Forma, Vol. 9 (No. 1), pp. 37-50, 1994
Original Paper

Instability of the Water-Ferrofluid Interface and the Formation of Labyrinthian Structure in a Hele-Shaw Cell

Takashi Chuda and Osamu Sano

Department of Physics, Faculty of General Education, Tokyo University of Agriculture and Technology, Fuchu, Tokyo 183, Japan

(Received February 26, 1994; Accepted April 11, 1994)

Keywords: Ferrofluid, Labyrinthian Structure, Numerical Simulation, Minimum Potential, Horton's Law

Abstract. An instability criterion of an initially flat interface of magnetic and nonmagnetic fluids confined in a Hele-Shaw cell, to which a uniform magnetic field is applied perpendicularly, is given analytically. Numerical simulation is made to investigate onset and further development of a perturbed interface. In the latter case, the direction of growth of the finger is determined each time by choosing the local minimum of the magnetic potential energy. Statistical properties of the resulting labyrinthian structure are similar to those observed in experiments.