Dynamics of cooling domes of viscoplastic fluid

A non-isothermal viscoplastic thin-layer theory is developed to explore the effects of surface cooling, yield stress, and shear thinning on the evolution of non-isothermal domes of lava and laboratory fluids. The fluid is modelled using the Herschel–Bulkley constitutive relations, but modified to have temperature-dependent viscosity and yield stress. The thin-layer equations are solved numerically to furnish models of expanding, axisymmetrical domes. Linear stability theory reveals the possibility of non-axisymmetrical, fingering-like instability in these domes. Finally, the relevance to lava and experiments is discussed.

[1]  Richard V. Craster,et al.  A consistent thin-layer theory for Bingham plastics , 1999 .

[2]  Herbert R. Shaw,et al.  Rheology of Basalt in the Melting Range , 1969 .

[3]  R. W. Griffiths,et al.  Radial spreading of viscous-gravity currents with solidifying crust , 1990, Journal of Fluid Mechanics.

[4]  Amy Q. Shen,et al.  Visco-plastic models of isothermal lava domes , 2000, Journal of Fluid Mechanics.

[5]  A. Borgia,et al.  Rheology of melts and magmatic suspensions: 1. Design and calibration of concentric cylinder viscometer with application to rhyolitic magma , 1988 .

[6]  Lincoln Paterson,et al.  Radial fingering in a Hele Shaw cell , 1981, Journal of Fluid Mechanics.

[7]  Dilhan M. Kalyon,et al.  Effects of temperature and surface roughness on time‐dependent development of wall slip in steady torsional flow of concentrated suspensions , 1994 .

[8]  J. Pearson.  Variable-viscosity flows in channels with high heat generation , 1977, Journal of Fluid Mechanics.

[9]  Brian J. Briscoe,et al.  The properties of drilling muds at high pressures and high temperatures , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[10]  Peter Ehrhard,et al.  Non-isothermal spreading of liquid drops on horizontal plates , 1991, Journal of Fluid Mechanics.

[11]  P. Ehrhard.  Experiments on isothermal and non-isothermal spreading , 1993, Journal of Fluid Mechanics.

[12]  Harry Pinkerton,et al.  Rheological properties of basaltic lavas at sub-liquidus temperatures: laboratory and field-measurements on lavas from Mount Etna. , 1995 .

[13]  P. Roberts,et al.  A THERMODYNAMICALLY CONSISTENT MODEL OF A MUSHY ZONE , 1983 .

[14]  M. Annis.  High-Temperature Flow Properties of Water-Base Drilling Fluids , 1967 .

[15]  A. McBirney,et al.  Rheological Properties of Magmas , 1984 .

[16]  L. Scriven,et al.  Dynamics of a fluid interface Equation of motion for Newtonian surface fluids , 1960 .

[17]  R. W. Griffiths,et al.  A laboratory analog study of the surface morphology of lava flows extruded from point and line sources , 1992 .

[18]  Oliver E. Jensen,et al.  The spreading of heat or soluble surfactant along a thin liquid film , 1993 .

[19]  Harry Pinkerton,et al.  Methods of determining the rheological properties of magmas at sub-liquidus temperatures. , 1992 .

[20]  R. Iverson,et al.  Lava Domes Modeled as Brittle Shells that Enclose Pressurized Magma, with Application to Mount St. Helens , 1990 .

[21]  Jonathan H. Fink,et al.  Effects of surface cooling on the spreading of lava flows and domes , 1993, Journal of Fluid Mechanics.

[22]  S. Blake.  Viscoplastic Models of Lava Domes , 1990 .

[23]  K. Helfrich,et al.  Instability of flow with temperature‐dependent viscosity: A model of magma dynamics , 1991 .

[24]  M. Grae Worster,et al.  CONVECTION IN MUSHY LAYERS , 1997 .

[25]  C. Jaupart,et al.  Influence of cooling on lava-flow dynamics , 1993 .

[26]  R. W. Griffiths,et al.  Morphology, eruption rates, and rheology of lava domes - Insights from laboratory models , 1998 .

[27]  H. Huppert,et al.  On lava dome growth, with application to the 1979 lava extrusion of the soufrière of St. Vincent , 1982 .

[28]  Jonathan H. Fink,et al.  Solidifying Bingham extrusions: a model for the growth of silicic lava domes , 1997, Journal of Fluid Mechanics.

[29]  A. Neri.  A local heat transfer analysis of lava cooling in the atmosphere: application to thermal diffusion-dominated lava flows , 1998 .

[30]  J. Wylie,et al.  Flow localization in fissure eruptions , 1999 .