Evolution of the impact force of supercooled water droplets with different shapes on a superhydrophobic cold surface

We conducted a numerical study on the evolution of the impact force of supercooled water droplets with different shapes when they do not fully rebound on a superhydrophobic cold surface. The evolution of peak impact forces and their characteristic times with Weber number (We) were focused. The presence of a cold surface had a relatively less influence on the evolution of the first peak impact force but had a significant influence on the second peak impact force when We > 60. The sudden increase in the second peak impact force was closely related to the formation and subsequent collapse of cylindrical-like structures inside impinging water droplets. To incorporate the quantitative influence of droplet shapes, we introduced correction factors based on the aspect ratio (AR) in the fitting expressions for peak impact forces and their characteristic times. Specifically, we utilized AR (AR <= 1.0) and AR(1/6) (AR >1.0) when 3 < We < 40, or AR(4/3) (AR <= 1.0) and AR(1/2) (AR > 1.0) when 40 < We < 100 as correction factors for the first peak impact force. Moreover, we employed AR(-2) as the correction factor for the first peak characteristic time and AR(-1/3) for the second peak characteristic time. These corrections extended the applicability of the fitting expressions to supercooled water droplets with different shapes.