Grotberg J B, Sheth B V, Mockros L F
Biomedical Engineering Department, Northwestern University, Evanston, Ill 60208.
J Biomech Eng. 1990 May;112(2):168-76. doi: 10.1115/1.2891168.
A mathematical model of ozone absorption, or for any soluble gas that has similar transport properties, is developed for a branching network of liquid-lined cylinders. In particular, we investigate specific flow regimes for finite length tubes where boundary layer phenomena and entrance effects exist in high Reynolds and Peclet (Pe) number airways. The smaller airways which have lower Reynolds and Peclet number flows are modelled by incorporating the detailed analysis found in [10] and modifying it for airways which have alveolated surfaces. We also consider a reacting gas and treat specific regimes where the reaction front is located at the air-liquid interface, within the liquid or at the liquid-tissue interface. Asymptotic methods are used in regions of the tracheobronchial tree where Pe much less than 1 and Pe much greater than 1. In addition, the fact that the radial transport parameter gamma much less than 1 for this toxin, and others such as nitrous oxides, is employed to simplify the analysis. The ozone concentrations, airway absorption and tissue dose are examined as a function of airway generation for several values of the governing parameters. The general result is a maximal dosing in airway generations 17 to 18 that is much larger (up to an order of magnitude) than the predictions of previous theories.
针对内衬液体的圆柱体分支网络，建立了臭氧吸收或任何具有相似传输特性的可溶性气体的数学模型。特别地，我们研究了有限长度管道中的特定流动状态，其中在高雷诺数和佩克莱特（Pe）数的气道中存在边界层现象和入口效应。对于雷诺数和佩克莱特数较低的较小气道，通过纳入文献[10]中的详细分析并针对具有肺泡表面的气道进行修改来建模。我们还考虑了反应气体，并处理反应前沿位于气液界面、液体内部或液 - 组织界面的特定状态。在气管支气管树中佩克莱特数远小于1和远大于1的区域使用渐近方法。此外，由于这种毒素以及其他如一氧化二氮等的径向传输参数γ远小于1，因此利用这一事实简化分析。针对几个控制参数值，研究了臭氧浓度、气道吸收和组织剂量随气道代次的变化情况。总体结果是，在第17至18气道代次中出现最大剂量，这比先前理论的预测值大得多（高达一个数量级）。
