Convection in a spherical capacitor

Abstract

Real-time holographic interferometry and shadowgraph visualization are used to study convection in the fluid between two concentric spheres when two distinct buoyancy forces are applied to the fluid. The heated inner sphere has a constant temperature that is greater than the constant temperature of the outer sphere by ΔT. In addition to the usual gravitational buoyancy from temperature induced density differences, another radial buoyancy is imposed by applying an a.c. voltage difference, ΔV between the inner and outer spheres. The resulting electric field gradient in this spherical capacitor produces a central polarization force. The temperature dependence of the dielectric constant results in the second buoyancy force that is especially large near the inner sphere. The normal buoyancy is always present and, within the parameter range explored in our experiment, always results in a large-scale cell that is axisymmetric about the vertical. We have found that this flow becomes unstable to toroidal or spiral rolls that form near the inner sphere and travel vertically upward when ΔT and ΔV are suffciently high. These rolls start near the centre sphere's equator and travel upward toward its top. The onset of this instability depends on both the temperature difference at onset ΔTc and the voltage difference at onset ΔVc and these two quantities appear to be related, within the parameter range accessible to our experimental system, by a power law ΔVc ∝ ΔT1/3c. Measurements of the heat transfer show that these travelling rolls increase the heat transfer at onset. Far above onset, the heat transfer may actually decrease with increasing ΔT. The travelling roll's frequency increases with increasing ΔT near onset and with increasing ΔV far above onset. These results have been interpreted in terms of a flow structure that includes a thermal boundary-layer-like behaviour. This layer has a radial width that increases from the bottom pole to an unstable ‘latitude’ near the equator where the rolls appear.