The reactions at a plasma–liquid interface often involve species such as the solvated electron or the hydroxyl radical, which initiate the reduction or oxidation of solution-phase reactants (so-called scavengers) or are consumed by their own second-order recombination. Here, the mathematical scaling of the reaction–diffusion equations at the interface is used to obtain a characteristic time that can be used to determine the transition from highly efficient scavenger reduction or oxidation to lower efficiencies due to transport limitations. The characteristic time (t_c) is validated using numerical solutions of the reaction–diffusion equations. When the scavenger kinetics are faster than second-order recombination, this characteristic transition time scales proportionally with the scavenger diffusivity (D_s) and the square of the scavenger bulk concentration (S_B) and inversely proportional to the electron flux (J) squared; that is, t_c = D_sS_B²F²/J², where F is Faraday's constant. However, when the scavenger kinetics are comparable or slower than second-order recombination, this scaling does not hold. Extending this analysis to three-dimensional systems shows that the profile of the electron flux on the surface affects the spatial location where reactions are most effective. Finally, the assessment of the implications of these behaviors for the reactor design highlights how effectively controlling the electron flux and solution transport may be necessary to improve the efficiency of scavenger reactions.

中文翻译：

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等离子体-液体界面溶液相化学中动力学和传输行为的标度

等离子体-液体界面的反应通常涉及诸如溶剂化电子或羟基自由基之类的物种，这些物种会引发溶液相反应物（所谓的清除剂）的还原或氧化，或者被其自身的二级重组所消耗。在这里，界面处反应扩散方程的数学缩放用于获得特征时间，该特征时间可用于确定从高效清除剂还原或氧化到由于运输限制而导致的低效率的过渡。特征时间（t _c）使用反应扩散方程的数值解进行了验证。当清除剂动力学快于二阶复合时，此特征跃迁时间与清除剂扩散率（D _s）和清除剂体积浓度的平方（S _B）成正比，与电子通量（J）的平方成反比。即t _c  =  D _s S _B ² F ² / J ²，其中F是法拉第的常数。但是，当清除剂动力学与二阶重组相当或较慢时，这种定标就不成立。将这种分析扩展到三维系统可以看出，表面上电子通量的分布会影响反应最有效的空间位置。最后，对这些行为对反应器设计的影响的评估突出了如何有效地控制电子通量和溶液传输对于提高清除剂反应的效率可能是必要的。