Magnetic susceptibility of magnetorheological fluids: Experimental assessment of mixing rules and an empirical formulation

This study systematically evaluates mixing-rule models for predicting the effective magnetic permeability of magnetorheological fluids (MRFs) from weak-field susceptibility measurements. Carbonyl iron powder suspensions in glycerol were prepared over 14 particle volume fractions, and their initial magnetic susceptibilities were measured experimentally. Additional measurements and validation tests were used to assess the robustness of the proposed empirical formulation beyond the primary fitted dataset. Nineteen classical and semi-empirical mixing rules were compared under identical experimental conditions. The results show that models neglecting concentration-dependent demagnetization effects may reproduce the overall monotonic trend but still produce systematic residual deviations across the investigated concentration range. Based on the Ollendorff and Gregorev–Kirko approaches, we propose an empirical OGK formulation that extends demagnetization-based mixing rules by introducing a concentration-dependent effective demagnetization correction. The OGK formulation is intended for low-field susceptibility/permeability data and should not be interpreted as a universal first-principles constitutive law. The three-parameter OGK 3 model is treated as the parsimonious baseline, whereas the four-parameter OGK 4 extension is retained only when supported by residual behavior, information criteria, cross-validation, and validation data. Within the investigated systems, this framework improves the representation of μ eff and of the inferred N eff , while requiring system-specific calibration.