Recoil Cavity Formation and Collapse for Drop Impact on Sieves

Abstract

The principle underpinning most printing technologies rely on is the formation and subsequent collapse of cavities to generate high-speed jets or droplets. Traditional methods, such as the Worthington jet or bubble-based cavity, utilize the collapse mechanism to give rise to a high-speed liquid jet. In contrast to known cavity collapse processes, a distinct phenomenon occurring during droplet impact on a superhydrophobic sieve is reported. Herein, the collapse of the impact cavity causes an air jet to rise through the sieve pore to form a "recoil cavity." Subsequently, the recoil cavity collapses to eject a jet (droplets). The notable discovery is the emergence of the recoil cavity as a result of the impact cavity's collapse, which has been absent on any other surfaces. The present research explores the underlying mechanism and develops a model of the phenomenon. It is found that the process follows the principle of energy conservation, with a threshold energy flux ratio between impact and recoil driving the ejection of a single drop. These findings provide valuable insights for understanding drop impact printing techniques, which can be applied across various fields, including electronics, biology, and structural printing.

Keywords: cavity collapse; droplet impact; recoil cavity; sieve; superhydrophobic.

Figure 1

Formation and collapse of a recoil cavity for impact on a superhydrophobic mesh. A) Schematic of cavity dynamics for drop impact over the superhydrophobic surface. Collapse of the impact cavity drives a jet from the top. B) For drop impact on a superhydrophobic sieve, the impact cavity pinch‐off drives the formation of the recoil cavity. The collapse of the recoil cavity leads to a single droplet ejection. C) Schematic showing the mechanism of recoil cavity formation.

Figure 2

Evolution of cavity dynamics for: A) We = 3.65; B) We = 5.47; and C) We = 7.66. Schematic in the red dotted box shows the transition of the pinch‐off cavity from cylindrical to spherical shape with increase in Weber number. The impact cavity pinch‐off dynamics in terms of D) retraction cavity width with time for two sieves with different pore openings. The fitted α for #0.009 and #0.0045 sieve are 0.41 and 0.42 respectively. E) Impact cavity pinch‐off velocity versus pinch‐off cavity width for different pore openings and liquid viscosities. Viscous forces affect the dynamics of recoil cavity formation and collapse. At significantly high viscosities (>5 mPas), the formation of recoil cavities is suppressed. In the regime of viscosities included in the study (1.03 mPas for 10 GW and 1.8 for 30 GW), the dynamics of recoil cavity formation and collapse are primarily explained by inertial and capillary forces. Viscosity can be neglected without affecting the analysis or the conclusion.

Figure 3

Plot of cavity velocities with Weber numbers A) sieve #0.009% and 10% glycerol water solution and B) sieve #0.009% and 30% glycerol water solution. The black and blue colors represent impact cavity pinch‐off velocity and recoil cavity formation velocity respectively. C) Plot of rate of change of kinetic energy fluxes between impact cavity pinch‐off and recoil cavity formation for different pore openings and viscosities. The black dotted line shows the scaling Equation (3). D) Plot between recoil cavity formation velocity versus radius factor ($R_{\mathrm{p}}^{2.5}{R}_{\mathrm{r}}^2$). The black dotted line in D shows the fitted scaling Equation (4).

Figure 4

A) Phase diagram showing recoil cavity formation and single droplet ejection in terms of pore opening and Weber number for 10% glycerol water mixture. The black‐dotted region shows the recoil cavity formation region. Different color points depict the droplet ejection zone. Black color shows no drop ejection regime. Red color shows the single‐drop ejection regime. And the blue represents the multiple droplet ejection zone. The same has been represented in the images below. B) shows the ratio of energy fluxes per unit time between recoil jet and recoil cavity collapse with Weber number. C) shows recoil radius width with Weber number. (I) Ejection of single drop through #0.009 sieve and recoil cavity width and (II) ejection of multiple jet through sieve #0.009. The difference between two scenarios is in the ejection process. Sieve #0.009 eject single droplet due to smaller cavity width. While for multiple jets, recoil radius increases (exceeding L + 2 W, where L is sieve pore length and W is sieve wire diameter), causing energy focusing to extend beyond a single pore, resulting in multiple droplet ejections. The open symbols represent single‐drop ejection.