An Energy Approach to the Calculation of Forces Acting on Solid Bodies in Ferrofluids

The main advantages of the energy approach to solving the problem of determining magnetic forces acting on solid bodies immersed into magnetized ferrofluids (FFs) are shown. Characteristic disadvantages of the standard approach to the calculation of magnetic forces using the Bernoulli equation for FFs and an equation for the magnetic pressure jump at the interface are considered. A review of works devoted to the study of forces acting on solid bodies immersed in magnetized FFs is presented. This literature review convincingly demonstrates the need for and potential advantage of using the energy approach to these problems, since the analytical expressions significantly depend on the body shape and obtaining the final numerical results is complicated by the error of magnetic field calculation at the "solid body-FF" interface where the normal component of induction and the tangential component of the magnetic field exhibit a discontinuity. In contrast, the energy approach allows using the standard functions of program packages for determining thermodynamic potentials. The choice of a thermodynamic potential correctly describing experimental data is discussed. The method of magnetic energy determination is justified by the problem setting and verified by comparison of the results of several numerical solutions obtained using the open software package FEMM for FFs obeying a nonlinear magnetization law. This analysis was previously performed neither experimentally nor theoretically in view of the commonly accepted use of simplifying assumptions (approximations of weak and strong magnetic fields or a noninductive approximation). Here, the energy approach to determining forces acting on solid bodies in FFs has been justified by pairwise comparison of the results obtained in the framework of this approach to the data of laboratory experiment and the results of standard calculations.