Shear-Dependent Power-Law Rheology Meets Nonlinear Thermocapillarity

The spreading of sessile droplets under thermocapillary actuation has been extensively studied; however, the interplay between nonlinear thermocapillary effects and shear-dependent rheology remains largely unexplored. Here, we present a theoretical framework to unravel this complex physics by considering a self-rewetting droplet that is subjected to a uniform temperature gradient, whereas the generalized Newtonian model captures the rheology of both shear-thinning and shear-thickening fluids. Departing from linear surface tension assumptions, we consider a nonlinear temperature dependence, revealing a different scaling law for droplet spreading. Three distinct spreading regimes emerge: degenerated Marangoni film, accelerated droplet, and a transition zone. The combined interplay between the nonlinear thermocapillary effect and the shear-dependent viscous nature of the fluid plays a critical role in determining the existence and characteristics of these regimes. Shear-thickening fluids flatten curvature but enhance spreading, while shear-thinning fluids delay entry into the nonlinear regime. Self-rewetting droplets show accelerated movement due to position-dependent Marangoni stress and may fragment under high stress in shear-thickening cases. The nonlinear relationship between viscous resistance and shear rate modifies the force balance governing spreading. These findings may enable new microfluidic methods for precise droplet control, mixing, and targeted delivery.