Journal of Volcanology and Geothermal Research 208 (2011) 86–98

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Journal of Volcanology and Geothermal Research

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Insights on tephra settling velocity from morphological observations

Fabrizio Alfano a,⁎, Costanza Bonadonna a, Pierre Delmelle b, Licia Costantini a

a Section des Sciences de la Terre et de l'environnement, Université de Genève, Rue des Maraîchers 13, 1205 Genève, Switzerlandb Earth & Life Institute, SST/ELI/ELIE - Environmental Sciences, Université catholique de Louvain, Croix du Sud 2 bte L7.05.10, B-1348 Louvain-la-Neuve, Belgium

⁎ Corresponding author.E-mail address: Fabrizio.Alfano@unige.ch (F. Alfano)

0377-0273/$ – see front matter © 2011 Elsevier B.V. Alldoi:10.1016/j.jvolgeores.2011.09.013

a b s t r a c t

a r t i c l e i n f o

Article history:Received 25 March 2011Accepted 27 September 2011Available online 5 October 2011

In this study we present a systematic and detailed morphological characterization of tephra particles fromdifferent eruptions (Fontana Lapilli, Masaya, Nicaragua; Keanakāko'i Formation, Kilauea, USA; recent domeexplosions of Soufriere Hills volcano, Montserrat) and the calculation of their Terminal Fall Velocity (TFV)as obtained based on different drag prediction models (i.e., Wilson and Huang, 1979; Haider and Levenspiel,1989; Ganser, 1993; Dellino et al., 2005). In particular, particle sphericity, and, therefore, particle surface area,is essential for the calculation of TFV of irregular-shape particles but is of complex determination. Various at-tempts have been proposed. According to our results, 2D morphological characterization of volcanic particlesis a fast and simple application for a wide range of particle size and provides consistent sphericity and set-tling-velocity values. 3D scanning also provides a promising tool for lapilli-sized tephra (N2 cm). In contrast,gas-adsorption-derived surface area is not suitable for the calculation of TFV of volcanic particles mostly be-cause it mainly describes the surface contribution of nanometric pores that are not expected to affect signif-icantly TFV and because bulk-sample analysis is representative of neither individual particles nor of thewhole particle population. Settling velocities calculated using values of surface area derived from gas adsorp-tion analyses are up to two orders of magnitude lower than the values obtained through 2D analysis. In ad-dition, our results also show how the influence of particle shape on TFV increases with particle size. Inparticular, calculated TFV converges at small particle sizes (≥3 ϕ) regardless of the model applied, suggestingthat the spherical assumption is appropriate for this size fraction (discrepancies with the spherical model arewithin 10%). Discrepancies with the spherical model increase with particle size up to about 50% and dependon the choice of both the TFV model and the morphological parameterization used.In particular, the drag prediction model of Ganser (1993) is sensitive to the effect of particle morphology onTFV and is well suited for all sizes and Reynolds numbers of typical tephra particles. Finally, our results showhow individual size categories (whole- and half-ϕ) are not associated with individual TFV values but with arange of values, which increases with class size. Nonetheless, the half-ϕ system is associated with a smallerstandard deviation than the whole-ϕ system, and is therefore more appropriate for the modeling of tephradispersal. In any case, for dispersal modeling purposes, it is more appropriate to indicate a range of settlingvelocities for each size class rather than giving an average value.

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© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Tephra is a collective term used to describe all particles ejectedduring explosive eruptions and transported in the atmosphere irre-spective of size, shape and composition (Thorarinsson, 1944). Blocksand bombs (i.e., diameter N64 mm) and lapilli-sized particles (i.e., di-ameters comprised between 64 and 2 mm) typically sediment closeto the vent, whereas ash particles (i.e. diameters b2 mm) can staysuspended for long times and can travel large distances (Durant etal., 2010) spreading over large areas up to several hundreds ofsquared kilometers (e.g., Mt St Helens, 1980; Holasek and Self,1995; Chaitén, 2008; Alfano et al., 2011).

Settling of volcanic particles depends on their Terminal Fall Velocity(TFV), which represents the dynamical balance between the gravityforce, that accelerates the object downward, and the aerodynamicdrag forces, that are opposed to the falling motion (e.g., Kunii andLevenspiel, 1969; Wilson and Huang, 1979; Haider and Levenspiel,1989; Ganser, 1993; Dellino et al., 2005). The precise determination ofthe aerodynamic drag forces requires a detailed parameterization ofparticle morphology (e.g., Ganser, 1993; Riley et al., 2003). A widelyused shape parameter is particle sphericity (Ψ), defined as the ratio be-tween the surface area of a sphere with the same volume as the particle(equivalent sphere) and the surface area of the particle. Sphericity canbe mainly derived based on approximations to simple equivalent geo-metric shapes (e.g., Aschenbrenner, 1956), from 2D image analysis ofthe projected surface of the particles (Riley et al., 2003) or 3D scan anal-ysis, and from directmeasurements of surface area through gas adsorp-tion (Dartevelle et al., 2002; Riley et al., 2003).

87F. Alfano et al. / Journal of Volcanology and Geothermal Research 208 (2011) 86–98

The aim of this study is to compare and assess the use of variousexisting models for the calculation of TFV (i.e., Wilson and Huang,1979; Haider and Levenspiel, 1989; Ganser, 1993; Dellino et al.,2005) and various approaches of morphological characterization(i.e., 2D and 3D). Tephra particles from three different eruptions areconsidered (Fontana Lapilli, Masaya, Nicaragua; Keanakāko'i Forma-tion, Kilauea, USA; recent dome explosions of Soufriere Hills volcano,Montserrat).

2. The shape of tephra particles and its influence on TerminalFall Velocity

An object which falls through the atmosphere accelerates until itreaches a maximum constant velocity, TFV. Particles with low TFVvalues can stay suspended in the atmosphere for longer times, andthus can travel greater distances, than particles with high TFV. TFVis defined by the so-called Impact Law (Wilson and Huang, 1979;Dellino et al., 2005):

TFV ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4gd ρs−ρð Þ

3CDρ

sð1Þ

where g is the gravitational acceleration, d is the diameter of the ob-ject, ρs and ρ are the density of the object and the density of the sur-rounding fluid, and CD is the drag coefficient (see Appendix 2 for allsymbols, abbreviations and dimensions). The drag coefficient is a di-mensionless number, which depends on particle shape and on theflow regime of the fluid around the particle. The flow regime is relat-ed to the particle Reynolds number (Re), which is the ratio betweeninertial resistance of the particle and viscous resistance of the sur-rounding fluid. High particle Reynolds numbers (N500) are associatedwith turbulent settling regime, whereas low particle Reynolds num-bers (b0.4) are associated with laminar settling regime (Kunii andLevenspiel, 1969). For intermediate values of particle Reynolds num-ber, the flow is transitional and changes progressively from laminar toturbulent (intermediate settling regime).

Irregularly-shaped particles are characterized by higher aerody-namic drag forces than regularly-shaped particles of the samesize and density. The assumption of spherical shape for irregular par-ticles only holds in the case of a laminar sedimentation regime(Bonadonna and Costa, 2010), but it is largely used in dispersal model-ing because it provides analytical solutions for TFV, whichare computationally more practical (e.g., Kunii and Levenspiel, 1969;Arastoopour et al., 1982). Attempts to provide analytical solutions ofsettling velocity for irregular particles have relied on simple parame-terizations of morphology, such as the ratio of the three orthogonalaxes (F=I+S/2 L, with L≥ I≥S; Wilson and Huang, 1979) and sphe-ricity (Ganser, 1993; Dellino et al., 2005).

3. Tephra samples

Tephra particles produced by three different eruptions were usedin this study in order to investigate a wide range of clast typology (i.e.,lithics, juvenile) and texture (i.e., various degrees of vesicularity). Allsamples were dry sieved in order to separate particles in grain sizeclasses according to a logarithmic distribution of particle diameters(ϕ=− log2 d). The analyzed samples are: i) Fontana Lapilli deposit(Masaya, Nicaragua; FL1 and FL2); ii) Mystery Unit of the Keanakāko'iFormation (Kilauea, USA; KMU); iii) 18th July 2005 explosion of Sou-friere Hills volcano andesitic dome (Monteserrat, West Indies; SHV).

The Fontana Lapilli deposit was erupted in the late Pleistocene(~60 ka) from a vent or multiple vents located near Masaya volcano,Nicaragua, and it represents the product of one of the few basaltic Pli-nian eruptions studied so far (Williams, 1983; Bice, 1985; Wehrmannet al., 2006; Costantini et al., 2009), and it is characterized by a

predominant juvenile component (N96 wt.%; SiO2 ~53 wt.%). Bubblenumber density value is ~107 cm−3 for the whole eruption (Costantiniet al., 2010). In this study, we analyzed two samples from two differenteruption phases: a moderate explosive phase at the beginning of theeruption (sample FL1), and themain eruption phase, which is of Plinianintensity (sample FL2). FL1 shows a bimodal grain size distribution andpoor sorting (MdΦ=−1.75; σΦ=2.20), while FL2 shows a unimodalgrain size distribution and moderate sorting (MdΦ=−2.49;σΦ=1.60) (parameters from Inman, 1952).

The Mystery Unit deposit is one of the youngest eruption units ofthe Keanakāko'i Ash Formation (McPhie et al., 1990) and was eruptedin the late 18th century toward the end of 300 years of sporadic ex-plosive activity of Kilauea (Swanson, personal communication). TheKMU sample corresponds to one of the most widespread layers ofthe Mystery Unit deposit (probably associated with phreatic activity),which is characterized by a dominance of lithic clasts (mostly lavafragments) and a basaltic juvenile content b10 wt.%. Both juvenileand lithic clasts are poorly vesiculated and the grain size distributionis unimodal and moderately sorted (MdΦ=−3.83; σΦ=1.55).

The current activity of Soufriere Hills volcano started in 1995 aftera quiescent period of about 400 years, and is mainly characterized bygrowth and collapse of an andesitic dome, explosive events (mainlydome and Vulcanian explosions) and ash venting (Kokelaar, 2002;Sparks and Young, 2002). The sample analyzed is composed of lithicash produced by the dome explosion of 18th July 2005 (SHV:MdΦ=5.24 and σΦ=2.74), with grain size N−1 Φ (i.e., db4 mm).

