Fall and fingering of miscible magnetic fluid drops in a Hele-Shaw cell

Abstract

The presented study is the experimental and numerical investigation of the fall and fingering of miscible magnetic fluid drops with variable properties in a vertical Hele-Shaw cell under a uniform field normal to the cell plane. We revealed that fingering is possible in magnetic fields that exceed the critical value. For the kerosene-based magnetic fluid used in the experiment and a droplet with a radius of about 3 mm, the critical value of the magnetic field strength was about 2 kA/m. It was found numerically that the distance between the fingers is linearly related to the width of the gap in the Hele-Shaw cell, and for the studied cases it is described by the expression λ = 1.19δ for the magnetic field of about 15 kA/m. The distance between the fingers decreases with the increase of the magnetic field in the region of weak magnetic fields, and with a further increase of the magnetic field, it hardly changes. The velocity of the droplet fall is determined by its morphology. With an increase in the number of fingers, the velocity of the fall decreases significantly. With the maximum value of the parameters numerically studied, the fall velocity decreased 2.5 times. As the number of fingers increases, the rate of mixing of magnetic fluid with the environment increases sharply. During the drop-fall time, the maximum concentration of magnetic fluid decreased 4 times at the maximum value of the parameters studied. However, in the absence of a magnetic field, without fingering, it remained practically unchanged.