Rheology and micromechanical constitutive modelling of Pickeringemulsion-stabilized bidisperse magnetorheological fluids via drying-free preparation

Magnetorheological (MR) fluids are field-responsive complex fluids whose macroscopic response is governed by magnetic-field-induced microstructural evolution, but whose use is limited by the trade-off between sedimentation stability and shear yield stress arising from the density mismatch between the particles and the carrier liquid. Classical micromechanical models assume idealized single-phase suspensions and cannot describe the transition from planar chains at low field to three-dimensional packing at high field, or the multiphase microstructure introduced by a secondary solvent. We study a ternary oil-to-ethanol-to-particle MR fluid in which amphiphilic multi-walled carbon nanotube/graphene oxide (MWCNT/GO)-coated bidisperse carbonyl iron particles stabilize a Pickering emulsion. Two sample series charged on different bases are reported separately and never combined. A hybrid planar close-packed to body-centered-cubic (PCP-BCC) model with Pickering-emulsion correction terms follows from the magnetic-dipole interaction energy. A continuous structural-transition coefficient describes the evolution from planar chains to three-dimensional BCC packing with field and concentration, calibrated over the 28-34 vol% range at one bidisperse size ratio, which is not an independent variable of the model. The mutually non-identifiable coefficients reduce to a single identifiable group, c₁λ = 1.53 × 10⁴. Within the second series the formulation carried forward (31 vol%, oil-to-ethanol mass ratio 4) gives a 60-day sedimentation ratio of 17.4%, a zero-field viscosity of 1.35 Pa·s at 92 s⁻¹ and a saturation yield stress of 24.8 kPa at 1.0 T. The hybrid model reaches a maximum fitting error of 4.74% at the intermediate volume fraction of 31 vol%, against 5.52% for the end-state chain model at 28 vol% and 3.40% for the end-state packing model at 34 vol%. Without adjustable parameters, the classical single-chain limit over-predicts the measured yield stress by a factor of about 3.4. The framework links Pickering-emulsion microstructure, field-driven assembly and macroscopic rheology in multiphase complex fluids.