Magnetic control of convection in nonconducting diamagnetic fluids

Abstract

Inhomogeneous magnetic fields exert a body force on electrically nonconducting, diamagnetic fluids. This force can be used to compensate for gravity and to control convection. The field effect on convection is represented by a dimensionless vector parameter ${\mathbf{R}}_{m}=({\ensuremath{\mu}}_{0}\ensuremath{\alpha}{\ensuremath{\chi}}_{0}{d}^{3}\ensuremath{\Delta}T/{\ensuremath{\rho}}_{0}\ensuremath{\nu}{D}_{T})(\mathbf{H}\ensuremath{\cdot}\mathbf{\ensuremath{\nabla}}\mathbf{H}{)}_{\mathbf{r}=0}^{\mathrm{ext}},$ which measures the relative strength of the induced magnetic buoyancy force due to the applied field gradient. The vertical component of this parameter competes with the gravitational buoyancy effect and a critical relationship between this component and the Rayleigh number is identified for the onset of convection. Magnetically driven convection should be observable even in pure water using current technology.