The impingement mechanism of a liquid droplet on a solid torus surface is demonstrated using numerical simulations and an analytical approach. A computational model employing the volume of fluid method is developed to conduct simulations for the present investigation. Several influencing parameters, namely, diameter ratio (Dt/Do), contact angle (θ), initial droplet velocity (described by Weber number, We), surface tension (specified by Bond number, Bo), and viscosity of liquid drop (described by Ohnesorge number, Oh) are employed to characterize the impacting dynamics of a water drop onto a stationary toroidal substrate. The pattern of temporal and maximum deformation factors is elaborated by considering various relevant influencing factors to describe the fluidic behavior of the drop impingement mechanism. The key findings indicate that the developed central film gets ruptured at the early stage when the value of Dt/Do is lower because a relatively thin film is developed. Concomitantly, the very tiny drops get pinched off at Dt/Do= 0.83, whereas the detached drops are relatively large-sized in the case of lower Dt/Do= 0.16 due to the higher drainage rate of liquid mass through the hole at lower Dt/Do. It is also revealed that the first pinch-off is found to be faster with the continual upsurge of We for a specific value of Dt/Do and θ. Aside from that, efforts are made to show a scattered regime map in order to differentiate the pattern of droplet configuration during impingement. We have also attempted to establish a correlation that effectively characterizes the maximum deformation factor, which closely matches with the numerical findings. The developed correlation exhibits a firm agreement with the numerical data within deviations of 8.5%. Finally, an analytical framework is formulated to predict the deformations factor, which closely agrees with the computational findings.
