Pulsating Reactions

Matkowsky, B. J., and Sivashinsky, G. 1., Propagation of a pulsating reaction front in solid fuel combustion. SIAM J. Appl. Math., 35,465 (1978). 

The net reaction is the disproportionation of H2O2 to H2O + 5O2 and the starch indicator oscillates between deep blue and colourless as the iodine concentration pulsates. 

The existence of pulsating motion of the liquid phase within the catalyst pellet indicates that under certain conditions a steady-state regime of reaction progress can become unstable due to the exothermicity of the reaction under study. Further... 

Abstract Acoustic cavitation is the formation and collapse of bubbles in liquid irradiated by intense ultrasound. The speed of the bubble collapse sometimes reaches the sound velocity in the liquid. Accordingly, the bubble collapse becomes a quasi-adiabatic process. The temperature and pressure inside a bubble increase to thousands of Kelvin and thousands of bars, respectively. As a result, water vapor and oxygen, if present, are dissociated inside a bubble and oxidants such as OH, O, and H2O2 are produced, which is called sonochemical reactions. The pulsation of active bubbles is intrinsically nonlinear. In the present review, fundamentals of acoustic cavitation, sonochemistry, and acoustic fields in sonochemical reactors have been discussed. 

In some literature, there is a description that a bubble with linear resonance radius is active in sonoluminescence and sonochemical reactions. However, as already noted, bubble pulsation is intrinsically nonlinear for active bubbles. Thus, the concept of the linear resonance is not applicable to active bubbles (That is only applicable to a linearly pulsating bubble under very weak ultrasound such as 0.1 bar in pressure amplitude). Furthermore, a bubble with the linear resonance radius can be inactive in sonoluminescence and sonochemical reactions [39]. In Fig. 1.8, the calculated expansion ratio (/ max / Rq, where f max is the maximum radius and R0 is the ambient radius of a bubble) is shown as a function of the ambient radius (Ro) for various acoustic amplitudes at 300 kHz [39]. It is seen that the ambient radius for the peak in the expansion ratio decreases as the acoustic pressure amplitude increases. While the linear resonance radius is 11 pm at 300 kHz, the ambient radius for the peak at 3 bar in pressure amplitude is about 0.4 pm. Even at the pressure amplitude of 0.5 bar, it is about 5 pm, which is much smaller than the linear resonance radius. 

To complete the set of kinetic equations we observe that ub = (A/ /Ac)b where Acb can be expressed in terms of <5 ,b. Finally, the requirement of mass conservation yields a further equation. Considering the inherent nonlinearities, this problem contains the possibility of oscillatory solutions as has been observed experimentally. Let us repeat the general conclusion. Reactions at moving boundaries are relaxation processes between regular and irregular SE s. Coupled with the transport in the untransformed and the transformed phases, the nonlinear problem may, in principle, lead to pulsating motions of the driven interfaces. 

Pump pulsation may significantly impact on mixing quality and in this way the whole reaction performance [108]. In order to minimize this detrimental effect, commercially available syringe pumps were modified in order to suppress temporary pulsations. By this measure, pulsation spikes could be damped after installation of an additional switching valve in combination with a microcontroller for the individual control of both pistons. 

Indeed, the pulsating character of chemical-reaction propagation has been demonstrated20 both in time (analysis of acoustical effects which accompany the sample fracture in the reaction front) and in space (investigation of the fine structure of the front by microfilming). 

For some reactions listed in Table 1-4A, the fixed-bed reactor is operated under cocurrent-upflow conditions. Unlike the trickle-flow condition, this type of operation is normally characterized by bubble-flow (at low liquid and gas rates) and pulsating-flow (at high gas flow rates) conditions. Normally, the bubble-flow conditions are used. In the SYNTHOIL coal-liquefaction process, both pulsating-and spray-flow conditions are used, so that the solid reactant (coal) does not plug the reactor. In bubble flow, the gas is the dispersed phase and the liquid Ls a continuous phase. In pulsating flow, pulses of gas and liquid pass through the reactor. In the spray-flow regime, the gas is a continuous phase and the liquid is a dispersed phase. 

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