Influence of yield stress and shear thinning on the capillary ridge formation of gravity-driven Herschel-Bulkley fluid on an incline*

In this work on gravity-driven spreading, we discuss the impact of surface tension on the spreading and free surface shape of a finite bolus of a Herschel-Bulkley fluid. We incorporate surface tension into a 2D (i.e. 1D spreading) Herschel-Bulkley thin film flow model. Studies have indicated that incorporating surface tension can result in the emergence of a capillary ridge in thin fluid films and the capillary ridge is strongly related to contact line fingering instability. Our previous numerical study showed that increased shear-thinning (in a fluid without yield stress) suppressed the capillary ridge. A previous linear stability analysis by Balmforth \textit{et al}. (2007) showed that the yield stress in a Bingham fluid dampens the instability. Our numerical results in this study will provide initial insight on the impact of yield strength, shear-thinning index, and inclination angle on the overall spreading and appearance of the capillary ridge in Herschel-Bulkley fluids.