A simple formula for calculating porosity of magma in volcanic conduits during dome-forming eruptions

Tomofumi Kozono, Takehiro Koyaguchi

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


We present a simple formula for analyzing factors that govern porosity of magma in dome-forming eruptions. The formula is based on a 1-dimensional steady conduit flow model with vertical gas escape, and provides the value of the porosity as a function of magma flow rate, magma properties (viscosity and permeability), and pressure. The porosity for a given pressure depends on two non-dimensional numbers ε and θ. The parameter ε represents the ratio of wall friction force to liquid-gas interaction force, and is proportional to the magma viscosity. The parameter θ represents the ratio of gravitational load to liquid-gas interaction force and is inversely proportional to the magma flow rate. Gas escape is promoted and porosity decreases with increasing ε or θ. From the possible ranges of ε and θ for typical magmatic conditions, it is inferred that the porosity is primarily determined by ε at the atmospheric pressure (near the surface), and by θ at higher pressures (in the subsurface region inside the conduit). The porosity near the surface approaches 0 owing to high magma viscosity regardless of the magnitude of the magma flow rate, whereas the subsurface porosity increases to more than 0.5 with increasing magma flow rate.

Original languageEnglish
Pages (from-to)483-488
Number of pages6
Journalearth, planets and space
Issue number5
Publication statusPublished - 2010
Externally publishedYes


  • Conduit flow
  • Dome-forming eruptions
  • Gas escape from magma
  • Magma porosity

ASJC Scopus subject areas

  • Geology
  • Space and Planetary Science


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