Numerical approach and experimental verification for interface shape determination between layered fluids subject to a magnetic field

Various applications of magnetic fluids involve interface phenomena. The analysis of the hydrostatic interface shape between two immiscible liquid layers, especially under magnetic field influence, is the first step to understand the accompanying complex dynamic phenomena as well as to providing reliable numerical capabilities for their accurate prediction. This study presents a relatively simple numerical approach, and the accompanying theory, to reliably define the meniscus shape in a two-layered fluid system in presence of a horizontal magnetic field with a vertical gradient. In the course of the study, two dimensionless parameters have been derived to describe the magnetic pressure jump at the interface and the magnetic body force throughout the volume. These parameters are used to interpret the results of the analysis and to show that a horizontal magnetic field tends to flatten the meniscus shape at the interface despite of the direction of its vertical gradient.