4. Morphological characterization of tephra particles

4.1. Density measurements

Bulk density was measured using a helium pycnometer (Micro-metrics Acoupyc 1330) at the Powder Technology Laboratory of theEPFL (Lausanne). Measurements have been carried out on the fineash fraction (ϕN4) of the samples FL1, KMU and SHV, resulting indensity values of 2953±15 kg/m3, 3280±21 kg/m3 and 2870±3 kg/m3 respectively. Pumice density was measured through hydro-static weight on particles size in the range −5≤ϕ≤−3 for the sam-ples FL1 and KMU resulting in an average density value of 990±380 kg/m3 and 2640±320 kg/m3 respectively.

The density distribution in relation with the grain size has beencalculated following Bonadonna and Phillips (2003). Juvenile densityhas been assigned to particles with ϕ≤−1, assuming a negligiblevariation of density in this range of dimension. A linear increase ofthe density with decreasing particle size (up to the value of bulk den-sity) was assumed for particles in the size range 4≥ϕ≥−1. Bulk den-sity has been assigned to particles with ϕ≥4 (Bonadonna andPhillips, 2003). For the sample SHV (dome-collapse tephra) we as-sumed a negligible vesicularity and, therefore, a constant bulk densityfor all particles.

4.2. 2D image analysis

2D images were taken using different devices in relation to the di-mension of the particles. For grain size classes ϕN3 (db125 mm) im-ages were taken using the integrated optical system of the particleanalyzer CILAS 1180 (http://www.cilas.com/), which allows for animage resolution of 1428 pix/mm. For grain size classes 3≥ϕ≥−1,images were taken with an optical microscope which allows forimage resolution of 112.9 pix/mm. For grain size classes ϕN−1 im-ages were taken using a digital scanner which allows for a resolutionof 63.0 pix/mm. Binary images were generated by automatic thresh-olding and manual corrected to reduce errors, then analyzed usingthe image analysis toolbox Jmicrovision 1.2.7 (http://www.jmicrovision.com/) developed at the University of Geneva. From theanalysis of the images several parameters were determined for each

88 F. Alfano et al. / Journal of Volcanology and Geothermal Research 208 (2011) 86–98

particle: projected area (AP); projected perimeter (PP); 90 feret diam-eters (Riley et al., 2003). Image analysis of tephra particle images wascarried out on individual particles of the samples FL1, SHV and KMU.

4.3. Gas adsorption

Gas adsorption is widely used in material science and catalysis andit has only recently been applied to volcanic particles (Dartevelle etal., 2002; Riley et al., 2003; Delmelle et al., 2005; Witham et al.,2005; Mills et al., 2007). The technique consists of measuring theamount of gas that can be adsorbed by a sample at different pressureconditions, which is related to the total exposed surface, expressed interms of specific surface area (as, m2/g). For this study, nitrogen gasadsorption analyses at 77 K were performed using an Autosorb-1V1.25 instrument (Quantachrome Inc.) at the University of Geneva.Prior to each measurement, tephra samples were outgassed in situovernight at 300 °C at a residual pressure b0.1 Pa.

The Brunauer, Emmett and Teller (BET) model (BET; Brunauer etal., 1938) is widely used to derive as from the gas adsorption data.The model is valid in the range 0.05≤P/P0≤0.20 (where P and P0are the equilibrium pressure and the saturation pressure of the gas,respectively). Using the as determinations on a known number of par-ticles (i), the average surface area, Ā, of the particles can be derived ifthe total mass, m, of the particles analyzed is known (Ā=as m/i). Ifthe analyses refer to individual particles (i=1), the absolute surfacearea (A=as m) of that particle is derived.

Pore size distribution analysis was also performed through com-plete cycles point-by-point measurements of volume of gas adsorbed(VGA) at P/P0 values in the range 0NP/P0N1.

The presence of micropores was investigated using the t-plotmethod (Deboer et al., 1966). The analysis is conducted by plottingthe volume of gas adsorbed at each step of P/P0 versus the statisticalthickness (t) of the adsorbed layer, assuming that this layer behavesas a normal liquid N2 layer, with a density value set by temperatureand a hexagonal dense packing. The resulting plot has a shapewhich depends on the pore size distribution of the sample. A solidwhich does not contain micropores produces a straight line in a t-plot diagram (Deboer et al., 1966). The total volume of mesopores(Vmeso) can be estimated from the total amount of N2 adsorbed atP/P0=0.95, when all the pores are assumed to be filled with con-densed N2. Under these conditions, the volume of N2 adsorbed relatesto the volume of condensed N2, and knowing the molar volume of N2

at ambient pressure (34.7 cm3/mol), Vmeso can be calculated(Rouquerol et al., 1999). Combining Vmeso and as and assuming acylindrical geometry of pores, the average diameter for the mesopores(dav) can be calculated (dav=2 Vmeso/as) (Rouquerol et al., 1999). Thepore size distribution of themesopores in the tephra sampleswas calcu-lated using the Density Functional Theory (DFT; Rouquerol et al., 1999).This method consists in the determination of a mass density profile(ρ(r), number of pores with radius r per unit mass) for a given set ofpores, and the calculation of the associated isotherm plot. The poresize distribution is determined based on the best fit between computedand measured adsorption isotherms (Rouquerol et al., 1999).

BET surface analyses have been carried out on bulk grain size frac-tions of samples FL1, FL2, KMU (ϕ=−1, 0, 1, 2, 3, 4, N4) and SHV(ϕ=2, 3, 4, N4), and on individual or known numbers of lithic and ju-venile clasts of the KMU sample (ϕ=−1, −2, −3, −4). Pore sizedistribution analyses have been carried out on the bulk grain sizefraction of the samples FL2 (ϕ=−1, N3) and SHV (ϕ=2, 3, 4, N4)and on individual lithic and juvenile clasts of sample KMU (ϕ=−1).

4.4. 3D scan

One sample (KMU−4 Φ lithic) was also analyzed with a 3D scan-ning system at the HEPIA (Haute École du Paysage d'Ingénierie etd'Architecture de Genêve), which provides a 3D digitalization of a

solid object based on a simple triangulation system, and is able togive a measurement of its main morphological parameters, such asvolume (V3D) and surface area (A3D). According to this method, ob-jects with dN2 cm are digitized with an ATOS II structured light scan-ning system. The digital model is obtained by recording the fringepattern projected on the object surface with a dedicated camera(Brajlih et al., 2007; Sugar et al., 2008; Barbero and Ureta, 2011).Two images are registered by the device in order to cover the wholesurface of the object. The images are elaborated by a software (gom-atos) which determines the 3D coordinates of each pixel composingthe image, producing a polygon mesh of the surface. The polygonmesh is again elaborated using a software (Imageware package)which allows the generation of a 3D digital model (contact surfacecomputation) and scale external dimension and volume. Unfortu-nately, the 3D scan measurement could not be carried out on particlesb2 cm.

4.5. Particle morphological parameters

The calculation of particle TFV is based on the determination ofseveral parameters and shape factors that characterize particle mor-phology. In detail, the diameter of the equivalent sphere (diameterof the sphere with the same volume of the particle), the shape factor(F) of Wilson and Huang (1979) and particle sphericity (Ψ) based onvarious models, were calculated from the morphological analyses de-scribed above (i.e., 2D image analysis, gad adsorption, 3D scan).

The diameter of the equivalent sphere (dV) was calculated basedon the ratio between AP and PP as described by Riley et al. (2003).The shape factor F depends only on the length of the three orthogonalaxes of the particle. This factor has been calculated based on the feretdiameters obtained through image analysis, assuming the maximumaxis equal to the largest feret diameter, the minimum axis equal tothe smallest feret diameter and the intermediate axis equal to the av-erage of the 90 measured feret diameters (Riley et al., 2003). Spheric-ity has been calculated applying different methods. A first value ofsphericity (ΨR) is calculated based on the ratio between AP and PP2

as described by Riley et al. (2003). A second method consists in calcu-lating the sphericity of an equivalent tetrakaidecahedron (i.e., 14-facesolid) which is considered as the geometrical solid figure that best ap-proximates a natural irregular particle (Aschenbrenner, 1956). Parti-cle sphericity (ΨA) is calculated assuming the shape equivalent to atetrakaidecahedron with the same orthogonal axes of the particle.The orthogonal axes of the particle were determined as describedabove for the calculation of the shape factor F. Finally, the shape fac-tors Ψ⁎R and Ψ⁎A were calculated by dividing ΨR and ΨA for particlecircularity (ratio between Pp and the perimeter of the circle witharea equal to Ap), as described by Dellino et al. (2005). Other valuesof sphericity have been calculated based on the direct surface areameasurements carried out on single particles using the gas adsorptiontechnique (ΨGA) and the 3D scan analysis (Ψ3D).

5. Results

5.1. Morphological characterization

The three samples considered (FL1, KMU, SHV) are characterizedby a similar range of values and trends of morphological parametersas a function of grain size (Fig. 1). Samples show average values ofparticle sphericity and of the shape factor F for each size class rangingbetween 0.6 and 1.0, and a standard deviation (δ) less than 0.14(Table 1). The average values of the morphological parameters donot show any clear correlation with grain size, and there is no signif-icant variability of their standard deviation within each individualgrain-size class. For all samples, ΨA (sphericity calculated accordingto Aschenbrenner (1956)) is characterized by the highest values(N0.9) and the lowest standard deviation (0.01≤δ≤0.03) with

-4 -3 -2 -1 0 1 2 3 4 >4

0.8

0.9

1.0

0.7

0.6

FL1

>4 43210-1

0.8

0.9

1.0

0.7

SHV

Grain Size (φ)

-3 -2 -1 0 1 2 >2 -4

0.8

0.9

1.0

0.7

0.6

KMU

Ave

rage

Mor

phol

ogic

al P

aram

eter

s

Ψ*R

Ψ*A

ΨA

ΨR

FW&H

MorphologicalParameters:

a

b

c

Fig. 1. Semi-log plot of the average values of the shape factor F of Wilson and Huang(1979), sphericity (ΨR) of Riley et al. (2003), sphericity (ΨA) of Aschenbrenner(1956) and sphericity divided by particle circularity (Ψ⁎

R and Ψ⁎A) as described by Del-

lino et al. (2005), measured for each grain size class of the samples FL1 (a), KMU (b)and SHV (c).

Table 1Average values and standard deviation of the morphological parameters for each grainsize class (ϕ) and for the whole sample of FL1, KMU and SHV.

