Coupled electrohydrodynamic and Carreau rheology effects on droplet migration in confined microchannels

Purpose This study aims to investigate the coupled effects of electrohydrodynamic (EHD) forcing, shear-thinning rheology, geometric confinement and electrical property contrasts on the lateral migration of a Newtonian droplet suspended in a Carreau fluid flowing through a confined microchannel. The objective is to establish the underlying migration mechanisms and identify controllable migration regimes for microfluidic applications. Design/methodology/approach A phase-field finite-element framework based on the coupled Cahn–Hilliard–Navier–Stokes equations and the Taylor–Leaky dielectric model is used to simulate droplet migration under plane Poiseuille flow subjected to a uniform transverse electric field. The effects of electric capillary number (CaE), Carreau number (Cu), confinement ratio and conductivity-to-permittivity ratio (R/S) are systematically examined to quantify their influence on droplet dynamics and migration behaviour. Findings The results reveal three distinct migration regimes: centreline focusing, off-centre equilibrium and wall-directed migration. The direction of migration is primarily governed by the R/S through the reversal of the EHD circulation, with inward migration occurring for R > S and outward migration for S > R. Increasing electric field strength enhances EHD-induced migration, while stronger shear-thinning reduces viscous resistance, accelerates transient migration and shifts regime boundaries towards weaker electric fields. Increased confinement suppresses outward migration by strengthening wall-induced hydrodynamic interactions. A comprehensive regime map is developed that predicts droplet migration behaviour under the combined influence of electric forcing and non-Newtonian rheology. Practical implications The results provide design guidelines for controlling droplet focusing, sorting and positioning in electro-microfluidic devices by independently tuning electric field strength, carrier-fluid rheology and channel confinement. Originality/value Unlike previous studies that primarily considered electric forcing, non-Newtonian rheology or confinement separately, this work systematically resolves their coupled influence on droplet migration in a confined microchannel. This study establishes the role of electrical-property contrast in reversing migration direction, identifies three distinct migration regimes through a (CaE–Cu) regime map and reveals non-monotonic migration with transient reversal under strong shear-thinning. These results provide a unified mechanistic framework for controlling droplet positioning through electric field strength, rheology and confinement.