Exploiting the Temperature Dependence of Magnetic Susceptibility to Control Convection in Fundamental Studies of Solidification Phenomena
It is well known that convection is a dominant mass transport mechanism when materials are solidified on Earth's surface. This convection is caused by gradients in density (and therefore gravitational force) that are brought about by gradients in temperature, composition or both. Diffusion of solute is therefore dwarfed by convection and the study of fundamental parameters, such as dendrite tip shape and growth velocity in the absence of convection is nearly impossible. Significant experimental work has therefore been carried out in orbiting laboratories with the intent of minimizing convection by minimizing gravity. One of the best known experiments of this kind is the Isothermal Dendritic Growth Experiment (IDGE), supported by NASA. Naturally such experiments are costly and one objective of the present investigation is to develop an experimental method whereby convection can be- halted, in solidification and other experiments, on the surface. A second objective is to use the method to minimize convection resulting from the residual accelerations suffered by experiments in microgravity. The method to be used to minimize convection relies on the dependence of the magnetic susceptibility of a fluid on temperature or composition (whichever is driving convection). All materials experience a force when placed in a magnetic field gradient. The direction and magnitude of that force depend on the magnetic susceptibility of the material. Consequently the force will vary if the susceptibility varies with temperature or composition. With a magnetic field gradient in the right direction (typically upward) and of the right magnitude, this variation in the magnetic force can be made to exactly cancel the variation in the gravitational force. Expressed another way, normal buoyancy is exactly countered by a "magnetic buoyancy". To demonstrate the principle, a solution of MnC12 in water has been used. First the variation of the susceptibility of this paramagnetic solution with temperature and concentration was measured. Then a "cell", containing this solution and 50mm long by 15mm high by 155mm wide, was placed in a superconducting magnet at Marshall Space Flight Center. The magnetic field was measured at various positions within the bore of the magnet using a Hall effect probe. In this way, a position was found where the magnetic field gradient was predominantly upward; the magnitude of the gradient could then be adjusted by adjusting the current of the magnet. The ends of the cell consisted of machined copper blocks maintained at controlled temperatures by circulating water from constant temperature baths. The walls of the cell were of rectangular section glass tubing so that the cell contents could be seen. Velocities arising from thermal gradients within the cell were measured by particle image velocimetry (PIV). Particles used for this purpose were silver-coated hollow glass spheres of micrometers diameter and nearly the same density as the solution. A central vertical plane of the cell was illuminated by a laser beam passing through a cylindrical lens. Digital images of the particles were captured on a CCD camera and fed to a computer so that frame-to-frame movements of particles traveling with the fluid were captured. These images were employed to compute velocity maps using commercial PIV software. In a typical experiment the cold end of the cell was maintained at 10C and the warm end at 30 C. With no current in the magnet, i.e.- with natural -convection allowed to occur, the fluid was observed to circulate with an average speed of approximately 0.3 millimeters per second. It was visually apparent that this circulation was diminished as the current was increased. At currents of approximately 20A the flow was halted, to within the precision of the PIV measurements. At yet higher currents the convection was reversed with the hotter solution sinking and the cooler solution rising. At 40A this reversed convection had speeds averaging 0.43 millimeters per second. The measurements of susceptibility and density allow an estimate of the field gradient necessary to halt convection in the experiment. That estimate was 7.8T (squared) per meter and the convection was observed to halt in the magnet at a current giving 7.21T (squared) per meter from the magnetic field measurements. Calculations of the flow have been carried out using the computational fluid dynamics software FLUENT and show good agreement with the measurements.