Staff profile

2007 –2012 — Lecturer in Volcanology, Department of Earth Sciences, Durham University

2006 – 2008 — NERC Blue Skies Research Fellow: BP Institute, University of Cambridge and Department of Earth Sciences, University of Durham

‘Explosive volcanic eruption processes: from mesoscopic simulations to constitutive laws.’

2003 – 2006 — NERC Research Fellow:  BP Institute, University of Cambridge, transferred from Department of Earth Sciences, University of Bristol, 2005.

‘Multiphase lattice-Boltzmann approaches to modelling the dynamics of volcanic eruptions.’

2002 – 2003 — Lecturer, Department of Earth Sciences, University of Bristol.

1998 – 2002 — PhD: ‘The rheology of bubbly magmas.’, Department of Earth Sciences, University of Bristol.

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Career Research Highlights

My prime research goal is to quantify the physical controls on volcanic eruptive style. In particular, my research focuses on the fundamental role played by magmatic processes and properties at the mesoscopic scale: i.e. at the lengthscale of intra-magmatic bubbles and crystals; and how these processes interact to determine eruptive behaviour at the volcano scale. My ongoing research in this field includes laboratory and numerical investigation of:

• the rheology of bubble- and particle-bearing magma,
• the flow of volcanic gases through permeable magma,
• Dynamics of strombolian eruptions

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Committee and Society Service

Founder and Director of Action on Natural Disasters Doctoral Training Centre, Durham University

Editorial Board member, Journal of Volcanology and Geothermal Research

Peer Review College Member; NERC

PubVolc – volcanology publication database, manager and developer

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Conferences and Workshops

2013 — ‘Dynamics of volcanic processes’ - Session convenor, IAVCEI General Assembly

2013 — ‘From conduit magma ascent to ash generation and dispersal’ -Session convenor: EGU General Assembly; 

2012 — Conference organiser; VMSG Annual Meeting – Durham 

2012 — ‘Volcanic conduits in nature, models, and experiments’ Session convenor - EGU General Assembly 

2008 — Session convenor: ‘Magma movement’ - IAVCEI General Assembly 

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Invited Talks (selected)

2016 — "Slugs and plugs: multiphase magma flow in basaltic volcanic conduits", Leeds University Fluids group seminar series.

2016 — "Down-flow evolution of the rheology of
the June 27th lava flow", Hawaiian Volcano Observatory seminar series.

2016 — "Slugs and Plugs: Big experiments in volcano physics", IUGG Conference on Mathematical Geophysics invited keynote.

2015 — "Bubble, burp, bang! Big experiments in volcano physics", University of Hawaii, SOEST seminar series.

2015 — "Slugs and Plugs: the role of conduit boundary conditions in shaping Strombolian explosive activity", AGU Fall Meeting invited keynote.

2013 — "Bubble, burp bang! Big experiments in volcano physics", NTU Singapore EOS seminar series.

2012 — “Bubble, burp bang! The physics of Strombolian volcanic eruptions”, Open University, Centre for Earth, Planetary, Space & Astronomical Research seminar series.

2011: — “Magma in motion: bubbles, crystals and the physics of volcanic eruptions”, University of Geneva, Department of Mineralogy departmental seminar.

2011: — ‘Why build a volcano? The science of Mt Boom’, INGV Roma.

2011: — ‘Bubbles, burps and bangs! Experimental and physical modelling of eruptions at Stromboli volcano, Italy’, University of Bristol, School of Earth Sciences seminar series.

2010: — ‘Bubbles and crystals in magma’, ETH, Zurich, Department of Earth Sciences seminar series

2009: — ‘Bubbles, crystals and the physics of volcanic eruptions’, University of Leeds, School of Earth and Environment seminar series

2008: — ‘Development of magma permeability during an eruption’, University of Lancaster, Environmental School seminar series.

