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<p>Magnetorheological (MR) fluids exhibit field-dependent rheological behavior arising from the reversible formation of particle chains under applied magnetic fields. Predicting the static yield stress of these systems remains a central challenge in their modeling and design. This work presents a closed-form analytical expression for the yield stress of MR fluids, derived from a particle-scale formulation that incorporates multipolar magnetic interactions and microstructural descriptors. The model explicitly accounts for the average number of interparticle contacts and the inclination angle of the chains relative to the internal magnetic field within the suspension, based on a simple microstructural hypothesis involving chain-like aggregates. A mechanical stability criterion is also formulated by identifying a critical inclination angle, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\theta _{\textrm{c}}\)</EquationSource> </InlineEquation>, below which chains remain stable under the combined influence of magnetic attraction and hydrodynamic shear. This condition is obtained from force and torque balance at the chain–particle level and is applicable over a wide range of experimental conditions. Model validation is performed through complementary comparisons: the yield stress predicted by the model is directly contrasted with experimental data, while the corresponding chain inclination angles reconstructed from these measurements are compared with theoretical predictions of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\theta _{\textrm{c}}\)</EquationSource> </InlineEquation>. The results show that the formulation captures observed trends and outperforms classical dipolar approaches across diverse particle sizes, magnetic properties, and field strengths, with confirmed applicability up to <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\phi \lesssim 0.20\)</EquationSource> </InlineEquation>. Additionally, an analysis of competing interparticle forces reinforces the assumptions underlying the model and its domain of applicability.</p>

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Contact distribution–based prediction of yield stress in magnetorheological fluids

  • 期刊论文

  • 发表日期：

    2025年11月14日

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  • Manuel J. Espín

摘要

Magnetorheological (MR) fluids exhibit field-dependent rheological behavior arising from the reversible formation of particle chains under applied magnetic fields. Predicting the static yield stress of these systems remains a central challenge in their modeling and design. This work presents a closed-form analytical expression for the yield stress of MR fluids, derived from a particle-scale formulation that incorporates multipolar magnetic interactions and microstructural descriptors. The model explicitly accounts for the average number of interparticle contacts and the inclination angle of the chains relative to the internal magnetic field within the suspension, based on a simple microstructural hypothesis involving chain-like aggregates. A mechanical stability criterion is also formulated by identifying a critical inclination angle, \(\theta _{\textrm{c}}\) , below which chains remain stable under the combined influence of magnetic attraction and hydrodynamic shear. This condition is obtained from force and torque balance at the chain–particle level and is applicable over a wide range of experimental conditions. Model validation is performed through complementary comparisons: the yield stress predicted by the model is directly contrasted with experimental data, while the corresponding chain inclination angles reconstructed from these measurements are compared with theoretical predictions of \(\theta _{\textrm{c}}\) . The results show that the formulation captures observed trends and outperforms classical dipolar approaches across diverse particle sizes, magnetic properties, and field strengths, with confirmed applicability up to \(\phi \lesssim 0.20\) . Additionally, an analysis of competing interparticle forces reinforces the assumptions underlying the model and its domain of applicability.