A Computer Model for Soda Bottle Oscillations: "The Bottelator"

Abstract

The behavior of oscillatory phenomena has become an active area of research in the past two decades, and many complex systems have been studied and modeled. The subject of this paper, the soda bottle oscillator, is relatively simple and easily observed: shake a bottle of soda water at room temperature several times, let it stand a minute, then puncture the cap with a thumb tack or similar object. As pressure is released from the bottle, the dissolved gas is seen to bubble off in oscillatory bursts rather than in a steady single flow.In order for far-from-equilibrium systems to exhibit oscillatory behavior, the mechanism must contain a nonlinear step and a step in which feedback inhibits the nonlinear step. Oscillations in reactions that are of interest to chemists can have either a chemical or a physical mechanism. Reactions such as the Belousov-Zhabotinsky (B-Z) reaction (1) exhibit chemical oscillations, whereas the oscillations in gas evolution processes, such as the Morgan reaction (2), have a physical origin.Chemical oscillations are an effect of reaction kinetics, and it is the concentration of intermediate chemical species that oscillates. To exhibit oscillatory behavior, a reaction mechanism must have an autocatalytic step and a step that produces a species that inhibits the autocatalysis. The inhibitory step provides the feedback that controls the nonlinear (autocatalytic) step. The complete mechanism for an oscillating chemical reaction is complex, as are the models that illustrate their behavior.In a gas evolution oscillator (GEO), a dissolved gas (carbon monoxide from formic acid in the Morgan reaction) is produced by chemical reaction at atmospheric pressure. Once the solution becomes fully supersaturated, homogeneous nucleation of bubbles occurs. Diffusion of dissolved gas into growing bubbles depletes the solution sufficiently to shut off further bubble formation, and this is the feedback responsible for oscillation (3). The oscillations are sustained by continuous chemical production of the dissolved gas.The mechanism for oscillation in the soda bottle oscillator is also physical. However, it is very different from the mechanism in a GEO. We believe that the oscillations in this case occur as the system returns to equilibrium in response to the changing pressure of CO 2 above the solution. The process starts with dissolved gas in equilibrium with gas in the headspace, in accordance with Henry's law:where c eq is the concentration of dissolved gas, p is the external pressure, and κ is the Henry's law constant, which for CO 2 is 0.034 M atm ᎑1 at 25 °C. When a small hole is made in the cap, the initial decrease in pressure causes the onset of bubble nucleation. As the bubbles escape into the headspace, they tend to increase the pressure, and if the rate of increase is greater than the rate of decrease due to the pinhole, then the net result is that the headspace becomes partially repressurized. This is the feedback that "turns off" the nucleation process. The cycle repeats several times before reach...

Origin of Shallow Volcanic Tremor: The Dynamics of Gas Pockets Trapped Beneath Thin Permeable Media

“…A second (and end‐member) option is that gas supply is highly periodic, a possibility proposed by several authors (e.g., Lesage et al, ; Ripepe et al, ) and that generates harmonic tremor in our thin‐caps model through a Dirac comb effect (Figures d, e, and f). Periodic gas supply could be controlled by rectified diffusion (Brodsky et al, ); the flow of bubbles through granular suspensions (i.e., crystal‐rich magma; Barth et al, ); the collapse of critically unstable bubble rafts, foams, or viscoelastic layers formed at the top of magma columns (Ritacco et al, ; Spina et al, ; Vidal et al, ); natural self‐organization of bubbles to produce gas waves (Manga, ; Michaut et al, ); and the coupling between gas exsolution and the pressure changes occurring below the permeable cap, as motivated by experiments performed with slightly open soda bottles (Hellweg, ; Soltzberg et al, ). These mechanisms may play an important role in generating periodic gas emissions in persistently outgassing volcanoes (e.g., Girona, Costa, Taisne, et al, ; Tamburello et al, ), although it is unclear whether they can supply gas at a sufficient degree of periodicity to produce a Dirac comb effect (Hagerty et al, ; Powell & Neuberg, ).…”

“…(d–f) Quasiperiodic gas supply into the gas pocket, ground displacement that it produces, and spectrum of the ground displacement, respectively. Quasiperiodic gas supply emulates the regular arrival of clouds of bubbles into the gas pocket due, for example, to the coupling between the pressure changes below the cap and the exsolution of volatiles in the magma column (Hellweg, ; Soltzberg et al, ). This gives rise to harmonic tremor with spaced peaks.…”

Explosion mechanisms at Arenal volcano, Costa Rica: An interpretation from integration of seismic and Doppler radar data

“…The soda‐bottle model was proposed by Hellweg [2000] as a possible source model for Lascar's harmonic tremor and cyclic degassing behavior. Following Soltzberg et al [1997], Hellweg [2000] described how a small opening in a soda bottle may generate cycles of pressure drop beneath the cap, which triggers bubble nucleation and ascent. Johnson et al [1998] and Johnson and Lees [2000], on the other hand, proposed a mechanism analogous to a pressure‐cooker for Karymsky, in which the plug atop the conduit acts as a valve.…”

Carbon dioxide controlled earthquake distribution pattern in the NW Bohemian swarm earthquake region, western Eger Rift, Czech Republic – gas migration in the crystalline basement

“…In relation to gas exsolution from gas‐supersaturated fluids, pressure oscillations have been observed during flow through narrowings (Soltzberg et al . ; Hellweg ). When CO 2 can escape slightly, by, for example a little opening, it gives rise to a cycle of bubble formation and pressure fluctuations.…”