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Prizes and Awards

Thermo-Fischer Scientific VMSG Award 2021

British Society of Rheology Annual Award 2016

Journal of Volcanology and Geothermal Research Most Cited Author 2003 – 2007 Award for Llewellin, E.W. and Manga, M., 2005

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Recent and Current Grants

‘Quantifying disequilibrium processes in basaltic volcanism.’ NERC/NSF Large Grant NE/N018443/1, awarded April 2016 (Durham PI; Lead PI Mike Burton, Manchester)

‘Quantifying disequilibrium processes in basaltic volcanism.’ NERC Standard Grant NE/N002954/1, awarded July 2015 (PI; Co-I Madeleine Humphreys)

‘Fissures, fountains and flows: quantifying the evolution of basaltic eruptions.’ Royal Society International Exchanges grant, awarded November 2013 (PI; Co-I Bruce Houghton)

‘Quantifying the dynamics of bubble growth in magma using SIMS profiling of water content in glass’ 120 hours of instrument time at the NERC Ion Microprobe Facility in Edinburgh, awarded December 2011 (PI)

‘Fault lubrication during earthquake propagation in thermally unstable rocks.’ NERC Standard Grant Number NE/H021744/1, awarded July 2010 (Co-I; PI Nic de Paola)

‘The importance of crystal exchange and magma mixing in volcanic systems: eruption-triggering mechanisms and timescales’ NERC Standard Grant Number NE/G002401/1, awarded December 2008 (Co-I; PI Jon Davidson)

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• Geodynamics Research Group
• Geohazards
• Volcanology Research Group

• 2019: Bubble Nucleation: The Root of Explosive Volcanic Eruptions(£6000.00 from )
• 2019: Facility for High-Temperature, High-Pressure Rheology of Geomaterials(£299818.61 from Natural Environmental Research Council)
• 2019: NSFGEO-NERC: Multi-scale investigation of the emplacement of multi-phase(£184457.00 from Natural Environmental Research Council)
• 2017: Scaling and design of laboratory experiments to understand environmental flows(£40249.00 from NERC - Natural Environment Research Council)
• 2016: NSFGEO-NERC Quantifying disequilibrium processes in basaltic volcanism(£454668.00 from NERC - Natural Environment Research Council)
• 2016: RF050291: Reconstructing eruptive processes from volatile distribution in volcanic glass, NERC - Natural Environment Research Council, £482k
• 2014: Understanding basaltic eruptions: the dynamics of magma flow in shallow conduits(£6000.00 from The Royal Society)

Available for media contact about:

• Volcanism: Volcanic Eruption Processes
• Geological hazards: Volcanic Eruption Processes