ϕ Morphologic parameters

F ΨR ΨA Ψ⁎R Ψ⁎

A

FL1N4 0.77±0.09 0.83±0.10 0.93±0.03 0.77±0.14 0.84±0.074 0.79±0.08 0.76±0.10 0.93±0.02 0.66±0.12 0.81±0.073 0.77±0.08 0.88±0.09 0.93±0.03 0.82±0.12 0.87±0.072 0.77±0.08 0.85±0.09 0.93±0.03 0.78±0.12 0.85±0.061 0.80±0.08 0.77±0.10 0.94±0.02 0.69±0.12 0.82±0.060 0.79±0.08 0.74±0.10 0.93±0.02 0.64±0.12 0.80±0.06−1 0.78±0.08 0.69±0.10 0.93±0.02 0.58±0.12 0.77±0.07−2 0.79±0.08 0.66±0.09 0.93±0.03 0.55±0.11 0.76±0.07−3 0.75±0.10 0.69±0.08 0.92±0.03 0.57±0.10 0.77±0.05−4 0.67±0.07 0.72±0.06 0.90±0.03 0.61±0.08 0.76±0.05Whole sample 0.78±0.08 0.76±0.11 0.93±0.02 0.67±0.14 0.81±0.07

KMUN2 0.77±0.08 0.93±0.06 0.93±0.02 0.90±0.09 0.90±0.052 0.77±0.08 0.87±0.08 0.93±0.02 0.81±0.11 0.87±0.061 0.81±0.07 0.82±0.09 0.94±0.02 0.75±0.12 0.85±0.050 0.81±0.07 0.81±0.09 0.94±0.02 0.73±0.12 0.84±0.06−1 0.81±0.07 0.82±0.09 0.94±0.01 0.74±0.12 0.85±0.06−2 0.82±0.07 0.72±0.13 0.94±0.01 0.61±0.16 0.79±0.08−3 0.82±0.06 0.70±0.13 0.94±0.01 0.59±0.16 0.78±0.08−4 0.72±0.10 0.86±0.05 0.91±0.03 0.80±0.07 0.85±0.04Whole sample 0.80±0.07 0.81±0.10 0.94±0.02 0.74±0.13 0.84±0.06

SHVN4 0.75±0.09 0.86±0.11 0.92±0.03 0.81±0.14 0.85±0.084 0.79±0.08 0.82±0.09 0.93±0.03 0.75±0.12 0.84±0.073 0.77±0.08 0.88±0.08 0.93±0.03 0.83±0.12 0.87±0.062 0.78±0.08 0.85±0.08 0.93±0.03 0.78±0.11 0.86±0.061 0.80±0.07 0.85±0.07 0.94±0.08 0.79±0.10 0.86±0.050 0.81±0.07 0.84±0.06 0.94±0.08 0.77±0.08 0.86±0.04−1 0.78±0.08 0.80±0.07 0.93±0.08 0.72±0.09 0.83±0.05Whole sample 0.78±0.08 0.85±0.09 0.93±0.03 0.79±0.12 0.86±0.06

F ¼ IþS2L ; where L, I, S are the three orthogonal axes of the particle (Wilson and Huang,

1979).ΨR ¼ 4π Ap

P2p; where Ap and Pp are the projected area and projected perimeter of the

particle (Riley et al., 2003).

ΨA ¼ 12:8ffiffiffiffiffiffip2q3

p1þp 1þqð Þþ6

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þp2 1þq2ð Þ

p ; p ¼ SI ; q ¼ I

L=�

; (Aschenbrenner, 1956).

Ψ⁎R, Ψ⁎A: ΨR and ΨA divided by particle circularity according to Dellino et al. (2005).

0.1

1

10

100

-1 0 1 4> 4Grain size (φ)

a s (m

2 /g)

FL1

FL2

SHV

KMU

32

Fig. 2. Log–log plot showing the BET as distributions on bulk individual ϕ fractions. An-alyses carried out applying an outgassing protocol at 300 °C under vacuum, for samplesFL1, FL2, KMU and SHV. All measurements are affected by a systematic error of 4%.

89F. Alfano et al. / Journal of Volcanology and Geothermal Research 208 (2011) 86–98

respect to the average values. In fact, F and ΨR (sphericity calculatedaccording to Riley et al. (2003)) are more sensitive to shape irregular-ity thanΨA, showing values ranging from 0.6 to 1.0 and a higher stan-dard deviation (0.05≤δ≤0.13). The morphological parameters Ψ⁎Rand Ψ⁎A (i.e., sphericity divided by particle circularity according toDellino et al. (2005)) follow the distribution of ΨR and ΨA, butshow lower values due to the effect of the correction for the particlecircularity.

Gas-adsorption-derived specific surface area, as, increases withdecreasing size for all bulk size fractions analyzed (Fig. 2), with FL1and FL2 tephra displaying higher as values (3.0–21 m2/g) than theKMU and SHV samples (b3.3 m2/g). In addition, juvenile clasts arecharacterized by higher as (2.2–7.9 m2/g, Fig. 3a) and A (0.11–

Table 2Summary of absolute surface area (A) and sphericity (Ψ) for individual lithic and juve-nile particles from KMU sample determined through gas adsorption, 3D scan analysesand geometrical assumption (i.e., sphere, tetrakaidecahedron).

Lithic Juvenile

−4 Φ −3 Φ −4 Φ −3 Φ

Absolute surface (A, m2)AGA 6.0 0.7 15.0 5.1AES (×10−3) 1.2 0.5 0.9 0.4AA (×10−3) 1.6 6.2 1.1 4.8A3D (×10−3) 1.4 – – –

Sphericity (Ψ)Ψ3D 0.9 – – –

ΨA 0.7 0.8 0.8 0.8ΨGA (×10−4) 0.8 0.9 0.9 0.8

GA: gas adsorption.ES: equivalent sphere.A: equivalent tetrakaidecahedron (Aschenbrenner, 1956).3D: scan 3D.

90 F. Alfano et al. / Journal of Volcanology and Geothermal Research 208 (2011) 86–98

15.00 m2, Fig. 3b) than lithic clasts (as=0.5–0.8 m2/g, Fig. 3a;A=0.03–3.36 m2, Fig. 3b). Absolute surface area values derivedfrom as measurements (AGA) carried out on single particles (0.7–15.0 m2) were compared with A calculated based on equivalent sim-ple shapes (i.e., equivalent sphere, AES and equivalent tetrakaidecahe-dron, AT). The resulting AGA values are up to four orders of magnitudelarger than the values based on the parameterization of simple shapes(Table 2). Fig. 4 shows the results of a 3D scan analysis carried out ona lithic particle of KMU −4 Φ: values of surface area (A3D) and vol-ume (V3D) increase with the resolution of the image (number ofpoints of the polygon mesh), up to a plateau which represents the an-alytical limit of the technique. A3D values (1.3–1.4×10−3 m2) areclose to the values calculated for the equivalent sphere and tetrakai-decahedron (Table 2), resulting in a sphericity value Ψ3D equal to0.9. On the other hand, AGA is three orders of magnitude larger thanA3D at its maximum resolution for the lithic particle KMU −4 Φ.

5.2. Pore size distribution

A pore size distribution analysis was carried out in order to betterunderstand and constrain the origin of particle surface area. Resultsare summarized in Table 3. FL1 −1 ϕ sample shows dav and Vmeso

values of 4.3 nm and 1.9×10−3 cm3/g, respectively, associated witha total volume of micropores of 4.4×10−4 cm3/g. A comparativelyhigher dav (7.2 nm), lower Vmeso (2.9×10−2 cm3/g) values and lackof micropores were obtained for FL1 N3 Φ. The dav of the SHV tephraranged from 7.7 to 9.9 nm, and the Vmeso ranged from 0.3 to0.6×10−2 cm3/g. The t-plot analysis did not reveal the presence of

a

b

Surf

ace

Are

a (m

2 )

Grain Size (φ)-4 -3 -2 -1

0.1

1.0

10.0

100.0

LithicJuvenile

Single particles

LithicJuvenile

Known number of particles

a s (m

/g)

Grain Size (φ)

2

4

6

8

-1-2-3-4

Juvenile

Lithic

Fig. 3. (a) Semi-log plot showing the comparison between the BET as values measuredon sample from KMU of lithic and juvenile origin. (b) Log–log plot of absolute surfacearea values for individual particles (full symbols) and of average surface area (opensymbols) values calculated for a known number of particles. The values are referredto juvenile and lithic clasts of the sample KMU. All measurements are affected by a sys-tematic error of 4%.

micropores in the SHV tephra. Finally, the juvenile clast from KMUshowed dav and Vmeso values of 5.1 nm and 3.9×10−3 cm3/g respec-tively, associated with a total volumes of micropores of7.6×10−4 cm3/g. A comparatively higher dav (7.8 nm), lower Vmeso

(0.9×10−3 cm3/g) and a total volumes of micropores of1.1×10−4 cm3/g were obtained for the lithic clast from KMU.

5.3. Terminal fall velocity characterization

Particle TFV was calculated based on a range of morphological pa-rameters and using the models of Wilson and Huang (1979) (TFVWH),Ganser (1993) (TFVG (ΨR) and TFVG (ΨA)), and Dellino et al. (2005),(TFVD (Ψ⁎R) and TFVD (Ψ⁎A)), at sea level. Resulting TFV values rangefrom a minimum of 0.05 m/s, for the small particles (N4 ϕ) of thesamples SHV, up to a maximum of about 35 m/s, for the coarse parti-cles (−4 ϕ) of the KMU sample. Average values for each grain sizeclass and the associated standard deviation are summarized inTable 4. TFVs increase with grain size classes, showing also an in-crease of the standard deviation. The distribution of the average TFVvalues for each ϕ class compared with the corresponding velocity cal-culated assuming a spherical shape (Haider and Levenspiel, 1989),shows a different behavior for the different models (Fig. 5). Forsmall particles (ϕ≥3), TFVWH, TFVG (ΨR) and TFVG (ΨA) values are

Fig. 4. Semi-log plot of surface (m2) and volume (cm3) obtained through 3D scan of thetephra particle KMU−4Φ lithic versus the resolution of the image (number of points).All measurements are affected by a systematic error of 4%.

Table 3Results of the pore size distribution analysis carried out using the gas adsorption technique on bulk sample of particles of different grain sizes and typologies.

