Magnetic permeability of inverse ferrofluid emulsion: Nonlinear ferrofluid magnetization law

•The droplets elongation provide a growth of permeability of the emulsion.•Ferrofluid magnetization law is provide a decline of permeability of the emulsion.•The polydispersity of droplets – a fitting parameter of the model. This paper is devoted to the mathematical modeling of the nonmonotonic and nonlinear behavior of the magnetic permeability of inverse ferroemulsion under the influence of a uniform external magnetic field (Dikansky et al., 2011). The presented model is an extension of the model developed for the case of weak external magnetic field (Subbotin, 2018), in which the ferrofluid magnetization law is linear. The nonlinear ferrofluid magnetization law is taken into account via the first-order modified mean-field theory (MMF1) (Ivanov et al., 2001). The results show a good qualitative and quantitative agreement with the experimental data.