Journal Article

• Gardner, James E., Wadsworth, Fabian B., Carley, Tamara L., Llewellin, Edward W., Kusumaatmaja, Halim & Sahagian, Dork (2023). Bubble Formation in Magma. Annual Review of Earth and Planetary Sciences 51(1): 131-154.
• Oláh, László, Gallo, Giuseppe, Hamar, Gergő, Kamoshida, Osamu, Leone, Giovanni, Llewellin, Edward W., Lo Presti, Domenico, Nyitrai, Gábor, Ohminato, Takao, Ohno, Shouhei, Tanaka, Hiroyuki K. M. & Varga, Dezső (2023). Muon Imaging of Volcanic Conduit Explains Link Between Eruption Frequency and Ground Deformation. Geophysical Research Letters 50(2): e2022GL101170.
• Wadsworth, Fabian B., Llewellin, Edward W., Castro, Jonathan M., Tuffen, Hugh, Schipper, C. Ian, Gardner, James E., Vasseur, Jérémie, Foster, Annabelle, Damby, David E., McIntosh, Iona M., Boettcher, Sina, Unwin, Holly E., Heap, Michael J., Farquharson, Jamie I., Dingwell, Donald B., Iacovino, Kayla, Paisley, Rebecca, Jones, Calvin & Whattam, Jack (2022). A reappraisal of explosive–effusive silicic eruption dynamics: syn-eruptive assembly of lava from the products of cryptic fragmentation. Journal of Volcanology and Geothermal Research 432: 107672.
• Romero, Jorge E., Burton, Mike, Cáceres, Francisco, Taddeucci, Jacopo, Civico, Riccardo, Ricci, Tullio, Pankhurst, Matthew J., Hernández, Pedro A., Bonadonna, Costanza, Llewellin, Edward W., Pistolesi, Marco, Polacci, Margherita, Solana, Carmen, D'Auria, Luca, Arzilli, Fabio, Andronico, Daniele, Rodríguez, Fátima, Asensio-Ramos, Maria, Martín-Lorenzo, Alba, Hayer, Catherine, Scarlato, Piergiorgio & Perez, Nemesio M. (2022). The initial phase of the 2021 Cumbre Vieja ridge eruption (Canary Islands): Products and dynamics controlling edifice growth and collapse. Journal of Volcanology and Geothermal Research 431: 107642.
• Orr, Tim R., Llewellin, Edward W. & Patrick, Matthew R. (2022). Development, structure, and behavior of a perched lava channel at Kīlauea Volcano, Hawaiʻi, during 2007. Journal of Volcanology and Geothermal Research 430: 107637.
• Jackson, Lucy E., Wadsworth, Fabian B., Mitchell, Joanne, Rennie, Colin, Llewellin, Edward W., Hess, Kai‐Uwe & Dingwell, Donald B. (2022). Bubble rise in molten glasses and silicate melts during heating and cooling cycles. Journal of the American Ceramic Society 105(12): 7238-7253.
• Arzilli, Fabio, Polacci, Margherita, La Spina, Giuseppe, Le Gall, Nolwenn, Llewellin, Edward W., Brooker, Richard A., Torres-Orozco, Rafael, Di Genova, Danilo, Neave, David A., Hartley, Margaret E., Mader, Heidy M., Giordano, Daniele, Atwood, Robert, Lee, Peter D., Heidelbach, Florian & Burton, Mike R. (2022). Dendritic crystallization in hydrous basaltic magmas controls magma mobility within the Earth’s crust. Nature Communications 13(1).
• Wadsworth, Fabian B., Llewellin, Edward W., Farquharson, Jamie I., Gillies, Janina K., Loisel, Ariane, Frey, Léon, Ilyinskaya, Evgenia, Thordarson, Thor, Tramontano, Samantha, Lev, Einat, Pankhurst, Matthew J., Rull, Alejandro Galdeano, Asensio-Ramos, María, Pérez, Nemesio M., Hernández, Pedro A., Calvo, David, Solana, M. Carmen, Kueppers, Ulrich & Santabárbara, Alejandro Polo (2022). Crowd-sourcing observations of volcanic eruptions during the 2021 Fagradalsfjall and Cumbre Vieja events. Nature Communications 13(1).
• Birnbaum, Janine, Lev, Einat & Llewellin, Ed W. (2021). Rheology of three-phase suspensions determined via dam-break experiments. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477(2254): 20210394.
• Le Gall, Nolwenn, Arzilli, Fabio, La Spina, Giuseppe, Polacci, Margherita, Cai, Biao, Hartley, Margaret E., Vo, Nghia, T., Atwood, Robert C., Di Genova, Danilo, Nonni, Sara, Llewellin, Edward W., Burton, Mike R. & Lee, Peter D. (2021). In situ quantification of crystallisation kinetics 1 of plagioclase and clinopyroxene in basaltic magma: implications for lava flow. Earth and Planetary Science Letters 568: 117016.
