Grain size-dependent viscosity convection and the thermal evolution of the earth

Scaling relationships for grain size-dependent viscosity convection are derived assuming that eutectoid-like transformations at 660 km depth produce very small grains and that the grain size is mainly controlled by a coupled Ostwald ripening of Mg-perovskite, Ca-perovskite and magnesiowüstite. Parameterized convection calculations based on these relationships show that the thermal evolution of the Earth strongly depends on the grain growth parameters. The Earth can either quickly forget the initial conditions with temperature and heat loss following the decaying radiogenic heat production (Tozer-type evolution) or the initial conditions can essentially determine the temperature and heat loss (Christensen-type evolution). Christensen-type models can easily satisfy both the present-day heat flux and geochemical constraints on abundances of radiogenic isotopes. For example, this happens if the rate-controlling process for both grain growth and viscous creep is volume diffusion and the activation enthalpy for grain growth is about 50% higher than that for viscous creep.