FL1 SHV KMU −1 Φ

−1 Φ N3 Φ 2 Φ 3 Φ 4 Φ N4 Φ Juvenile Lithic

as (m2/g) 1.7 15.8 1.4 1.7 1.8 2.4 3.0 0.4Vmeso (cm3/g) 1.9×10−3 2.9×10−2 3.2×10−3 3.2×10−3 4.2×10−3 5.9×10−3 3.9×10−3 0.9×10−3

Vmicro (cm3/g) 4.4×10−4 – – – – – 7.6×10−4 1.1×10−4

dav (nm) 4.3 7.2 9.4 7.7 9.1 9.9 5.1 7.8

as: BET specific surface area (m2/g).Vmeso: total volume of the mesopores (cm3/g).Vmicro: total volume of the micropores (cm3/g).dav: average pore diameter calculated assuming a cylindrical pore geometry (nm).

91F. Alfano et al. / Journal of Volcanology and Geothermal Research 208 (2011) 86–98

close to the TFV calculated for the equivalent sphere, whereas TFVD

(Ψ⁎R) and TFVD (Ψ⁎A) values are higher, reflecting the limitation of ap-plicability of the empirical model of Dellino et al. (2005) that was ex-perimentally validated down to Re of about 100. For larger grain sizeclasses (ϕb2) all the considered models show the same trend, withvalues of TFV smaller than TFV calculated for equivalent spheres.TFV values calculated for individual particles of the sample KMUusingΨGA are up to two orders of magnitude lower than TFV calculat-ed based on image analysis and 3D scan derived sphericities (Fig. 5b).On the other hand, TFV of the KMU lithic particle based onΨ3D falls inthe range of values of TFV calculated based on image analysis derivedsphericity (Fig. 5b).

Table 4Average values and standard deviation of the calculated TFV for each grain size class (ϕ) of

ϕ Terminal Fall Velocity(m/s)

TFVHL TFVWH TFVG (ΨR)

FL1N4 0.10±0.07 0.08±0.06 0.09±0.064 0.53±0.13 0.54±0.16 0.46±0.123 1.17±0.30 1.17±0.33 1.08±0.372 2.09±0.33 1.97±0.30 1.90±0.361 4.09±0.62 3.23±0.44 3.08±0.570 5.84±0.78 3.96±0.54 3.67±0.74−1 8.14±0.78 4.90±0.65 4.11±0.70−2 11.23±1.17 6.94±0.96 5.11±0.88−3 14.63±1.07 9.23±0.82 6.63±1.06−4 20.39±1.78 12.37±1.19 10.40±1.42

KMUN2 1.69±0.20 1.75±0.23 1.82±0.262 2.56±0.44 2.45±0.37 2.51±0.441 5.86±0.90 4.54±0.59 4.68±0.810 8.65±1.09 5.93±0.70 6.02±1.14−1 13.78±1.58 8.64±1.10 8.44±1.35−2 18.35±1.36 11.74±1.28 9.66±1.75−3 25.57±2.17 17.33±2.12 11.78±3.49−4 35.24±3.04 22.79±1.82 22.25±3.54

SHVN4 0.06±0.05 0.05±0.05 0.06±0.054 0.55±0.14 0.57±0.16 0.51±0.133 1.45±0.33 1.48±0.34 1.41±0.372 2.68±0.54 2.51±0.44 2.48±0.511 5.70±0.92 4.32±0.54 4.68±0.840 9.72±1.28 6.40±0.77 6.76±0.93−1 13.99±0.92 8.10±0.75 7.98±0.94

TFVHL=TFV according to the model of Haider and Levenspiel (1989) assuming a sphericalTFVWH=TFV according to the drag prediction model of Wilson and Huang (1979) calculateTFVG=TFV according to the drag prediction model of Ganser (1993) calculated using ΨR aTFVD=TFV according to the model of Dellino et al. (2005) calculated using Ψ⁎

R and Ψ⁎A.

(See also caption of Table 1).

The determination of TFV significantly depends on the morpho-logical parameter and the model used in the calculation (Fig. 6). Inparticular, TFV based on ΨR and Ψ⁎R results in a range of values thatcover a wider area than the values resulting using the other morpho-logical parameter, and are characterized also by higher values of stan-dard deviation (cf., Table 4), reflecting the high sensitivity to theshape of these morphological parameters. The model of Ganser(1993) appears to be more sensitive to the particle morphologythan the other models, as it results in values of TFV reduced up to50% with respect to the TFV of equivalent spheres. The same behavioris shown by the model of Dellino et al. (2005) for grain size classlarger than 0 ϕ.

the samples FL1, KMU and SHV.

TFVG (ΨA) TFVD (Ψ⁎R) TFVD (Ψ⁎

A)

0.10±0.07 0.81±0.19 0.89±0.200.54±0.15 1.28±0.23 1.53±0.181.17±0.34 1.97±0.45 2.12±0.342.11±0.36 2.60±0.38 2.79±0.293.97±0.61 3.35±0.57 3.88±0.455.13±0.67 3.87±0.80 4.64±0.646.29±0.67 4.57±0.87 5.73±0.738.37±0.90 6.23±1.27 8.14±1.17

10.71±0.71 8.68±1.57 11.30±1.1514.39±1.49 14.53±2.16 17.40±1.95

1.79±0.22 2.88±0.28 2.87±0.212.67±0.46 3.30±0.42 3.44±0.345.73±0.77 4.95±0.76 5.50±0.607.67±0.76 6.34±1.14 7.14±0.85

10.65±1.04 9.65±1.60 10.74±1.3813.73±1.12 12.04±2.13 14.40±1.3019.47±1.88 15.80±5.20 20.95±3.7125.97±2.04 31.22±4.71 33.56±2.49

0.06±0.05 0.74±0.19 0.78±0.190.57±0.15 1.49±0.23 1.66±0.181.49±0.35 2.41±0.44 2.53±0.332.75±0.55 3.23±0.47 3.44±0.415.46±0.76 4.96±0.75 5.37±0.628.26±0.84 7.16±0.94 7.86±0.85

10.16±0.66 8.98±0.99 10.03±0.78

shape of the particles.d using F.nd ΨA.

TFV

(m

/s)

20 2515105

20

25

15

10

5

FL1

TFV of sp

heres

1/2 TFV of spheres

30 402010

30

40

20

10

KMU

TFV of sp

heres

1/2 TFV of spheres

12 15963

12

15

9

6

3

SHV

TFV of sp

heres

1/2 TFV of spheres

TFVof equivalent sphere (m/s)

Average TFV of grain size classes (φ)

VWH

VG

(ΨR)

VG

(ΨA)

VD

(Ψ∗R)

VD

(Ψ∗A)

TFV of individual particles

VG

(Ψ3D

)

VG

(ΨGA

) Lithic

VG

(ΨGA

) Juvenile

>4φ

-4φ

>2φ

-4φ

>4φ

-1φ

a

b

c

Fig. 5. Average TFV values of bulk grain size fraction of the samples FL1 (a), KMU (b)and SHV (c), calculated using the model of Wilson and Huang (1979), the model ofGanser (1993) based on ΨR and ΨA, and the model of Dellino et al. (2005) based onΨ⁎

R andΨ⁎A, plotted vs. the terminal velocity of the equivalent sphere (Kunii and Leven-

spiel, 1969). TFVs of individual particle of the sample KMU calculated based on gas ad-sorption derived sphericity (ΨGA) and 3D scan derived sphericity (Ψ3D) are included inthe KMU plot.

TFVof the equivalent sphere (m/s)

TFV

(m

/s)

5 10 15 20 25

5

10

15

20

25

Sphere

sTFV

G (Ψ

R)

TFVWH

TFVG

(ΨA)

TFVD

(ΨA)

TFVD

(ΨR)

Fig. 6. Areas of dispersion of individual particle TFV for the sample FL1, calculated usingthe model of Wilson and Huang (1979), the model of Ganser (1993) based on ΨR andΨA, and the model of Dellino et al. (2005) based onΨ⁎

R andΨ⁎A in relation with the TFV

of the equivalent sphere.

92 F. Alfano et al. / Journal of Volcanology and Geothermal Research 208 (2011) 86–98

Fig. 7a shows the relation between particle TFV, calculated usingthe method of Ganser (1993) and the sphericity of Riley et al.(2003) for the different grain size classes of samples FL1, KMU andSHV. The influence of shape on TFV increases with particle size asthe ratio TFV/ΨR (represented by the linear trends indicated in theplot) increases for the coarsest grain size classes. In fact, fine particles(ϕ≥3) show that for a sphericity varying in the range 0.4–1.0, TFV re-mains almost constant. For larger particles (ϕb3) the variation of TFVincreases progressively with the size for a same range of variation ofsphericity. Particle TFV becomes progressively smaller than TFV ofthe equivalent sphere with increasing particle size. In fact, the differ-ence between particle TFV and the TFV of the equivalent sphere (ΔTFV %; Fig. 7b and Appendix 1) is b10% for small particles (ϕ≥3)and reaches 50% for large particles (ϕ≤−1). The two breaks-in-slope A and B in Fig. 7b A range correspond to Reynolds number 7–30 and 600–2300, corresponding roughly to the transition of settlingregime laminar to intermediate (0.4) and intermediate to turbulent(500) (Kunii and Levenspiel, 1969; Bonadonna et al., 1998).

Individual size classes (e.g., whole-ϕ and half-ϕ classes) are asso-ciated with a range of particle sizes and, therefore, also with a rangeof TFV values, which increases with class size. As an example, the am-plitude of the TFV ranges (expressed as 2δ) increases from a mini-mum of 0.1 m/s for the N4 ϕ classes (SHV sample) to a maximum of9.4 m/s for the −4 ϕ class (KMU sample) (cf., Table 4). Values of 2δare smaller for the half-ϕ system, reaching a maximum 2δ of8.2 m/s for the −4.5 ϕ class of the KMU sample (Table 5). In Fig. 8the standard deviation of TFVG (ΨR) for the sample FL1, KMU andSHV is plotted in relation with the grain size classes for both thewhole-ϕ and half-ϕ systems. Parallel linear trends of the two systemshave been plotted, corresponding to an average reduction of 2δ equalto 0.24 m/s for samples FL1, 0.27 m/s for KMU and 0.31 m/s for SHV.Even though 2δ values in each system are larger for coarse-size frac-tions, the reduction of 2δ from the whole-ϕ to the half-ϕ systems ismore relevant for small-size classes (N20% for ϕ≥0) rather than forcoarse-size classes (b20% for ϕb0).