• Houghton, B.F., Tisdale, C.M., Llewellin, E.W., Taddeucci, J., Orr, T.R., Walker, B.H. & Patrick, M.R. (2021). The Birth of a Hawaiian Fissure Eruption. Journal of Geophysical Research: Solid Earth 126(1): e2020JB020903.
• Wadsworth, Fabian B., Vasseur, Jérémie, Llewellin, Edward W., Brown, Richard J., Tuffen, Hugh, Gardner, James E., Kendrick, Jackie E., Lavallée, Yan, Dobson, Katherine J., Heap, Michael J., Dingwell, Donald B., Hess, Kai-Uwe, Schauroth, Jenny, von Aulock, Felix W., Kushnir, Alexandra R.L. & Marone, Federica (2021). A model for permeability evolution during volcanic welding. Journal of Volcanology and Geothermal Research 409: 107118.
• La Spina, G., Arzilli, F., Llewellin, E.W., Burton, M.R., Clarke, A.B., de' Michieli Vitturi, M., Polacci, M., Hartley, M.E., Di Genova, D. & Mader, H.M. (2021). Explosivity of basaltic lava fountains is controlled by magma rheology, ascent rate and outgassing. Earth and Planetary Science Letters 553: 116658.
• Jones, Thomas J. & Llewellin, Edward W. (2021). Convective tipping point initiates localization of basaltic fissure eruptions. Earth and Planetary Science Letters 553: 116637.
• Dobson, Katherine J., Allabar, Anja, Bretagne, Eloise, Coumans, Jason, Cassidy, Mike, Cimarelli, Corrado, Coats, Rebecca, Connolley, Thomas, Courtois, Loic, Dingwell, Donald B., Di Genova, Danilo, Fernando, Benjamin, Fife, Julie L., Fyfe, Frey, Gehne, Stephan, Jones, Thomas, Kendrick, Jackie E., Kinvig, Helen, Kolzenburg, Stephan, Lavallée, Yan, Liu, Emma, Llewellin, Edward W., Madden-Nadeau, Amber, Madi, Kamel, Marone, Federica, Morgan, Cerith, Oppenheimer, Julie, Ploszajski, Anna, Reid, Gavin, Schauroth, Jenny, Schlepütz, Christian M., Sellick, Catriona, Vasseur, Jérémie, von Aulock, Felix W., Wadsworth, Fabian B., Wiesmaier, Sebastian & Wanelik, Kaz (2020). Quantifying Microstructural Evolution in Moving Magma. Frontiers in Earth Science 8.
• Coumans, J.P., Llewellin, E.W., Wadsworth, F.B., Humphreys, M.C.S., Mathias, S.A., Yelverton, B.M. & Gardner, J.E. (2020). An experimentally validated numerical model for bubble growth in magma. Journal of Volcanology and Geothermal Research 402: 107002.
• Capponi, Antonio, Crosby, Andrew C., Lishman, Stephen & Llewellin, Edward W. (2020). A novel experimental apparatus for investigating bubbly flows in a slot geometry. Review of Scientific Instruments 91(4): 045110.
• Jones, Thomas J, Llewellin, Edward W & Mader, Heidy M (2020). The use of a shear thinning polymer as a bubbly magma analogue for scaled laboratory experiments. Journal of Volcanology and Geothermal Research 392: 106768.
• Wadsworth, Fabian B., Llewellin, Edward W., Vasseur, Jérémie, Gardner, James E. & Tuffen, Hugh (2020). Explosive-effusive volcanic eruption transitions caused by sintering. Science Advances 6(39): eaba7940.
• Arzilli, F., La Spina, G., Burton, M., Polacci, M., Le Gall, N., Hartley, M., Di Genova, D., Cai, B., Vo, N., Bamber, E., Nonni, S., Atwood, R., Llewellin, E., Brooker, R., Mader, H. & Lee, P. (2019). Magma fragmentation in highly explosive basaltic eruptions induced by rapid crystallisation. Geoscience 12: 1023-1028.
• Gardner, James E., Wadsworth, Fabian B., Llewellin, Edward W., Watkins, James M. & Coumans, Jason P. (2019). Experimental constraints on the textures and origin of obsidian pyroclasts. Bulletin of Volcanology 81: 22.
• Capponi, Antonio & Llewellin, Edward W. (2019). Experimental observations of bubbling regimes at in-line multi-orifice bubblers. International Journal of Multiphase Flow 114: 66-81.
• Jones, T.J., Houghton, B.F., Llewellin, E.W., Parcheta, C. & Höltgen, L. (2018). Spatter matters – distinguishing primary (eruptive) and secondary (non-eruptive) spatter deposits. Scientific Reports 8: 9179.
• Polacci, M., Arzilli, F., La Spina, G., Le Gall, N., Cai, B., Hartley, M. E., Di Genova, D., Vo, N. T., Nonni, S., Atwood, R. C., Llewellin, E. W., Lee, P. D. & Burton, M. R. (2018). Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography. Scientific Reports 8(1): 8377.
