Local Concentration of Magma as a Stationary Irreversible Process

Abstract

The fact that the volcanic zones are notably localized on the Earth's surface is not so far explained well enough, though several studies have been made about the mechanism of production of liquid magma. The process proposed in the present paper will be the fundamental process which results in the localized activity of volcanism. We suppose that our system is of single component, which consists of two magma reservoirs connected by a channel. The interaction of heat flow and flow of matter through the channel and phase transformation in each reservoir give rise to certain cross-phenomena, of which the most important one is that occurs when there is a gravitational potential difference between the two reservoirs. In this case the liquid magma becomes to be localized to the reservoir of higher gravitational potential. In the present paper the above process is studied by the method of irreversible thermodynamics, and the rate of increase of liquid magma at the reservoir of higher potential is derived. with some assumptions the rate J* can be expressed as J* = kAT/(Q^2)(Δυ/υ)(1-Δυ/υ)Δφ/l here κ; thermal conductivity T; absolute temperature υ; specific volume Δυ; increase of specific volume by fusion Q; latent heat A; cross-sectional area through which heat flows l; length of the channel Δφ; difference of gravitational potential. The value of the rate derived by the above formula is found to coincide, at least in its order, with the observed value. The geographical relation between the distribution of gravity anomalies and that of volcanoes may be explained by the process proposed here.