The compressive stress in the Van der Waals state equation is coupled into the SPH model to simulate the droplet's surface tension. To improve model's stress stability, the tensile stress and compressive stresses are calculated, respectively with a modified Quintic kernel function and a Bell-Shaped kernel function. The model is verified by simulating the droplet impact on super hydrophobic surface, and the numerical result is in good agreement with experiment data. Furthermore, the solid surface's frictional stress and its effective region are analyzed. It is shown that, when the wall relative infiltration diameter φ<1, the effect of the solid surface viscosity υ' on the droplet's spreading is not significant. When φ≥1, under the same condition, the droplet spreading velocity and φ_max (maximum φ) will decrease with the increase of υ'. During the spreading process φ≥1 is the main effective region of the frictional stress. The time taken to achieve the φ_max at different υ' sees very small change, so υ' has little influence on the spreading time. Under the same solid boundary condition, the frictional stress of the spreading droplet will increase with the increase of the impact velocity ν₀. The relation between υ' and ν₀ is roughly in a parabola.

SPH  /  tension instability  /  kernel function  /  droplet impact  /  super-hydrophobic surface