Modeling the Squeeze Flow of Droplet over a Step

In this paper, we study the squeeze flow of a droplet confined between two plates in the presence of a step. Understanding this fluid mechanics problem is of the utmost importance particularly for nanoimprint lithography, wherein the photoresist droplets are dispensed on a substrate and imprinted and cured into a desired pattern. Often, the desired pattern includes various steps and trenches, and the droplets need to flow over. Here, we use the lubrication theory to find the instantaneous pressure and velocity fields. A volume-of-fluid advection algorithm is also used for evolving the volume fraction in time. The obtained results reveal that for step sizes comparable to the gap between plates, the squeeze flow characteristics become quite distinct across the step. Under such circumstances, the fluid finds it less expensive to reverse its flow direction toward the deep region to pass through the low-resistance zone, which leads to a net mass flow rate across the step from a shallow to deep region. Such a mass transfer is found to be enhanced by applying larger squeezing forces. This phenomenon becomes less noticeable for liquid film thicknesses much larger than the step size. As a result, it takes large droplets a longer time to reach to the regime wherein a substantial mass flow rate occurs. In addition, the results suggest that the dimensionless characteristic features, such as the ratios of volume and area of liquid in the deep (or shallow) region to those of the total liquid, collapse onto their corresponding master curves.