Formation of the Apparent-Density Field in Ferrofluids Under Gradient Magnetic Fields: Theory and Quantification Through Magnetic Additional Pressure

Abstract

Spatially nonuniform magnetic fields generate magnetic body forces in ferrofluids, causing internal pressure redistribution and altering the effective buoyancy of immersed objects. This effect is often described as an apparent-density field, yet direct quantification remains difficult in opaque ferrofluids under strong field gradients. Here, we establish a quantitative relationship between magnetic additional pressure and apparent density. Internal pressure is directly measured using an immersed pressure sensor, and the apparent-density distribution is reconstructed accordingly. The model is validated by experiments and multiphysics simulations incorporating measured magnetization curves rather than assuming saturation. Infrared thermography of density-calibrated spheres is used to identify equilibrium levitation positions and independently assess the predicted field. The measured pressure agrees closely with simulations. The inferred apparent density matches levitation positions with a mean relative error of 3.9%, while reconstructed profiles agree with simulations, with errors below 10% for water-based ferrofluid and below 5% for oil-based ferrofluid.