6. Discussion

6.1. Morphological characterization

Several methodologies exist to describe particle morphology, withdistinct advantages and disadvantages. Our analysis confirms the

0%

25%

50%

75%

0.1

0123456- 1- 2- 3- 4- 5- 6 φ

1.0

B

A

10.0 100.0 (mm)

Grain size

Δ T

FV (

%)

FL1 KMU SHV

0.2

5

10

15

0.4 0.6 0.8 1.0>4φ

4φ3φ2φ

1φ0φ

−1φ−2φ

−3φ

−4φ

ΨR

TFV

(m

/s)

a b

Fig. 7. (a) Particle TFV of the sample FL1 plotted vs sphericity (ΨR) showing the influence of the shape for each grain size class fraction. (b) Difference (Δ %) between particle TFV,calculated using the model of Ganser (1993) and the sphericity of Riley et al. (2003), of the samples FL1, KMU and SHV and the TFV of the equivalent sphere plotted vs particle grainsize showing the influence % of the shape on the calculated TFV. Red areas A and B indicate the break-in-slope of the trend of the points.

93F. Alfano et al. / Journal of Volcanology and Geothermal Research 208 (2011) 86–98

finding of previous studies (e.g., Riley et al., 2003) that 2D image anal-ysis is a powerful tool that allows for a large number of data to beobtained over a relatively short time regardless of particle size. Eventhough it has the limitation to asses only the 2D shape, the resultingrange of values of sphericity suggests that this method can capturemost of the essential information of particle morphology as long aswe assume that a generic projected image can be representative ofthe whole irregularity of the particle (Blott and Pye, 2008). In fact,ΨR is characterized by a higher variability for all size classes, andwithin individual classes, than F andΨA (cf., Table 1).ΨA is character-ized by a low variability and average values higher than 0.9 for allgrain size classes. Mele et al. (2011) had shown how particle irregu-larity (quantified by particle circularity) decreases with grain sizefor particles larger than 0.5 mm. Nonetheless, the morphological pa-rameters of the samples analyzed in this work all fall in a narrowrange (about 0.7–0.9) regardless of particle size.

Specific surface area analyses carried out with gas adsorption onbulk size fractions show an inverse correlation of as with grain size(cf., Fig. 2) due to the increase of particle number in the measurementcell and therefore to the increase of exposed surface. In contrast, asderived frommeasurements on individual or known number of parti-cles shows a direct correlation with size (cf., Fig. 3b). This implies thatas measured on bulk samples is not representative of all sizes andcannot be directly related to A of individual particles. An averagevalue of absolute surface area can be determined only if the numberof particles in each bulk sample is known. However, the determina-tion of the number of particles in a sample of fine ash can be cumber-some, as it requires to know the density and the mass of all individualparticles. Another possible method has been suggested by Riley et al.(2003) that propose a correction factor (Fa) for the surface area equalto the ratio between the specific surface area of the bulk sample andthe calculated specific surface area of a particle assuming a sphericalshape. They estimated correction factors in the range between 7 and38. Nonetheless, correction factors based on individual bulk-sampleanalysis cannot be extrapolated to individual particles or to thewhole particle population for the reasons described above and, there-fore, cannot be used to correct particle TFV for the whole size range.Gas-adsorption-derived values of A are several orders of magnitudelarger than surface area values calculated for equivalent shapes or de-termined using the 3D scan analysis. These values produce extremelylowΨGA values, which are outside the range of sphericity determined

in this study (cf., Tables 1 and 2), but also outside of the range ofsphericity for natural silicic particles (0.3–0.9; Blott and Pye, 2008).In fact, as values determined through gas adsorption describe the con-tribution of micro- and mesoporosity and, in general, of all features atthe scale of the dimension of the cross sectional area of the adsorptiveused in the measurement (i.e., 0.13–0.20 nm2 for N2; Gregg and Sing,1982).

As demonstrated by gas adsorption and 3D scan analysis, themeasurement of particle surface area is dependent on the scale of ob-servation: the smaller the scale of observation, the larger the mea-sured surface area. This trend is due to the fact that smallerirregularities can be detected when the observation scale is reducedresulting in larger surface area. Thus, it is not surprising that gas ad-sorption, which accounts for irregularities at themolecular scale, canproduce such high values of particle surface area. PSD results showthat all samples analyzed are mesoporous (4–50 nm). Microporosity(pores b4 nm) is generally absent or represents a small fraction ofthe total porosity. Nonetheless, some samples are more porousthan others, resulting in a larger as. As an example, the juvenile sam-ples FL1 and FL2 show higher as than the lithic-rich samples SHV andKMU. Sample FL1 N3Φ is characterized by a large as (15.8 m2/g) anda large volume of mesopores. The origin of mesoporosity in tephraparticles is not known. The minimum size of gas vesicles in juvenilepyroclasts produced by strong explosive activity varies from a fewmicrons in silicic material to 5–10 μm in basaltic Plinian scorias.Larger bubble size (20–25 μm) is recorded in pyroclasts from mildexplosive basaltic activity (Klug and Cashman, 1994; Klug et al.,2002; Polacci et al., 2003; Gurioli et al., 2005; Adams et al., 2006;Sable et al., 2006; Lautze and Houghton, 2007; Gurioli et al., 2008;Carey et al., 2009; Costantini et al., 2009; Sable et al., 2009). Thus,the gas vesiculation process during magma degassing is unlikely tobe the source of the mesoporosity measured in volcanic tephra. Mi-cron-scale angular voids between microlites in the clast groundmasshave been observed in volcanic particles, but the origin is stillunclear (Sable et al., 2006). These voids may have been formed bycontraction of the bubbles during microlite crystallization. Delmelleet al. (2005) suggested that high as values of fine volcanic ash(b100 μm) were due to the presence of secondary minerals, includ-ing clays and sulfate salts. However, chemical analysis (XRF) and X-Ray Diffraction (XRD) indicated that the FL tephra were relativelyfresh, lacking evidence of alteration mineralogy (Costantini et al.,

Table 5Average values and standard deviation of the calculated TFV for each grain size class (half-ϕ) of the samples FL1, KMU and SHV.

ϕ Terminal Fall Velocity(m/s)

TFVHL TFVWH TFVG (ΨR) TFVG (ΨA) TFVD (Ψ⁎R) TFVD (Ψ⁎

A)

FL1N4 0.10±0.07 0.08±0.06 0.09±0.06 0.10±0.07 0.81±0.19 0.89±0.204 0.36±0.05 0.34±0.07 0.31±0.06 0.36±0.06 1.11±0.18 1.33±0.113.5 0.61±0.07 0.63±0.09 0.53±0.07 0.63±0.08 1.36±0.21 1.62±0.123 0.84±0.10 0.82±0.12 0.71±0.15 0.81±0.12 1.60±0.24 1.79±0.142.5 1.38±0.16 1.39±0.16 1.32±0.21 1.40±0.13 2.20±0.31 2.33±0.182 1.86±0.14 1.79±1.19 1.72±0.26 1.87±0.20 2.48±0.32 2.63±0.201.5 2.40±0.24 2.21±0.24 2.14±0.33 2.44±0.26 2.76±0.40 3.00±0.261 3.39±0.27 2.82±0.30 2.73±0.44 3.32±0.36 3.10±0.47 3.48 ±0.300.5 4.51±0.33 3.48±0.30 3.29±0.53 4.36±0.32 3.51±0.56 4.12±0.330 5.22±0.26 3.59±0.31 3.29±0.55 4.61±0.34 3.46±0.60 4.18±0.35−0.5 6.58±0.50 4.41±0.39 4.11±0.69 5.74±0.41 4.36±0.74 5.19±0.47−1 7.52±0.39 4.44±0.36 3.93±0.63 5.78±0.35 4.25±0.71 5.21±0.41−1.5 8.81±0.49 5.40±0.49 4.32±0.72 6.83±0.47 4.91±0.89 6.28±0.57−2 10.42±0.48 6.35±0.53 4.76±0.76 7.80±0.48 5.66±1.02 7.40±0.64−2.5 12.59±0.58 7.93±0.67 5.70±0.76 9.33±0.56 7.18±1.07 9.38±0.74−3 14.31±0.61 9.11±0.79 6.45±0.86 10.59±0.64 8.39±1.25 11.02±0.84−3.5 16.87±0.90 10.02±0.49 7.90±1.48 11.53±0.63 10.63±2.19 13.23±1.14−4 19.50±0.81 11.84±0.74 9.95±1.12 13.80±1.00 13.82±1.64 16.54±1.11−4.5 22.93±1.22 13.87±0.89 11.65±1.49 16.05±1.41 16.55±2.25 19.83±1.78

KMUN2 1.69±0.20 1.75±0.23 1.82±0.26 1.79±0.22 2.88±0.28 2.87±0.212 2.35±0.22 2.30±0.25 2.36±0.33 2.46±0.27 3.22±0.34 3.32±0.231.5 3.17±0.32 2.87±0.32 2.94±0.46 3.27±0.37 3.57±0.51 3.82±0.341 4.77±0.43 3.93±0.37 4.15±0.59 4.82±0.44 4.50±0.59 4.87±0.390.5 6.44±0.43 4.86±0.40 4.97±0.76 6.21±0.38 5.19±0.73 5.83±0.390 7.98±0.51 5.59±0.47 5.64±0.95 7.25±0.46 5.89±0.89 6.68±0.51−0.5 9.89±0.72 6.56±0.61 6.73±1.14 8.47±0.55 7.16±1.11 7.99±0.70−1 12.45±0.69 7.87±0.68 7.95±1.01 9.86±0.54 8.83±0.98 9.71±0.65−1.5 15.26±0.76 9.49±0.81 8.98±1.47 11.53±0.69 10.57±1.66 11.87±1.04−2 17.70±0.75 11.26±0.95 9.79±1.68 13.25±0.71 12.10±1.99 14.00±1.08−2.5 20.20±0.90 13.10±1.13 9.27±1.88 15.10±0.91 11.86±2.49 15.53±1.20−3 24.01±1.18 15.96±1.34 9.55±2.20 18.13±1.04 12.44±3.40 18.32±2.20−3.5 27.69±1.18 19.19±1.44 14.80±2.51 21.30±1.04 20.38±3.42 24.52±1.94−4 32.67±1.62 22.25±1.94 20.04±3.30 24.97±1.43 27.95±4.12 30.98±2.58−4.5 37.82±1.53 23.33±1.57 24.47±2.14 26.96±2.11 34.50±2.44 36.13±2.08

SHVN4 0.06±0.05 0.05±0.05 0.06±0.05 0.06±0.05 0.74±0.19 0.78±0.194 0.39±0.07 0.39±0.08 0.37±0.07 0.41±0.07 1.32±0.19 1.47±0.133.5 0.63±0.09 0.66±0.10 0.59±0.09 0.66±0.09 1.58±0.19 1.76±0.123 1.03±0.15 1.08±0.19 0.97±0.22 1.06±0.17 1.98±0.35 2.14±0.222.5 1.65±0.17 1.67±0.19 1.62±0.22 1.70±0.18 2.61±0.30 2.71±0.192 2.31±0.26 2.24±0.26 2.20±0.32 2.38±0.28 3.04±0.36 3.20±0.241.5 3.25±0.33 2.92±0.34 2.91±0.46 3.30±0.37 3.52±0.49 3.81±0.321 4.94±0.51 3.96±0.38 4.19±0.62 4.87±0.47 4.54±0.57 4.92±0.400.5 6.50±0.47 4.71±0.39 5.20±0.73 6.08±0.46 5.41±0.65 5.85±0.430 8.40±0.63 5.72±0.49 6.21±0.76 7.44±0.49 6.47±0.67 7.04±0.47−0.5 10.61±0.70 6.86±0.55 7.13±0.85 8.83±0.50 7.64±0.79 8.42±0.55−1 12.80±0.66 8.01±0.68 7.93±0.90 10.07±0.58 8.89±0.91 9.89±0.64−1.5 15.11±0.52 9.09±0.69 8.51±1.17 11.21±0.58 10.04±1.22 11.46±0.70

(Captions same as Table 4).

