Dependence of the parameters of equations of viscous flow on chemical composition of silicate melts

The temperature dependence of viscosity of silicate melts is discussed in the framework of the Avramov–Milchev (AM) equation. The composition is described by means of two parameters: the molar fraction, x, and the “lubricant fraction”, l. The molar fraction is the sum of the molar parts x_i of all oxides dissolved in SiO₂, the molar fraction of the latter being 1 ? x. It is shown that, with sufficient precision, two of the parameters of the AM equation can be presented as unique functions of the molar fraction. On the other hand, x is not sufficient to determine properly the reference temperature T_r , at which viscosity is η_r = 10¹³ dPa.s]. Therefore, additional parameter, “lubricant fraction” l, is introduced. For each of the components, l_i is a product of molar part x_i and a specific dimensionless coefficient 0 ≤ k_i ≤ 1 accounting for the specific contribution of this component to the increased mobility of the system. It is demonstrated that, for l > 0, the reference temperature is related to the “lubricant fraction” l through the reference temperature T_r,SiO2 of pure SiO₂.