Suppression of channel convection in solidifying Pb-Sn alloys via an applied magnetic field

Abstract

Channel convection through the porous, dendritic mushy zone in solidifying alloys results from a nonlinear focusing mechanism, whereby liquid enriched in the solute melts dendrites as it convects away from the solid. The local melting reduces the parameterized (Darcy) viscous force and increases the flow speed to form a convective channel. However, it has been predicted that an applied magnetic field might prevent channels from forming because, as the Lorentz force replaces the Darcy force as the primary resistance to flow, the retarding force becomes less sensitive to the lengthscale of the flow, so that the focusing mechanism no longer operates. In this study, it is found experimentally that, as predicted, an applied horizontal magnetic field can suppress channel convection when Q m , the Chandrasekhar number appropriate to a mushy zone, exceeds an order of one. The nondimensional number Q m is a measure of the strength of the Lorentz force relative to the Darcy force in the mushy zone and, for a given magnetic field, is much smaller than the analogous Chandrasekhar number (Q) for the fluid melt, since the Darcy force in the mushy zone far exceeds the viscous force in the fluid. Previous experimental work failed to find that magnetic fields could suppress channel convection because, although Q exceeded an order of one, Q m did not. For experiments with a smaller cooling rate, and, thus, a larger permeability and larger mushy zone Rayleigh number (Ra m ) a stronger magnetic field is necessary to suppress channel convection. The longitudinal macrosegregation is not affected by the absence of channel convection, suggesting that such channels are not always primarily responsible for the mass flux between the mushy zone and the melt.