Heat transfer during partial melting: An experimental study of a simple binary silicate system

Abstract Heat transfer during partial melting of a composition in a simple binary silicate system relevant to geological processes was investigated experimentally. A 600-g cylindrical charge of nepheline (85.8 wt.%)-sodium disilicate (14.2 wt.%) contained in a platinum crucible was brought to its solidus temperature, 768°C. The crystalline mass was then suddenly heated from below to an interface temperature of 1175°C. The heat flux just below the bottom of the crucible, measured with a heat-flux gauge consisting of 750 differential thermocouples, was time-dependent at both the top and bottom of the charge and can be described by functions of the type F (1 − e − bt ), where b is a constant. The composition and temperature range were selected so that the degree of melting under equilibrium conditions would be 40% at the base of the charge and 20% at the top. The temperature profiles were recorded sequentially every 47 seconds by a vertical planar array of 54 thermocouples in the charge. A quasi-steady-state thermal profile resulted after 2.5 hours. The thermocouple array within the charge was effectively supported during the 5-day experiment because crystal bridging, observed in independent experiments, was within the Einstein limit. The observed thermal profiles were similar to those obtained independently on a refractory aluminosilicate (75% Al 2 O 3 and 25% SiO 2 ) in which no melting took place. The enthalpy of melting of the sodium-bearing system was, therefore, treated as an anomalous heat capacity. The calculated Stefan number, C p ΔT / ΔH , is about 5.6. Independent time studies revealed that more than several hours were required to achieve phase equilibrium, hence the melting process is slower than that of heat transfer. The melting process appears to be decoupled from the heating process so that melting takes place simultaneously throughout the silicate charge at various rates depending on the degree of superheat above the solidus temperature. No adiabatic regions were observed in the thermal profiles, hence it is concluded that convection did not occur through the porous media. Convection, therefore, may not be a principal factor in the generation of homogeneous magma at the site of origin, but may be of importance after segregation. In the absence of abrupt changes in the thermal profiles, expected from the enthalpy of partial melting, there was no evidence of a Stefan boundary marking the progressive advance of a melt front. The relatively high viscosity of the melt in the temperature range investigated (10 3 –10 8 poises) and the sluggish melting kinetics even for small ( μ m) crystals may be the principal rate-controlling factors in the partial melting process in silicate systems relevant to magma generation. The results indicate that magma is generated throughout a mass at temperatures above its solidus where the rate of increase of the thermal gradient greatly exceeds the rate of melting. Permeability and porosity are established simultaneously in those parts of the mass at temperatures above the beginning of melting. The advancement of melting in a granitic mass would be expected to be much slower than that in a basaltic mass with the same heat flux. Migmatization appears to be an incomplete, rate-determined process tending toward anatexis if the bulk compositions are at or near a minimum- or eutectic-like invariant point. In applications to contact metamorphism, the experiments suggest that the heating process is decoupled from the reaction process, and, therefore, contact metamorphism will not be progressive, each zone recording only that reaction taking place at the highest temperature sustained by the imposed thermal profile.