94 F. Alfano et al. / Journal of Volcanology and Geothermal Research 208 (2011) 86–98

2010). Mesopores can also be associated with surface roughness(Riley et al., 2003; Carter et al., 2009).

6.2. Terminal Fall Velocity of the particles

The settling of a tephra particle is influenced by shape, which af-fects the drag forces acting against the volume forces. Several drag-prediction models have been developed during the last few decadesthat account for the irregularity of particle shape based on variousmorphological parameters. Results using different morphological pa-rameters and different TFV models span over a wide range of values,up to ~50% less than TFV of the equivalent sphere.

TFV based on ΨA and Ψ⁎A does not vary significantly with particleshape and is up to 40% higher than TFV based on ΨR and Ψ⁎R (Fig. 1).As a result, we recommend the use of the sphericity of Riley et al.(2003) (ΨR and Ψ⁎R) as the sphericity of Aschenbrenner (1956) (ΨA

and Ψ⁎A) might systematically overestimate TFV. Values of ΨR andΨ⁎R show the same behavior in relation with the grain size of the sam-ples (cf., Fig. 1). This shape descriptor is based on the assumption thata volcanic particle can be described approximating the shape to a sca-lene ellipsoid; the correction for particle circularity is then used totake into account particle roughness. The main difference in the re-sults is the absolute values of the parameters that are lower for Ψ⁎R.As a result, both parameters are able to catch roughly in the sameway the irregularity of the shape, and it is not possible to understand

φ 1/2 φ

2δ (

TFV

) (m

/s)

Grain Size (φ)

FL14

3

2

1

4-3 -2 -1 0 1-4 >4

KMU

2-3 -2 -1 0-4 >2

9

3

5

7

1

SHV

4-1 0 >4

3

2

1

2 3

1

321

Fig. 8. Plot showing the variation of the standard deviation (2δ; m/s) of TFV of the sam-ples FL1, KMU and SHV, calculated using the model of Ganser (1993) based on thesphericity of Riley et al. (2003), for different grain size categories and for both thewhole-ϕ and half-ϕ system. Parallel linear trends are showed, with correlation coeffi-cients R2 of the whole-ϕ and half-ϕ system equal to 0.96 and 0.97 for FL1, 0.99 and0.96 for KMU and 0.95 and 0.97 for SHV. Empty circles indicate data points have notbeen taken into account in the calculation of the trend lines as they are obtainedfrom limited number of particles and consequently are affected by a high scattering,which is not statistically representative.

95F. Alfano et al. / Journal of Volcanology and Geothermal Research 208 (2011) 86–98

a priori which method gives a more suitable shape description for TFVcalculation.

Our analysis and results show how gas-adsorption-derived surfacearea is not suitable for the determination of particle TFV, at least untilcomplex correction factors are introduced. In fact, gas adsorptiongives very high values of surface area resulting in very low values ofTFV (cf., Fig. 5). This is due to the contribution of morphological fea-tures down to the range of nanometers. The influence of very smallmorphological features on drag forces is not totally understood. Spe-cific studies have shown how small scale surface irregularities influ-ence the drag in the intermediate flow regime by anticipating thetransition to turbulent flow (Loth, 2008), but it is not clear howthey affect particle TFV. More studies are required to characterizethe scale of superficial roughness that significantly influences particlesettling processes.

The models of Ganser (1993) and Dellino et al. (2005), based onΨR and Ψ⁎R, show a higher variability of the results than the model

of Wilson and Huang (1979), as they are very sensitive to the effectof the shape (cf., Fig. 6). Nonetheless, all drag-predictionmodels con-sidered (i.e., Wilson and Huang (1979), Ganser (1993) and Dellino etal. (2005)) are empirical, so they should only be applied within ex-perimental conditions. In particular, the model of Dellino et al.(2005) should only be applied to particles with Re N100 as it isbased on large pumices (ϕb1) with density ranging from 750 to2000 kg/m3. In fact, TFV of small particles (ϕ≥1) determined withthe model of Dellino et al. (2005) are higher than TFV calculatedfor equivalent spheres. In addition, the model of Dellino et al.(2005) is originally based on the measurement of the three orthogo-nal axes of a particle, and, therefore, the morphologic characteriza-tion based on the approximation of the three orthogonal axes usingthe feret diameters (Riley et al., 2003) can be inappropriate. Howev-er, for larger particles (ϕ≥1) values of TFV derived using the modelof Dellino et al. (2005) are consistent with the values calculatedusing the model of Wilson and Huang (1979) and Ganser (1993).The model presented by Wilson and Huang (1979) is validated forparticles with grain size ϕ≥1. TFV calculated for particle size ϕ≤1results in values up to 20% higher than values obtained with themodel of Ganser (1993) based on ΨR. However the model of Ganser(1993) is validated in a wider range of Reynolds number (up to 105).We can conclude that, out of all the models considered in this work,the model of Ganser (1993) based onΨR represents the best methodto calculate TFV of volcanic particles, as also suggested by Chhabra etal. (1999).

The influence of particle morphology on TFV depends on particlesize. In particular, the discrepancy between TFV calculated for irregu-lar particles and TFV calculated for the equivalent sphere increaseswith grain size (Fig. 5). This behavior is confirmed by the small ratioTFV/Ψ of small particles and the increasing trend of Δ TFV % withgrain size (cf., Fig. 7; i.e., sphericity between 0.4 and 1.0). Our resultsshow how the error associated with the assumption of a sphericalshape is low (b10%) for small particles (ϕ≥3), but it increases pro-gressively up to 50% for coarser grain size classes (ϕb3). In addition,the variation of Δ TFV % with grain size is also related to flow–regimetransition. In fact, the range of Reynolds number of the particles forthe size and TFV range in which the trending points in Fig. 7b producea break-in-slope are roughly coincident with the values of Reynoldsnumber in which the flow regime passes from laminar, to intermedi-ate to turbulent.

Finally, our study shows how the range of variability (i.e., 2δ) of TFVG

(ΨR) varies in relation to the definition of the dimensional bins used tocharacterize grain size distributions (e.g., whole-ϕ versus half-ϕ sys-tem).Wehave demonstrated how thehalf-ϕ system can describe betterthe variability of particle TFV of a wide size population typical of explo-sive volcanic eruptions, as associated values of 2δ are reduced of ap-proximately 0.2–0.3 m/s when the half-ϕ system is used as supposedto the whole-ϕ system. Nonetheless, for both systems it is more appro-priate to indicate a range of settling velocities for each size class (e.g.,average±standard deviation) rather than giving a single value (e.g.,as in Tables 4 and 5). Further statistical studies are needed in order toidentify a grain size system that can better characterize the variabilityof particle size and TFV for large particles.

7. Conclusions

Our results provide important insights both on the morphologicalcharacteristics of volcanic particles and on the determination of Ter-minal Fall Velocity.

Particle morphology: (1) Our dataset shows that there is no clearcorrelation between morphological parameters (i.e., sphericity andshape factor) and grain size. All particle morphological parametersare comprised in a narrow range of values (0.7–0.9) and are charac-terized by small standard deviations (~0.1) among all class sizes;we can conclude that a mean value for each morphological parameter

96 F. Alfano et al. / Journal of Volcanology and Geothermal Research 208 (2011) 86–98

can be derived that is representative of the whole particle population.(2) Sphericity calculated according to Riley et al. (2003) and the shapefactor F of Wilson and Huang (1979) are more sensitive to shape varia-tion than the sphericity of Aschenbrenner (1956). The correction basedon circularity suggested byDellino et al. (2005) results in lower spheric-ity values but it does not modify the general trend with grain size. As aresult the sphericity of Dellino et al. (2005) can be considered a goodshape descriptor, but dedicated experiments on particle TFV are neededto understand if this shape parameter can be applied also to othermodels. (3) 2D image analysis represents an easy method for particlecharacterization, allowing for the characterization of a large amount ofparticles in a relatively short time, with the only limitation of inferringa 3D characterization of the particles based on a 2D analysis. However,2D analysis is able to catchmorphological features of irregular particlesand can be applied to calculate of TFV of volcanic particles. (4) There isan inverse correlation between values of gas-adsorption-derived specif-ic surface area andmean diameter of the bulk samples analyzed relatedto the increase of particle number in a given sample volume. In contrast,measurements of absolute surface areas of individual particles show apositive correlationwith particle diameter. As a result, as values derivedfor a given size fraction (e.g., a given ϕ class) represent the contributionof all the particles analyzed in the sample and cannot be considered rep-resentative of the surface area of individual particles or of the total par-ticle population.

