Numerical study of the contact angle influence on equilibrium ferrofluid shapes

Abstract

The problem of forming equilibrium ferrofluid free surfaces, realized under the action of the magnetic field of a vertical line conductor and gravity, is considered. A ferrofluid drop is in contact with the vertical conductor and the horizontal plane on which it is located. The goal is to investigate the influence of contact angles of ferrofluid surface with solid boundaries of the conductor and the plane on equilibrium shapes of the free surface using numerical modelling. The mathematical model contains ordinary differential equations for the parametric representation of an axisymmetric free surface for a known magnetic field, generated by the conductor with a given current. The computational algorithm is constructed on a non-uniform adaptive mesh, based on a finite-difference approximation, in the form of recurrence relations. A comparative analysis of the equilibrium surface shapes is carried out for acute and obtuse contact angles