Analysis of magnetic fluid displacement in capillaries

Abstract

This work presents a theoretical, numerical and experimental investigation on the shape and vertical displacement of a free surface formed in the interface between a magnetic fluid and a non-magnetic one. The magnetic fluid is confined between two parallel vertical flat plates. The presence of an external magnetic field applied by a permanent magnet arbitrarily positioned in space is considered. A new mathematical model is proposed, leading to a nonlinear differential equation that governs both the shape and the vertical displacement of the free surface due to capillary and magnetic effects. The applied field considered in this work satisfies the Ampere–Maxwell equation in the magnetostatic limit. This equation is numerically solved by direct integration using a fourth-order Runge–Kutta method coupled with a Newton–Raphson scheme. The numerical code is validated by means of some analytical solutions valid on specific asymptotic limits and by experimental results. Experimental measurements of surface tension, density and vertical displacement of Newtonian fluids in capillaries are also presented in order to provide a new methodology to estimate the contact angle combining experiments and numerical integration results. The influence of the variation of the physical variables concerning the physics of the problem on the shape and on the vertical displacement is evaluated. An increase in the intensity of the magnetic effects resulting in an increase in the vertical displacement and in the asymmetry degree of the free surfaces is observed. Finally, relevant physical discussions exploring how this long range interaction between the applied field and the magnetic liquid could be applied to promote fluid displacement in capillaries are presented.