Impact of oscillating bubbles

Vanitas vanitatum et omnia vanitas : bubbles are emptiness, non-liquid, a tiny cloud shielding a mathematical singularity. Born from chance, a violent and brief life ending in the union with the (nearly) infinite”, as described by Prosperetti (2004). Those tiny objects (1um to 1mm in radius usually) might be a unique spot for amazing events to occur. Bubbles can enhance the bulk concentration of surfactants, dragging the flavorful molecules of Champagne to our taste buds. Strongly oscillating bubbles can focus the energy so much that the gas it contains is turned into plasma (10000 Kelvin) and may emit light ([2]). Although small, bubble physics is worth the huge literature dedicated to them, with counter-intuitive and unique events having been discovered in the past few years, and applications for future technology having been designed (Dijkink (2006), Yuan (1999)).

Here we study the mixed case of low amplitude ultrasonic field and bubble-boundary interactions, which in practice finds its interest in the cleaning ability of the oscillating bubbles (automotive, marine, pharmaceutical, silicone industries…). The long term dynamics of the bubble may be strongly affected by the complex hydrodynamics interaction between the bubble oscillations and the solid wall proximity, leading to cases of permanent rebounds similar to walking droplets on free surfaces.


During impact on a solid substrate, a bubble stores kinetic energy into surface deformation. A capillary spring then restores the shape of the bubble, leading eventually to a rebound (see figure 1 left). The bouncing is also associated with the formation of a film between the bubble and the wall, the drainage of this film generating the formation of a dimple on the bubble surface, which can be explained by simple lubrication theory (Klaseboer (2000)). As the surrounding liquid has a finite viscosity, it takes time for it to flow out of the film. If the capillary spring time is faster than the typical flowing time, the bubble may rebound. However, in the opposite case, the bubble would come in direct contact with the substrate and lead to permanent trapping. Due to its complex shape, a bubble under a sound wave at the right frequency (see figure 2 right) experience different dynamics that may lead to change of behavior in interaction with the thin liquid film.

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Figure 1- Rebound of a bubble on a rigid substrate. The deformation and subsequent change of direction can be observed on the second and third insets.

The challenge here is to understand the similarities and differences of the impact of oscillating/non-oscillating bubbles. Expectingly, the oscillations of the bubbles (which may be non-spherical) hold much more complex behavior and interesting treasures. As a model experiment for this problem, we design a setup which allows one to characterize the dynamics of this thin (several um) film, through high-speed imaging (54000 fps) of a laser interference pattern, and synchronization with a direct optical high-speed imaging (see figure 2 left).

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Figure 2- Left: Experimental setup used to study the dynamics of the impact of oscillating bubbles and related thin liquid film behavior. Right: A bubble tethered to a syringe tip is under the influence of a sound wave, which activates an oscillatory pattern resulting from the Faraday instability.

The main result is that for low amplitude oscillations, the rebounds are lessened, owing to Bjerknes forces and the so-called Narcissus effect (Marmottant (2006)). However, at high amplitude oscillations, a surprising regime occurs. The thin liquid film can be stabilized, leading to permanent rebound or stationary non vanishing bubble-wall distance. This is reminiscent of the drop on oscillatory free surface of Couder et al (2005), which led to a macroscopic analogy of the quantum pilot wave theory. In the case of an oscillating bubble impacting on a solid wall, we attribute the liquid film stabilization to a boundary layer effect. Due to boundary conditions, the inflow is higher that the outflow on a bubble oscillation cycle, leading to a net positive inflow. It counterbalances the film drainage and leads to stabilization.

 

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Figure 3- Left: Interference pattern of the thin film trapped between an oscillatory bubble and a rigid substrate, revealing the existence of surfaces waves  on the otherwise flat film. Center: An oscillating bubble is held at a stable distance from the solid surface. Right: 45 ms after the sound wave is stopped, the liquid film has drained and the bubble unwets the substrate. The scale bar is 100 microns.
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