Convection experiments in high Prandtl number silicones, Part 1. Rheology, equipment, nomograms and dynamic scaling of stress- and temperature-dependent convection in a centrifuge

Abstract

It has been impossible to model mantle convection by other than numerical methods, because dynamically scaled laboratory experiments (of practical size) in high Prandtl number fluids, would require a temperature gradient reaching far above the sublimation temperature of any known fluid. However, convection can be established in high Prandtl number fluids without large temperature gradients and length scales if the thermal buoyancy forces are enhanced by increasing the gravitational acceleration. This has been realized by placing the test tank in a high speed centrifuge (up to 3000 rpm) at The Hans Ramberg Tectonic Laboratory (Uppsala); the centrifugal acceleration imposes an apparent gravity field several thousand times the Earth's gravity. By using this method, supercritical Rayleigh numbers up to 10 6 can be achieved in a transparent polymer fluid (SGM36) of Prandtl number 10 8. The carefully developed test tank and control unit, and a rigorous derivation of the conditions for dynamic similarity of convection in fluids with temperature- and stress-dependent rheology facilitates detailed laboratory studies of high Prandtl number convection. The working philosophy (section 2), equipment (section 3), non-Newtonian and temperature-dependent scaling procedure (section 4), and practical nomograms (section 5) are presented here to aid such laboratory studies. The significance of this new laboratory method for studying convection is outlined in section 6. Real convection experiments in high viscosity polydimethylsiloxanes now have the potential to contribute to the understanding of six major aspects of convection. These are: 1. (1) progressive deformation and displacement in three-dimensional convective flow fields, 2. (2) convective mixing, 3. (3) convection with high Prandtl numbers, 4. (4) non-Newtonian flow, 5. (5) temperature-dependent flow, and 6. (6) high Rayleigh number convection. Detailed applications will be discussed in a companion paper (Part 2 of the present project).