Retraction of a highly viscous shear-thinning liquid sheet

The retraction of liquid sheets arises in many applications, such as atomization and coating. For example, atomization processes involve a cascade from fluid volumes to sheets to filaments to droplets and require an understanding of the retraction dynamics. While the retraction dynamics of Newtonian sheets have been studied extensively, that of non-Newtonian sheets, characterized by complex rheological behavior, remains largely unexplored. Here, we analyze the retraction of a highly viscous shear-thinning liquid sheet. Using the Carreau constitutive model and 1D slender-sheet equations, we derive asymptotic solutions for the evolution of the tip velocity and maximum film thickness for three different regimes of the Carreau number, representing the relative importance of shear thinning to viscous-capillary effects. Our analysis also provides insight into the retraction of shear-thickening sheets. We show that while shear-thinning rheology expedites the retraction dynamics of highly viscous sheets, the shear thickening slows it down. We supplement our analytical results with numerical simulations and find excellent agreement.