Electroosmotic flow of Jeffrey ternary hybrid nanofluids in converging–diverging ciliary microvessels

The intricate behavior of blood flow conveying multiple nanoparticles through micro-scale biological channels remains insufficiently understood, particularly under physiological conditions involving diverging and converging ciliary microvessels. A key challenge lies in capturing the combined effects of complex body forces and non-Newtonian fluid characteristics when ternary-hybrid nanoparticles specifically tricalcium phosphate Ca₃(PO₄)₂,TiO₂ (titanium dioxide), and Cu (copper) are introduced into the bloodstream. Existing models often fail to represent the synergistic interactions among electrokinetic, magnetic, and elastic influences in such flows. This study addresses the gap by formulating a mathematical model for the dynamics of a Jeffrey fluid representing blood, embedded with Ca₃(PO₄)₂, TiO₂, and Cu ternary-hybrid nanoparticles, flowing through a diverging/converging ciliary micro-vessel. The model accounts for electroosmosis forces, Lorentz forces, buoyancy, heat generation, and ciliary movement. The governing nonlinear equations are non-dimensionalized and solved using the homotopic perturbation method (HPM) to derive analytical approximations. Findings reveal that electro-osmosis and the Helmholtz-Smoluchowski slip velocity significantly enhance fluid motion in the central region of the vessel, whereas resistance dominates at the periphery. Cilia elongation reduces the circulation efficiency of the nanofluid. In addition, diverging vessels facilitate higher heat dissipation than converging ones, making them preferable for biomedical procedures requiring precise thermal control.