Rheology dictated spreading regimes of a non-isothermal sessile drop

Abstract

In the present work, within the framework of thin film theory, we delineate the interaction between the interfacial dynamics of thermal Marangoni flow and non-Newtonian rheology by considering a spreading droplet over a non-isothermal substrate. The numerical simulations, performed at different equilibrium contact angles $(\theta _e)$ , dimensionless thermocapillary strengths $(\beta )$ and shear-dependent viscosities $(n)$ , reveal that the fluid rheology nonlinearly influences the mechanisms of disjoining pressure and Marangoni stress. Accordingly, three distinct spreading regimes for non-Newtonian drops arise. Results indicate that the Marangoni film regime, having an approximate linear drop shape, sustains at lower $\theta _e$ , higher $\beta$ and $n$ ranges. Also, shear-thickening drops display an early onset of thermocapillary time scale and a steeper advancing front, while their shear-thinning counterparts retain a significant curvature for a much longer time. Contrastingly, the droplet regime is identified by fixed shape and uniform speed $(U)$ at higher $\theta _e$ and lower $(\beta$ , $n)$ combinations. Here, an intricate interplay between $\beta$ and $n$ realizes a sharp increase in $U$ for shear thinning compared with its invariance for shear-thickening droplets. The transition regime appears as an intermediate regime between the other two and involves multiple ruptured droplets. In all the regimes, we observe slower (faster) spreading of shear-thinning (thickening) droplets than the Newtonian droplets. In addition, the variations in $n$ cause intense characteristic modulations to spreading attributes like droplet morphology and transient spreading behaviour, and also act as a switching mechanism between different spreading regimes. These unique results may be utilized for superior control of non-isothermal biofluid droplets in microfluidics.