Terminal Fall Velocity: (1) The choice of the model used to derivespecific morphological parameters (Ψ and F) and to calculate TFV sig-nificantly affects the resulting TFV values. TFV discrepancies with thespherical model are up to 50% for the dataset analyzed. (2) The modelof Ganser (1993) combined with the sphericity of Riley et al. (2003) isconsidered as the best model for the calculation of TFV of volcanicparticles as it is highly sensitive to the effect of the morphology onTFV and can be applied to all particle dimensions and Reynolds num-ber in the typical volcanic range. However, dedicated experimentalstudies of volcanic particle settling are required to evaluate the

ϕ Δ TFVWH Δ TFVG (ΨR)

FL1N4 0.15±0.09 0.03±0.094 −0.01±0.10 0.14±0.093 0.00±0.08 0.09±0.132 0.06±0.07 0.09±0.111 0.21±0.07 0.24±0.120 0.32±0.05 0.37±0.10−1 0.40±0.05 0.49±0.08−2 0.38±0.05 0.54±0.07−3 0.37±0.05 0.55±0.06−4 0.39±0.03 0.49±0.06

KMUN2 −0.04±0.08 −0.08±0.112 0.04±0.07 0.01±0.121 0.22±0.06 0.19±0.130 0.31±0.05 0.30±0.11−1 0.37±0.04 0.38±0.09−2 0.36±0.04 0.47±0.10−3 0.32±0.04 0.55±0.11−4 0.35±0.05 0.37±0.07

SHVN4 0.18±0.09 0.02±0.074 −0.03±0.09 0.07±0.083 −0.02±0.08 0.03±0.122 0.05±0.08 0.07±0.121 0.23±0.07 0.17±0.110 0.33±0.05 0.30±0.09−1 0.37±0.05 0.38±0.07

Appendix 1

Average values and standard deviation of the difference between the Tgrain size class (ϕ) of the samples FL1, KMU and SHV.

reliability of different models and different morphological parame-ters. (3) Gas-adsorption-derived surface area of volcanic particles ismainly due to porosity and surface irregularity on the scale of thenanometers. As a result sphericity based on gas-adsorption-derivedsurface area results in very small values (~10−5), which are outsidethe range of sphericity typical for natural particles (0.3–0.9) and areassociated with very low TFV (one or two orders of magnitudelower than the TFV calculated according to the other methods pre-sented in this study) suggesting that this technique is not suitablefor the determination of TFV of volcanic particles. (4) The applicationof 3D scan analysis represents a promising technique to be used insurface analysis and TFV determination for lapilli-size tephra particles(N2 cm). (5) The influence of particle shape on TFV increases withparticle grain size. For the smallest granulometric classes, this influ-ence is negligible (b0.3 m/s) and particles can be approximated asspherical (ϕ≥3; laminar flow regime). (6) Both the whole-ϕ andhalf-ϕ systems are associated with a range of TFV values that in-creases with class size. However, the use of the half-ϕ system isrecommended as it provides a more accurate distribution of TFVvalues for the different grain size classes. For both systems it ismore appropriate to indicate a range of settling velocities for eachsize class (e.g., average±standard deviation) rather than giving a sin-gle value.

Acknowledgments

Dr. Dietmar Klank andDr. Christian Oetzel of Quanthacrome, Dr. PaulBowen of the EPFL (École Polytechnique Fédérale de Lausanne) arethanked for their contribution on the gas adsorption data interpretation.Prof. Jacques Richard of the Hepia (Haute École du Paysage d'Ingénierieet d'Architecture de Géneve) is thanked for providing their facilities for3D scanning analysis. The authors are grateful to Adam Durant andPiero Dellino for their detailed and constructive reviews.

Δ TFVG (ΨA) Δ TFVD (Ψ⁎R) Δ TFVD (Ψ⁎

A)

−0.02±0.03 −12.79±11.69 −13.75±12.63−0.02±0.05 −1.55±0.62 −2.03±0.59

0.00±0.06 −0.72±0.28 −0.87±0.27−0.01±0.05 −0.26±0.19 −0.35±0.12

0.03±0.05 0.17±0.14 0.04±0.080.12±0.05 0.34±0.11 0.20±0.060.23±0.05 0.44±0.09 0.30±0.060.25±0.04 0.45±0.09 0.28±0.050.27±0.04 0.41±0.09 0.23±0.040.29±0.04 0.29±0.08 0.15±0.05

−0.06±0.04 −0.72±0.20 −0.72±0.15−0.04±0.04 −0.31±0.18 −0.36±0.13

0.02±0.04 0.14±0.14 0.05±0.080.11±0.04 0.27±0.10 0.17±0.050.22±0.03 0.30±0.09 0.22±0.040.25±0.02 0.34±0.12 0.21±0.050.24±0.02 0.39±0.16 0.19±0.090.26±0.04 0.11±0.09 0.04±0.04

−0.01±0.03 −18.92±13.42 −19.57±13.02−0.04±0.03 −1.85±0.64 −2.16±0.61−0.03±0.04 −0.71±0.29 −0.80±0.27−0.02±0.05 −0.23±0.20 −0.31±0.15

0.04±0.05 0.12±0.11 0.04±0.080.15±0.05 0.26±0.08 0.19±0.040.22±0.04 0.31±0.07 0.23±0.04

FV of the equivalent sphere and the calculated TFV (Δ TFV %) for each

97F. Alfano et al. / Journal of Volcanology and Geothermal Research 208 (2011) 86–98

(See also caption of Table 4).

Appendix 2. Symbols, abbreviations and dimensions

A absolute surface area (L2)Ā average surface area (L2)A3D absolute surface area measured through 3D scan analysis

(L2)AA absolute surface area of the equivalent tetrakaidecahedron

(Aschenbrenner, 1956) (L2)AES absolute surface area of the equivalent sphere (L2)AGA absolute surface area measured through gas adsorption (L2)Ap projected area a particle (L2)as specific surface area (L2/M)BET Brunauer et al. (1938) method for gas adsorption specific

surface area determinationCD drag coefficientDFT Density Functional Theoryd diameter of a generic particle (L)dav average diameter of the mesopores (L)dv diameter of the equivalent sphere (L)F shape factor (Wilson and Huang, 1979)FL Fontana Lapillig gravity acceleration (L/T2)KMU Kilauea Mystery UnitL, I, S main orthogonal axes of the particle (Large, Intermediate,

Small) (L)m mass of a particle (M)Mdϕ, σϕ median ϕ and sorting (Inman, 1952)Pp Projected perimeter of a particle (L)P/P0 relative pressureRe Reynolds numberSHV Soufriere Hills volcanoTFV Terminal Fall Velocity (L/T)TFVKL TFV calculated using the model of Kunii and Levenspiel

(1969) (L/T)TFVWH TFV calculated using the model of Wilson and Huang

(1979) (L/T)TFVG TFV calculated using the model of Ganser (1993) (L/T)TFVD TFV calculated using the model of Dellino et al. (2005)

(L/T)V volume of a particle (L3)V3D 3D scan derived volume of a particle (L3)VGA volume of gas adsorbed (L3/M)Vmeso volume of the mesopores (L3/M)Vmicro volume of the micropores (L3/M)δ standard deviationΔ TFV difference fraction between particle TFV and TFV of the

equivalent sphere (%)ϕ grain size class, with ϕ=log2 d, with d in mmMϕ median grain sizeσϕ sorting, difference between the 16 and 84 percentile.ρ density of the air (M/L3)ρ(r) pores density profile (L−3)ρs density of a generic particle (M/L3)Ψ sphericityΨΑ sphericity calculated according to Aschenbrenner (1956)Ψ3D 3D scan derived sphericityΨGA gas-adsorption-derived sphericityΨR sphericity calculated according to Riley et al. (2003)Ψ⁎ sphericity divided by particle circularity (Dellino et al.,

2005)Ψ⁎R sphericity calculated according to Riley et al. (2003) divided

by particle circularity (Dellino et al., 2005)Ψ⁎Α sphericity calculated according to Aschenbrenner (1956)

divided by particle circularity (Dellino et al., 2005)

Appendix 3. Drag prediction models

Wilson and Huang (1979)

According to the model of Wilson and Huang (1979) the drag co-efficient is expressed by the following equation:

CD ¼ 24Re

F−0:828 þ 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1:07−F

pðA1Þ

where F is the shape factor.

Haider and Levenspiel (1989)

The model of Haider and Levenspiel (1989)gives an estimation ofthe drag coefficient for particles with different shapes in relation oftheir Reynolds number. Here it is used to estimate the TFV of spheri-cal particles. According to this model the drag coefficient of a spheri-cal object is given by the following equation:

CD ¼ 24Re

1þ 0:1806Re0:6459h i

þ 0:42511þ 6880:95

Re

: ðA2Þ

Ganser (1993)

The model of Ganser (1993) is an improvement of the model ofHaider and Levenspiel (1989), as it gives a more accurate predictionof the drag coefficient for particle with irregular shape (Chhabra etal., 1999). According to this model the drag coefficient is expressedby the following equation:

CD ¼ 24ReK1K2

1þ 0:1118 ReK1K2ð Þ0:6567h i

þ 0:43451þ 3305

ReK1K2

( )K2: ðA3Þ

The two coefficients K1 and K2 are respectively the Stokes' shapefactor ant the Newton's shape factor, and they express the influenceof the morphology on the drag coefficient. They are expressed accord-ing to the following equations:

K1 ¼ 13

IDv

þ 23ϕ−1

=2

� �−1−2:25

Dv

3305ðA4Þ

K2 ¼ 101:8148 − logϕð Þ0:5743 ðA5Þ

where ϕ and I are the sphericity and the average diameter of the pro-jected area of the particle respectively. The model of Ganser is recom-mended to be used in a range of values with Re K1 K2≤105.

Dellino et al. (2005)

According to the model of Dellino et al. (2005) the Terminal FallVelocity is expressed by the following equation:

TFV ¼1:2065μ D3

vg ρs−ρð ÞΨ1:6=μ2

h i0:5206Dvρ

: ðA6Þ

Where Ψ is the sphericity of the particle divided for the ratio be-tween the projected perimeter of the particle and the perimeter of acircle with the same projected area of the particle.

References

Adams, N.K., Houghton, B.F., Hildreth, W., 2006. Abrupt transitions during sustainedexplosive eruptions: examples from the 1912 eruption of Novarupta, Alaska. Bulle-tin of Volcanology 69 (2), 189–206.

98 F. Alfano et al. / Journal of Volcanology and Geothermal Research 208 (2011) 86–98

Alfano, F., Bonadonna, C., Volentik, A.C.M., Connor, C.B., Watt, S.F.L., Pyle, D.M., Connor,L.J., 2011. Tephra stratigraphy and eruptive volume of the May, 2008, Chait, n erup-tion, Chile. Bulletin of Volcanology 73 (5), 613–630.

