Energy absorption in a bamboo foam

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"Energy absorption in a bamboo foam"
A. Le Goff, L. Courbin, H.A. Stone, and D. Quere
Europhysics Letters 84 36001 (2008)

Soft Matter Keywords

bamboo foam, surface tension, energy absorption, Weber number

Figure 1. Image sequence showing a delrin sphere falling through a soap film. The sphere has a radius of 1.6mm and consecutive image frames are 0.8ms apart.
Figure 2. (a) Experimental setup for studying bamboo films. The sphere is released from a height h above the first film and comes to rest on the N+1 film. The bottom of the tube supporting the films is submerged in a water bath to prevent gravitational descent of the films and limit evaporation of the foam. (b) Spatio-temporal diagram showing trajectory of a particle through the foam. The y-axis is the vertical position of the projectile, while the x-axis is time. The slope of the projectile's trajectory is decreasing with time, indicating that the velocity is decreasing.
Figure 3. Plot of number of films, N, crossed by a projectile with impact velocity, V. Impact velocity is defined as the velocity of the projectile when it hits the first film.
Figure 4. Total surface energy, <math>E_S</math>, dissipated by the N crossed soap films as a function of total mechanical energy, <math>E_p</math>, injected by the projectile.
Figure 5. (a) Deflected trajectory of a stainless-steel sphere pass through a soap film at an oblique angle. (b) Maximum deformation of the film during the sphere's crossing. Note that the deformation occurs in the direction normal to the film surface.
Figure 6. Variation of the quantity <math>\beta We</math> as a function of <math>\alpha</math>. Angles <math>\alpha</math> and <math>\beta</math> are as labeled in Figure 5a.


This article presents experiment and simple theory for the interaction between projectiles and thin liquid films. The authors perform experiments on an idealized bamboo foam, observing that such a foam is capable of absorbing energy from a projectile passing through the foam, eventually bringing the projectile to rest. The authors also study the deflection of a projectile by a film oriented obliquely to the projectile's trajectory. For both studies, simple scaling arguments are developed that capture the main features of the film/projectile interaction.

Practical Application of Research

Foams are under consideration for use in systems designed to absorb kinetic energy from projectiles. These systems are deployed to protect internal contents, people, precious objects, and other fragile items. Foams present an attractive option because they are light, simple and fast to form, and inexpensive. This work shows that foams are capable of absorbing kinetic energy from projectiles and will eventually arrest them. Though not immediately practical, this work with ideal foams opens up the way for future studies of projectile interaction with real foams. The initial work to characterize projectile interaction with bamboo, staircase, and oblique foams will contribute to the understanding of interaction with real foams.

Projectile Interaction with Foams

As shown in figure 1, it is possible for an object to pass through a thin liquid film without popping the film. The sphere stretches the film until the point where the distance between the sphere and the unperturbed part of the film is of the order of the sphere radius. At that point, the film pinches off, but does not break. The time interval between successive images in figure 1 is constant and the vertical position of the sphere appears to be linear in time. This indicates that the velocity of the sphere is nearly constant during the short interval from the first to the last image and the energy transmitted to the film during this single event is quite small relative to the total kinetic energy of the sphere. However, the vibration of the film after impact indicates some transfer of energy from the sphere to the film and so the authors create the system shown in figure 2, to observe the effect of multiple interactions between projectile and film.

A bamboo foam (with films separated by 0.6mm) is created inside a transparent cylindrical tube and a solid sphere dropped from above the first film. Since the sphere is smaller than the capillary length of the film, it will float on the surface of the film, if deposited gently. In this size regime, gravity is dominated by surface tension, so the beads are incapable of crossing the films using their weight alone. Figure 2b is created from high-speed movies of the falling sphere. The slope of the line gives the sphere's velocity, which is decreasing with time as the sphere crosses each film. The velocity of the sphere finally falls below the entrapment threshold of the film and the sphere is arrested on the lowest film shown.

written by Donald Aubrecht