Energy approach to calculation of forces acting on solid bodies in ferrofluids

For calculations of magnetic forces acting on solid bodies immersed in magnetized ferrofluid (FF), use of the energy approach is discussed The limitations of the standard approach to the calculation of these magnetic forces are analyzed using the Bernoulli equation for the FF and the equation for the magnetic pressure jump at the interface. The literature review reveals the advantages of the energy approach over the standard approach, in which the analytical expressions for the forces depend on the body shape, and the final numerical result is affected by a significant error in calculating the magnetic fields at the "solid body-FF" interface. The energy approach, on the contrary, allows using standard functions of computational packages. Choosing a thermodynamic potential for the adequate description of experimental measurements is discussed. The energy method is justified via the statement of the problem and verified by comparing the numerical results obtained for the FF with the nonlinear magnetization law, which has not yet been carried either analytically or numerically due to the widespread use of simplifying assumptions (approximation of weak and strong magnetic fields, non-induction approximation). A pairwise comparison of the magnetic forces calculated in the framework of the energy approach with the results of the laboratory experiment and the data obtained by a standard approach provides evidence that the energy approach can be used to calculate forces acting on solids in the FF.