We numerically investigate wettability-gradient-driven propulsion of a shear-thinning droplet on micro-textured and confined substrates. The droplet rheology is modelled using the Carreau–Yasuda constitutive relation, and interfacial dynamics are resolved using a finite-element level-set framework incorporating consistent slip regularization and mesh-independent resolution. We develop a scaling analysis from the numerical framework, establishing the coupled dependence of droplet propulsion on wettability gradient, confinement, roughness, and contact-line dynamics. This is achieved through non-dimensional parameters including capillary number (Ca), roughness height ( \(\upbeta \) ), and rescaled slip length ( \(\varepsilon \) ), providing mechanistic insights into wettability-driven transport of non-Newtonian fluids. A theoretical scaling relation describing roughness-dependent propulsion is further developed and validated against numerical results. Droplet propulsion exhibits a non-monotonic dependence on the flow behaviour index, with optimal transport arising in shear-thinning regimes that enhance internal circulation while balancing kinetic energy generation and viscous dissipation. Surface texture strongly modulates contact-line stresses; triangular asperities generate the highest propulsion by amplifying local shear and sustaining pressure imbalance. Roughness height and confinement ratio both display optimal intermediate ranges, beyond which contact-line distortion, curvature-induced resistance, and increased hydrodynamic resistance suppress motion. The results identify the coupled roles of rheology, texture, confinement, and energetics in governing passive droplet transport on wettability-graded surfaces.
