Prediction and optimization of large-scale droplet evaporation dynamics using a critical spacing algorithm

The large-scale droplet evaporation mechanism has a key impact on industrial applications such as spray cooling and printed displays. In this study, we developed a theoretical algorithm based on the concept of a critical shading distance to predict the evaporation rate and lifetime of droplet arrays. Exceptionally, the analysis was extended to an array containing 10 000 droplets. The results reveal that the evaporation lifetime gradually increases from the array edges toward the center, eventually converging to a stable value at the center. Notably, the width of the transition region, where the evaporation lifetime increases, does not continue to expand with the overall size of the array. However, the topological characteristics of the droplet array, such as droplet spacing and contact angle, exert a significant influence on the size of this transition region. Among these factors, increasing the droplet spacing is the only adjustment that effectively enhances the uniformity of evaporation time across the array. Finally, experimental measurements confirm the accuracy of the proposed theory, demonstrating that the evaporation times of corner and center droplets remain essentially unchanged as the array size increases.