# Bubble formation via multidrop impacts

Entry by Helen Wu, AP225 Fall 2010

## Reference

"Bubble formation via multidrop impacts"

A. G. Bick, W. D. Ristenpart, E. A. van Nierop, H. A. Stone, Physics of Fluids, 22, 042105 (2010).

Figure 1. (a) experimental setup used in paper - syringe pump suspended over liquid. (b) sequence of drop images. the crater can be seen in the center panels and a bubble is in the rightmost one.

bubbles

## Overview

Figure 6. (a) histograms showing $\delta t$ for impacts that didn't form a bubble, and (b) ones that did.
Figure 2. (a) phase diagram of the bubble formation regimes. (b) phase diagram comparing regular and multidrop bubble formation regions, Froude vs Weber numbers.

Foams consist of many gas bubbles trapped in a continuous solid or liquid phase. One common scenario where a foam arises is when 2 liquids are mixed, which can be an undesirable state for certain procedures.

Foams have been studied for a long time, but their generation is not well characterized, especially in situations with less control (liquid being poured into another liquid). This group of researches demonstrated that bubbles could be formed by the impact of smaller and faster drops than previously used (Figure 2, Franz label) if the timing between 2 successive drops is correct. They call this using a "multidrop impact" to create a bubble. Their results suggest mechanical reasons for lack of bubble formation when liquids are mixed.

## Results and discussion

The geometry of the surface as the drop falls was seen to be a crater (Figure 1b). When nothing else impacts the area afterwards, the surface recovers its initial flat state. Occasionally (~2% of the time), bubbles can be generated by vortices created by the single drop. When a second drop does hit the surface, a bubble can be formed. Qualitatively, a similar result was obtained both in cases where a surfactant was added and in carbonated liquids (they used beer).

Part of the analysis was based on the Froude number (comparision between the inertial and gravitational effects) and the Weber number (comparision between inertial to surface tension effects). Figure 2 shows that multidrop bubbles formed at similar Froude numbers as regular bubbles, but the Weber numbers were an order of magnitude lower (higher surface tension effect).

Analysis of crater depths showed that there is a critical depth which the crater must exceed in order for bubbles to form, and that depth was about the same as the capillary length $\ell_c=\sqrt{\gamma / \rho y} \approx 2mm$. <5% of craters fulfilled this criterion. Drop size and order did not seem to affect probability of bubble generation.

Figure 6 in the paper contains a histogram indicating that the critical time between drops is $\delta t \le 5-20ms$.

The authors propose that capillary forces and inertia govern the crater dynamics, and that this determines that the critical time interval is $t_c ~ (\frac{\rho h^3}{\gamma})^{1/2}$.

## Description of Experimental Setup

Drops were formed using a syringe pump suspended over a pool of liquid, usually distilled water, shown in Figure 1a.

A high speed camera was used to observe the drops.