Predicting High-Concentration Aggregation in Magnetic Colloidal Suspensions Using Tunnel Theory

Accurate prediction of aggregation in suspensions is crucial for diverse engineering applications. This paper develops a sequential theoretical strategy, based on tunnel theory, to predict the aggregation configuration in magnetic compound fluids (MCF) by evaluating their volume concentration Cv. We formulated the viscosity η, resistance R, and capacitance C resulting from aggregation as functions of Cv. This involved a theoretical procedure using tunnel theory, refined using experimental data, including vertical force Fv arising from the concentration gradient, as well as electrical conductivity σ and permittivity ε. The theoretical formulation for η was further refined by considering hypothetical aggregation configurations, specifically non-uniform particle distribution and agglomerations approximated as spheroids with axis ratio κ, along with experimental data on shear flow. For R and C, the formulations were refined using experimental data for σ and ε, together with the relationship between Cv and the applied magnetic field Hv derived from tunnel theory and Fv. This sequential theoretical analysis yielded final formulations for η, R, and C as functions of Hv and initial volume concentration Cv,o. Specifically, η was expressed as a function of κ and Cv,o for the shear and stress‒shear strain γ’ relationship under conditions of Hv < 200 mT, 11 < Cv,o < 30 vol.%, and γ’ < 300 1/s. R and C were determined under conditions of Hv < 150 mT and 11 < Cv,o < 30 vol.%. These findings pave the way for novel theoretical predictions of Cv, R, and C based solely on Hv data, a capability crucial for designing diverse materials.