Arastoopour, H., Wang, C.H., Weil, S.A., 1982. Particle–particle interaction force in adilute gas–solid system. Chemical Engineering Sciences 37 (9), 1379–1386.

Aschenbrenner, B.C., 1956. A new method of expressing particle sphericity. Journal ofSedimentary Petrology 26 (1), 15–31.

Barbero, B.R., Ureta, E.S., 2011. Comparative study of different digitization techniquesand their accuracy. Comput Aided Design 43 (2), 188–206.

Bice, D.C., 1985. Quaternary volcanic stratigraphy of Managua, Nicaragua: correlationand source assignment for multiple overlapping Plinian deposits. Geological Soci-ety of America Bulletin 96, 553–566.

Blott, S.J., Pye, K., 2008. Particle shape: a review and new methods of characterizationand classification. Sedimentology 55, 31–63.

Bonadonna, C., Costa, A., 2010. Modeling of tephra sedimentation from volcanicplumes. In: Fagents, S., Gregg, T., Lopes, R. (Eds.), Modeling Volcanic Processes:The Physics and Mathematics of Volcanism. Cambridge University Press.

Bonadonna, C., Phillips, J.C., 2003. Sedimentation from strong volcanic plumes. Journalof Geophysical Research 108 (B7), 2340–2368.

Bonadonna, C., Ernst, G.G.J., Sparks, R.S.J., 1998. Thickness variations and volume esti-mates of tephra fall deposits: the importance of particle Reynolds number. Journalof Volcanology and Geothermal Research 81 (3–4), 173–187.

Brajlih, T., Valentan, B., Drstvensek, I., Balic, J., Pogacar, V., 2007. Testing the accuracy ofATOS (TM) 3d optical scanner measuring volumes. Annals of Daaam for 2007 &Proceedings of the 18th International Daaam Symposium, pp. 111–112.

Brunauer, S., Emmett, P.H., Teller, E., 1938. Adsorption of gases in multimolecularlayers. Journal of American Chemistry Society 60, 309–319.

Carey, R.J., Houghton, B.F., Thordarson, T., 2009. Abrupt shifts between wet and dryphases of the 1875 eruption of Askja Volcano: microscopic evidence for macro-scopic dynamics. Journal of Volcanology and Geothermal Research 184 (3–4),256–270.

Carter, A.J., Ramsey, M.S., Durant, A.J., Skilling, I.P., Wolfe, A., 2009. Micron-scale rough-ness of volcanic surfaces from thermal infrared spectroscopy and scanning electronmicroscopy. Journal of Geophysical Research, Solid Earth 114.

Chhabra, R.P., Agarwal, L., Sinha, N.K., 1999. Drag on non-spherical particles: an evalu-ation of available methods. Powder Technology 101 (3), 288–295.

Costantini, L., Bonadonna, C., Houghton, B.F., Wehrmann, H., 2009. New physical char-acterization of the Fontana Lapilli basaltic Plinian eruption, Nicaragua. Bulletin ofVolcanology 71 (19), 337–355.

Costantini, L., Houghton, B.F., Bonadonna, C., 2010. Constraints on eruption dynamics ofbasaltic explosive activity derived from chemical and microtextural study: The ex-ample of the Fontana Lapilli Plinian eruption, Nicaragua. Journal of Volcanologyand Geothermal Research 189 (3–4), 207–224.

Dartevelle, S., Ernst, G.G.J., Stix, J., Bernard, A., 2002. Origin of the Mount Pinatubo cli-mactic eruption cloud: implications for volcanic hazards and atmospheric impacts.Geology 30 (7), 663–666.

Deboer, J.H., Lippens, B.C., Linsen, B.G., Broekhof, Jc, Vandenhe, A., Osinga, T.J., 1966. T-curve of multimolecular N2-adsorption. J Colloid Interf Sci 21 (4), 405–413.

Dellino, P., Mele, D., Bonasia, R., Braia, G., La Volpe, L., Sulpizio, R., 2005. The analysis ofthe influence of pumice shape on its terminal velocity. Geophysical Research Let-ters 32 (21), 4.

Delmelle, P., Villieras, F., Pelletier, M., 2005. Surface area, porosity and water adsorptionproperties of fine volcanic ash particles. Bulletin of Volcanology 67 (2), 160–169.

Durant, A.J., Bonadonna, C., Horwell, C.J., 2010. Atmospheric and environmental im-pacts of volcanic particulates. ELEMENTS 6 (4), 235–240.

Ganser, G.H., 1993. A rational approach to drag prediction of spherical and nonspheri-cal particles. Powder Technology 77 (2), 143–152.

Gregg, S.J., Sing, K.S.W., 1982. Adsorption, Surface Area and Porosity, 2ed. AcademicPress, London.

Gurioli, L., Houghton, B.F., Cashman, K.V., Cioni, R., 2005. Complex changes in eruption dy-namics during the 79 AD eruption of Vesuvius. Bulletin of Volcanology 67, 144–159.

Gurioli, L., Harris, A.J.L., Houghton, B.F., Polacci, M., Ripepe, M., 2008. Textural and geo-physical characterization of explosive basaltic activity at Villarrica volcano. Journalof Geophysical Research, Solid Earth 113 (B8).

Haider, A., Levenspiel, O., 1989. Drag coefficient and terminal velocity of spherical andnonspherical particles. Powder Technology 58 (1), 63–70.

Holasek, R.E., Self, S., 1995. GOES weather-satellite observations and measurements ofthe May 18, 1980, Mount-St-Helens Eruption. Journal of Geophysical Research,Solid Earth 100 (B5), 8469–8487.

Inman, D.L., 1952. Measures for describing the size distribution of sediments. Journal ofSedimentary Petrology 22, 125–145.

Klug, C., Cashman, K.V., 1994. Vesiculation of May 18, 1980, Mount St-Helens Magma.Geology 22 (5), 468–472.

Klug, C., Cashman, K.V., Bacon, C.R., 2002. Structure and physical characteristics ofpumice from the climatic eruption of Mt Mazama (Crater Lake) Oregon. Bulletinof Volcanology 64, 486–501.

Kokelaar, B.P., 2002. Setting, chronology and consequences of the eruption of SoufrièreHills Volcano, Montserrat (1995–1999). In: Druitt, T.H., Kokelaar, B.P. (Eds.), TheEruption of Soufrière Hills Volcano, Montserrat, from 1995 to 1999. Geological So-ciety, London, Memoir, pp. 1–43.

Kunii, D., Levenspiel, O., 1969. Fluidisation Engineering. Wiley and Sons, New York.Lautze, N.C., Houghton, B.F., 2007. Linking variable explosion style and magma textures

during 2002 at Stromboli volcano, Italy. Bulletin of Volcanology 69 (4), 445–460.Loth, E., 2008. Drag of non-spherical solid particles of regular and irregular shape. Pow-

der Technology 182 (3), 342–353.McPhie, J., Walker, G.P.L., Christiansen, R.L., 1990. Phreatomagmatic and phreatic fall

and surge deposits from explosions at Kilauea volcano, Hawaii, 1790 A.D.: Keana-kakoi Ash member. Bulletin of Volcanology 52, 334–354.

Mele, D., Dellino, P., Sulpizio, R., Braia, G., 2011. A systematic investigation on the aero-dynamics of ash particles. Journal of Volcanology and Geothermal Research 203(1–2), 1–11.

Mills, O.P., Rose, W.I., Durant, A.J., 2007. Comparison of 3D stereo SEM shape data with2D projections and BET surface area data for volcanic ash: when 3D might be ad-vantageous. Eos Transactions AGU 88 (52) Fall Meet. Suppl., Abstract V31A-0298.

Polacci, M., Pioli, L., Rosi, M., 2003. The Plinian phase of the Campanian Ignimbriteeruption (Phlegrean Field, Italy): evidence from density measurements and textur-al characterization of pumice. Bulletin of Volcanology 65, 418–432.

Riley, C.M., Rose, W.I., Bluth, G.J.S., 2003. Quantitative shape measurements of distalvolcanic ash. Journal of Geophysical Research, Solid Earth 108 (B10).

Rouquerol, F., Rouquerol, J., Sing, K., 1999. Adsorption by powders and porous solids.Principles, Methodology and Applications. Academic Press. 467 pp.

Sable, J.E., Houghton, B.F., Del Carlo, P., Coltelli, M., 2006. Changing conditions ofmagma ascent and fragmentation during the Etna 122 BC basaltic Plinian eruption:evidence from clasts microtextures. Journal of Volcanology and Geothermal Re-search 158, 333–354.

Sable, J.E., Houghton, B.F., Wilson, C.J.N., Carey, R.J., 2009. Eruption mechanism duringthe climax of the Tarawera 1886 basaltic Plinian eruption inferred from microtex-tural characteristics of the deposit. In: Thordarson, S.S.T., Larsen, J., Rowland, K.,Hoskuldsson, A. (Eds.), Studies in Volcanology: The Legacy of George Walker. Geo-logical Society, London.

Sparks, R.S.J., Young, S.R., 2002. The eruption of Soufrière Hills Volcano, Montserrat(1995–1998): overview of scientific results. In: Druitt, T.H., Kokelaar, B.P. (Eds.),The Eruption of Soufrière Hills Volcano, Montserrat, from 1995 to 1999. GeologicalSociety, London, Memoir, pp. 45–69.

Sugar, P., Sugarova, J., Morovic, L., 2008. Application of 3d optical scanning for theshape accuracy analysis of machine parts produced by multi-pass metal spinning.Ann Daaam, pp. 1331–1332.

Thorarinsson, S., 1944. Petrokronologista Studier pa Island. Geographes AnnualesStockholm 26, 1–217.

Wehrmann, H., Bonadonna, C., Freundt, A., Houghton, B.F., Kutterolf, S., 2006. A MaficPlinian Eruption Revisited: Case Study of Fontana Tephra, Nicaragua. GeologicalSociety of America Special Paper, Volcanic Hazards in Central America.

Williams, S.N., 1983. Plinian airfall deposits of basaltic composition. Geology 11, 211–214.Wilson, L., Huang, T.C., 1979. The influence of shape on the atmospheric settling veloc-

ity of volcanic ash particles. Earth and Planetary Science Letters 44, 311–324.Witham, C.S., Oppenheimer, C., Horwell, C.J., 2005. Volcanic ash-leachates: a review

and recommendations for sampling methods. Journal of Volcanology and Geother-mal Research 141 (3–4), 299–326.