The maximum spreading of a shear-thinning fluid droplet impacting on solid surfaces

The maximum spreading diameter of shear-thinning fluid droplets impacting a solid surface is critical due to its important role in industrial applications. We have numerically simulated the shear-thinning fluid droplet impacting on a solid surface by phase-field method and investigated the maximum spreading ratio βmax. The shear rate is a crucial parameter for analyzing βmax of the shear-thinning fluid droplets. We observe variations in the shear rate during droplet spreading and find the shear rate increases as impact velocity increases and viscosity decreases. In addition, a new expression for the effective shear rate γ̇eff is proposed, which primarily depends on the shear rate in the high-shear rate region. Then, the maximum spreading of shear-thinning fluid droplets with various rheological parameters are investigated. The results indicate that the shear-thinning property affects droplet maximum spreading when the second critical shear rate is high and the shear-thinning fluid droplet can be regarded as a Newtonian droplet with a viscosity of infinite shear viscosity when the second critical shear rate is low. To determine whether the second critical shear rate is either high or low, the shear rate difference γ̇d is defined. The scaling of βmax for the shear-thinning fluid droplet is also proposed and can be applied to various rheological models for shear-thinning fluids.