1. a numerical program for steady flow through volcanic conduits Larry G. Mastin U.S. Geological Survey

2. Assumptions and simplifications Steady-state Vertical conduit 1-dimensional homogeneous flow Equilibrium degassing (distributed version) No heat or mass flow through conduit walls

3. Main features User-friendly, visual interface Publicly-documented, open-source code See http://vulcan.wr.usgs.gov/Projects/Mastinhttp://vulcan.wr.usgs.gov/Projects/Mastin Calculates solubility & thermodynamics using Full MELTS equations (Ghiorso & Sack, 1995) for melts Full equation of state for gas (H2O) Uses viscosity of bubbly melts formulation based on Capillary number. Fragmentation criterion based either on volume fraction gas or strain rate.

4. Weaknesses of this model (and others) Poorly characterized rheology Kinetics of degassing, crystallization Magma-host rock interaction Conduit geometry Difficulty in comparing results with observations

5. ODE for 1-D flow Option 1: specify conduit geometry, solve for pressure A=x-sectional arear=radius f=friction factor  =density M=Mach # u=velocity gravity friction geometry Mach #

6. ODE for 1D flow Option 2: Specify pressure gradient and calculate conduit geometry Pressure gradient gravity friction

7. Friction Factor Log Re 27 f.001 1 16/Re laminar turbulent viscosity

8. Viscosity Melt viscosity SiO 2 >70 wt%: Hess & Dingwell (1996) SiO 2 <70 wt%: Shaw (1972) Effect of Crystals <40%: Roscoe-Einstein (Marsh calibration) Volume fraction crystals Melt viscosity

9. Viscosity (cont’d) Effect of bubbles -1<n<1 Depending on Capillary number

10. Relationship between n and Ca Log 10 (Ca) n

11. Calculating Capillary number   =Surface tension=0.34 N/m  r=avg. bubble radius = (3v g /(4  Nv m )) 1/3, where  V g, v m are volume fractions gas and melt, respectively  N=nuclei per unit volume; log(N) =~0.2*wt%SiO 2   =avg. shear-strain rate=~4u/3D under laminar flow Conduit flow profile

12. Demo of the program

13. Ongoing & future work Kinetics of magma degassing (with M. Mangan) Calculating bubble-size distributions Improved fragmentation criterion Improved rheology of bubbly magmas Elastic coupling of fluid & host rock 2-D, transient flow (with R. Denlinger) Etc. etc.

14. Kinetics of magma degassing In collaboration with Margaret Mangan, Tom Sisson Data from Mangan & Sisson (2001)

15. Sample Results Depend significantly on fragmentation criterion (v g =.75 or strain-rate)