Kg-1
0.9*EXP(-0.16*flow velocity) 13 12452 370000
5
10
Table S4: FLOWGO parameters used to calculate the heat loss for the flowing mercury lava. More details are reported in Harris and Rowland (2001).
For details about the above parameters please refer to Harris and Rowland [2001]

Figure 1
Figure 1. Back scattered electron images of representative experimental products. a)
Experiment at temperature T=1502 K and shear rate γ=5.0 s-1; b) experiment at same
temperature as (a) with a shear rate γ=0.1 s-1. The two experiments show comparable
crystal contents. Labelled crystal phases are olivine (Ol), clinopyroxene (Cpx) and
glass.
Figure 2
Figure 2. Viscosity data for melts at superliquidus conditions. The continuous line
represents the predictive model given in Eq. (1). Black full triangles are repeated
measurements; green squares represent experiments performed at different shear
rates.

Figure 3
Figure 3. Variation of viscosity as a function of temperature showing the comparison
between data presented in this work and literature data using possible Mercury
compositions. Icp-HCT and E_B refer to basaltic komatiites and Enstatite Basalt,
respectively, as reported in Sehlke and Whittington [2015]

Figure 4
Figure 4. a) Variation of viscosity [log(η)] as a function of crystal content (Φ area %)
at different shear rates (γ); b) variation of viscosity [log(η)] as a function of
temperature for crystallization experiments at different shear rates (γ). Measurement
errors in Figure 4b are comparable or lower than symbol size.

Figure 5
Figure 5. Comparison between crystal content obtained by image analysis (area %)
and mass balance calculations (vol.%). Errors in area % are on the order of 10 %
relative.

Figure 6
Figure 6. Change of the residual glass composition (in wt.% of element
concentrations) upon crystallization of the silicate melts. Triangle, circle and square
indicate experiments performed at shear rate of 0.1, 1.0 and 5.0 s-1, respectively.

Figure 7
Figure 7. a-c-e): Variation in viscosity as a function of time and temperature at
different shear rates; b-d-f): corresponding BSE images and phases after reaching the
saturation threshold (flat part of profiles in the plots on the left) for experiments
performed at ! =5 s-1. Dashed-lined arrows indicate flow direction; Ol and Cpx refer
to olivine and clinopyroxene, respectively.

Figure 8
Figure 8. a) Linear regressions of ln(σ) (shear stress) against ln (γ) (shear rate) for
the studied composition. Linear regressions for each dataset are also shown. Note the
drastic change in slope when passing from the super-liquidus experiment (1600 K) to
the crystal-bearing experiments due to the onset of crystallization; b) flow index
derived from the linear regression of data in (a). Estimated rheological parameters (n
and k) are given in Table 3.

Figure 9
Figure 9. Flow curves for the analog Mercury lavas from this work superimposed on
the pahoehoe to `a`a transition diagram from Sehlke et al. [2014]. Coloured lines from
right to left refer to data from Sehlke et al. [2014] for Hawaiian lavas; dots refer to
data from this study. Lava on Mercury start the transition from pahoehoe to `a`a at a
temperature of ~1533 ± 10 K. The question mark, as reported in Sehlke and
Whittington [2015], emphasizes the approximate location of the end of the transition
threshold zone TTZ.

Figure 10
Figure 10. Relationship between relative viscosity (ηr) and crystal fraction
(Φ; measured by image analysis, see text for details) for the analog melt in this study
(coloured symbols) and literature data. Curves correspond to different models: ER,
Einstein-Roscoe model [Einstein, 1906; Roscoe, 1952]; KD, Krieger-Dougherty
model [Krieger and Dougherty, 1959]; Sato model [Sato, 2005]; Mader model
[Mader et al., 2013]; Vona model [Vona et al., 2011] see also supplementary
information for details).

Figure 11
Figure 11. Variation of lava flow velocity as a function of topographic slope for three
lava flows with thickness of 1 m, 5 m and 10 m (Eq. 2–4).

Figure 12
Figure 12. Variation of heat loss (in K/km) as a function of effusion rates for a lava
flowing in 100, 1000 and 30000 m width channels, with velocities of 0.7 and 7.2 m/s
respectively. Details are provided in the main body of text.

Figure S1
Figure S1
Variation of the apparent
viscosity as a function of crystal
content for NVP-Na, NVP and
EB compositions Studied by
Sehlke and Whittington [2015]
and our new experimental data.