Gum rosin (colophony): A suitable material for thermomechanical modelling of the lithosphere

We investigate the use of a ductile material with temperature-sensitive viscosity for thermomechanical modelling of the lithosphere. First, we consider the scaling of mechanical and thermal properties. For a normal field of gravity, the balance of stresses and body forces sets the stress scale, in proportion to the linear dimensions and the densities. The equation of thermal conduction sets the time scale. The activation enthalpy for creep sets the temperature scale; but the thermal expansivity provides an additional constraint on this temperature scale.

Gum rosin appears to be a suitable material for lithospheric modelling. We have measured its flow properties, at various temperatures, in a specially designed rotary viscometer with unusually low machine friction. The rosin is almost Newtonian. Strain rate depends upon stress to the power n, where 1.0 <n < 1.14. The viscosity varies over 5 orders of magnitude, from about 10² Pa s at 80°C, to about 10⁷ Pa s at 40°C. The activation enthalphy is thus about 250 kJ/mol. Measured with a needle probe, the thermal conductivity is 0.113 ± 0.001 W m⁻¹K⁻¹; the thermal diffusivity, (6±3) ×10⁻⁷ m² s⁻¹. Calculated from X-ray profiles, the thermal expansivity is about 3 × 10⁻⁴ K⁻¹. These thermal and mechanical properties make gum rosin suitable for thermomechanical models, where linear dimensions scale down by a factor of 10⁶; time, by 10¹¹; viscosity, by 10¹⁷; and temperature change, by 10¹.