Tunneling of Micro-sized Droplets Through a Flowing Soap Film

TL;DR

This study investigates the impact dynamics of micron-sized water droplets on soap films, identifying a critical velocity for penetration that depends on film thickness and involves deformation energy considerations.

Contribution

It introduces a quantitative analysis of droplet penetration through soap films, highlighting the role of deformation energy and establishing a critical Weber number for penetration.

Findings

Critical impact velocity approaches 520 cm/s as film thickness approaches zero.

Droplets penetrate the film without breaking it when impact velocity exceeds the critical velocity.

Deformation energy corresponds to creating approximately 14 times the droplet's cross-sectional area.

Abstract

When a micron-sized water droplet impacts on a freely suspended soap film with speed $v_{i}$, there exists a critical impact velocity of penetration $v_{C}$. For the droplet with $v_{i}<v_{C}$, it flows with the soap film after the impact whereas with $v_{i}>v_{C}$, it tunnels through. In all cases, the film remains intact despite the fact that the droplet radius ($R_{0}=26\,\mu m$) is much greater than the film thickness ($0<h\lesssim10\,{\mu}m$). The critical velocity $v_{C}$ was measured as a function of $h$, and interestingly $v_{C}$ approaches an asymptotic value $v_{C0}\simeq520\,$ cm/s in the limit $h\rightarrow0$. This indicates that in addition to an inertial effect, a deformation or stretching energy of the film is required for penetration. Quantitatively, we found that this deformation energy corresponds to the creation of $\sim14$ times of the cross-sectional area of the droplet ($14\pi R_{0}^{2}$) or a critical Weber number ${\rm We_{C} } (\equiv2R_{0}\rho_{w}v_{C0}^{2}/\sigma)\simeq44$, where $\rho_{w}$ and $\sigma$ are respectively the density and the surface tension of water. Key results: The interaction between liquid droplet and soap films is studied. When the impact velocity is higher than a critical velocity, the droplet penetrates the soap film without breaking it. The experimental results are rationalized using the mechanical collision model with the film stretching.