Contribution of wedge and bulk viscous forces in droplets moving on inclined surfaces

Employing direct numerical simulations, we investigate water and water-glycerol (85 wt%) droplets ( \(\sim \) $\sim$ 25 µL) moving on smooth surfaces, with contact angles of around 90 \(^{\circ }\) ${}^{\circ }$ , at varying inclinations. Our focus is on elucidating the relative contribution of local viscous forces in the wedge and bulk regions in droplets to the total viscous force. We observe that, for fast-moving droplets, both regions contribute comparably, while the contribution of the wedge region dominates in slow-moving cases. Comparisons with existing estimates reveal the inadequacy of previous predictions in capturing the contributions of wedge and bulk viscous forces in fast-moving droplets. Furthermore, we demonstrate that droplets with identical velocities can exhibit disparate viscous forces due to variations in internal fluid dynamics.