Motion of Miscible Magnetic Fluids in a Vertical Capillary Tube

An experimental study of miscible magnetic fluid motion in a vertical capillary tube is presented. Transporting ferrofluids is dominated by a dimensionless magnetic number Ma, which characterizes the ratio of upward magnetic force to the downward gravity. Two distinct stages of motion, referred to as the sub-critical mode of finite lift and the effective transportation, are identified. These two modes are determined by the values of the sub-critical magnetic number Ma(sub) and critical magnetic number Ma(cr) respectively. For the cases of sub-critical mode (Ma(sub) < Ma < Ma(cr)), the ferrofluids are lifted to quasi-equilibrium heights, which are nearly proportional to the magnetic number Ma. As for the situations of effective transportation (Ma > Ma(cr)), a penetrating finger of ferrofluids is formed similar to the conventional miscible displacements. A dimensionless proportionality of fingertip velocity v, magnetic number Ma and field distribution profile f(z) is obtained as v similar to Ma(1/2) f(z) by scaling arguments. This proportional correlation shows a good agreement with the experiments.