• Gardner, James E., Wadsworth, Fabian B., Llewellin, Edward W., Watkins, James M. & Coumans, Jason P. (2018). Experimental sintering of ash at conduit conditions and implications for the longevity of tuffisites. Bulletin of Volcanology 80(3): 23.
• Polacci, M., de' Michieli Vitturi, M., Arzilli, F., Burton, M., Caricchi, L., Carr, B., Cerminara, M., Cimarelli, C., Clarke, A., Colucci, S., Costa, A., Degruyter, W., Druitt, T., Engwell, S., Esposti Ongaro, T., Giordano, D., Gurioli, L., Haddadi, B., Kendrick, J., Kueppers, U., Lamur, A., Lavallée, Y., LLewellin, E., Mader, H., Metrich, N., Montagna, C., Neri, A., Rivalta, E., Saccorotti, G., Sigmundsson, F., Spina, L. & Taddeucci, J. (2017). From magma ascent to ash generation: investigating volcanic conduit processes by integrating experiments, numerical modeling, and observations. Annals of Geophysics 60(6): S0666.
• Jones, T.J., Llewellin, E.W., Houghton, B.F., Brown, R.J. & Vye-Brown, C. (2017). Proximal lava drainage controls on basaltic fissure eruption dynamics. Bulletin of Volcanology 79(11): 81.
• Wadsworth, FB Vasseur, J, Llewellin, EW, Dobson, KJ, Colombier, M, von Aulock, FW, Fife, JL, Wiesmaier, S, Hess, K-U, Scheu, B, Lavallée, Y & Dingwell, DB (2017). Topological inversions in coalescing granular media control fluid-flow regimes. Physical Review E 96(3): 033113.
• McIntosh, I.M., Nichols, A.R.L., Tani, K. & Llewellin, E.W. (2017). Accounting for the species-dependence of the 3500 cm-1 H2Ot infrared molar absorptivity coefficient: implications for hydrated volcanic glasses. American Mineralogist 102(8): 1677-1689.
• Wadsworth, Fabian B., Vasseur, Jérémie, Llewellin, Edward W., Genareau, Kimberly, Cimarelli, Corrado & Dingwell, Donald B. (2017). Size limits for rounding of volcanic ash particles heated by lightning. Journal of Geophysical Research - Solid Earth 122(3): 1977-1989.
• Wadsworth, Fabian B., Vasseur, Jérémie, Llewellin, Edward W. & Dingwell, Donald B. (2017). Sintering of polydisperse viscous droplets. Physical Review E 95(3): 033114.
• Gardner, J.E., Llewellin, E.W., Watkins, J.M. & Befus, K.S. (2017). Formation of Obsidian Pyroclasts by Sintering of Ash Particles in the Volcanic Conduit. Earth and Planetary Science Letters 459(1): 252-263.
• Wadsworth, Fabian B., Vasseur, J., Llewellin, E., Schauroth, J., Dobson, K.J., Scheu, B. & Dingwell, D. B (2016). Sintering of viscous droplets under surface tension. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 472(2188): 20150780.
• Reynolds, P., Brown, R.J., Thordarson, T. & Llewellin, E. (2016). The architecture and shallow conduits of Laki-type pyroclastic cones: insights into a basaltic fissure eruption. Bulletin of Volcanology 78(5): 36.
• Reynolds, P.R., Brown, R.J., Thordarson, T., Llewellin, E. & Fielding, K. (2015). Rootless cone eruption processes informed by dissected tephra deposits and conduits. Bulletin of Volcanology 77(9): 72.
• Del Bello, E., Lane, S.J., James, M.R., Llewellin, E.W., Taddeucci, J., Scarlato, P. & Capponi, A. (2015). Viscous plugging can enhance and modulate explosivity of strombolian eruptions. Earth and Planetary Science Letters 423: 210-218.
• Truby, J.M., Mueller, S.P., Llewellin, E.W. & Mader, H.M. (2015). The rheology of three-phase suspensions at low bubble capillary number. Proceedings of the Royal Society A 471(2173): 20140557.
• Wilson, J.T., Eke, V.R., Massey, R.J., Elphic, R.C., Jolliff, B.L., Lawrence, D.J., Llewellin, E.W., McElwaine, J.N. & Teodoro, L.F.A. (2015). Evidence for explosive silicic volcanism on the Moon from the extended distribution of thorium near the Compton-Belkovich Volcanic Complex. Journal of Geophysical Research: Planets 120(1): 92-108.
• Damby, D.E., Llewellin, E.W., Horwell, C.J., Williamson, B.J., Najorka, J., Cressey, G. & Carpenter, M.A. (2014). The α-β phase transition in volcanic cristobalite. Journal of Applied Crystallography 47(4): 1205-1215.
