Two-dimensional stokes flow around a heated cylinder: A Possible application for diapirs in the mantle

Kurzfassung

It is widely assumed that the separation of metal and silicates in a homogeneously accreted protoplanet occurred rather rapidly. The process of core formation through the descent of large, hot, iron-rich bodies through a cold, silicate protoplanet is discussed. If iron diapirs sink toward the planet center with the Stokes velocity, they would require more than 800 Ma to form a core in the case of a planet similar to the Earth. We therefore implement a temperature-dependent rheology for the silicate material surrounding the diapir, which leads to a reduction of the drag force exerted on the iron drop. We compare the drag force for different sinking velocities to the body force on the diapir and find that the terminal velocity in the temperature-dependent viscosity model is a factor of 30 higher than that in an isoviscous medium. On the basis of these results, the core formation time for the Earth could be as little as 30 Ma.