• McIntosh, I.M., Llewellin, E.W., Humphreys, M.C.S., Nichols, A.R.L., Burgisser, A., Schipper, C.I. & Larsen, J.F. (2014). Distribution of dissolved water in magmatic glass records growth and resorption of bubbles. Earth and Planetary Science Letters 401: 1-11.
• Horwell, C.J., Hillman, S.E., Cole, P.D., Loughlin, S.C., Llewellin, E.W., Damby, D.E. & Christopher, T. (2014). Controls on variations in cristobalite abundance in ash generated by the Soufrière Hills volcano, Montserrat in the period 1997-2010. Memoir of the Geological Society of London 39: 399-406.
• Horwell, C.J., Williamson, B.J., Llewellin, E.W., Damby, D.E. & Le Blond, J.S. (2013). The nature and formation of cristobalite at the Soufrière Hills volcano, Montserrat: implications for the petrology and stability of silicic lava domes. Bulletin of Volcanology 75: 696.
• Mader, H.M., Llewellin, E.W. & Mueller, S.P. (2013). The rheology of two-phase magmas: A review and analysis. Journal of Volcanology and Geothermal Research 257: 135-158.
• Del Bello, E., Llewellin, E.W., Taddeucci, J., Scarlato, P. & Lane, S.J. (2012). An analytical model for gas overpressure in slug-driven explosions: insights into Strombolian volcanic eruptions. Journal of Geophysical Research 117: B02206.
• Llewellin, E.W., Del Bello, E., Taddeucci, J., Scarlato, P. & Lane, S.J. (2011). The thickness of the falling film of liquid around a Taylor bubble. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468(2140): 1041-1064.
• James, M.R., Llewellin, E.W. & Lane, S.J. (2011). Comment on "It takes three to tango: 2. Bubble dynamics in basaltic volcanoes and ramifications for modeling normal Strombolian activity" by J. Suckale, B. H. Hager, L. T. Elkins-Tanton, and J.-C. Nave. Journal of Geophysical Research 116: B06207.
• Mueller, S., Llewellin, E.W. & Mader, H.M. (2011). The effect of particle shape on suspension viscosity and implications for magmatic flows. Geophysical Research Letters 38: L13316.
• Llewellin, EW (2010). LBflow: An extensible lattice Boltzmann framework for the simulation of geophysical flows. Part I: theory and implementation. Computers & Geosciences 36(2): 115-122.
• Williamson, B.J., Di Muro A., Horwell C.J., Spieler O. & Llewellin E.W. (2010). Injection of vesicular magma into an andesitic dome at the effusive–explosive transition. Earth and Planetary Science Letters 295(1-2): 83-90.
• Mueller, S, Llewellin, EW & Mader, HM (2010). The rheology of suspensions of solid particles. Proceedings Of The Royal Society A-mathematical Physical And Engineering Sciences 466(2116): 1201-1228.
• Llewellin, EW (2010). LBflow: An extensible lattice Boltzmann framework for the simulation of geophysical flows. Part II: usage and validation. Computers & Geosciences 36(2): 123-132.
• Nabovati, A., Llewellin, E.W. & Sousa, A.C.M. (2010). Through-thickness permeability prediction of three-dimensional multifilament woven fabrics. Composites Part A: Applied Science and Manufacturing 41(4): 453-463.
• Nabovati, A, Llewellin, EW & Sousa, ACM (2009). A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method. Composites Part A: Applied Science And Manufacturing 40(6-7): 860-869.
• Witham, F. & Llewellin, E.W. (2006). Stability of Lava Lakes. Journal of Volcanology and Geothermal Research 158(3-4): 321-332.
• Llewellin, E.W. & Manga, M. (2005). Bubble suspension rheology and implications for conduit flow. Journal of Volcanology and Geothermal Research 143(1-3): 205-217.
• Llewellin, E.W., Mader, H.M. & Wilson, S.D.R. (2002). The constitutive equation and flow dynamics of bubbly magmas. Geophysical Research Letters 29(24): 2170.
• Llewellin, E.W., Mader, H.M. & Wilson, S.D.R. (2002). Correction to the constitutive equation and flow dynamics of bubbly lava. Geophysical Research Letters 30(6): 1340.
• Llewellin, E.W., Mader, H.M. & Wilson, S.D.R. (2002). The rheology of a bubbly liquid. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 458(2020): 987-1016.