Grotberg J B
Biomedical Engineering Department, Northwestern University, Evanston, Ill 60208.
J Biomech Eng. 1990 May;112(2):177-82. doi: 10.1115/1.2891169.
A mathematical model is presented that investigates the mass transport of a diffusible and soluble gas contaminant through a liquid-lined tube when the Peclet number is small. The transport is determined by four dimensionless parameters: lambda, the tube aspect ratio; d, the relative difference in end concentrations; gamma, the radial transport coefficient; and Pe, the Peclet number. The problem is formulated for arbitrary gamma, but in the case of ozone and nitrous oxides the value of gamma is small. An asymptotic analysis for Pe much less than 1 and gamma much less than 1 is presented which yields the concentration field and transport characteristics we seek. It also provides a low Peclet number analysis for the conjugate problem of mass and heat transfer that is not currently available in the literature. The application to transport in the small airways of the lung is discussed, particularly the radial absorption differences in inspiratory and expiratory flow. Depending on the relative sizes of gamma and Pe, fractional uptake decreases with increasing Pe during inspiration but can increase during expiration.
本文提出了一个数学模型，用于研究当佩克莱数较小时，一种可扩散且可溶的气体污染物在衬有液体的管道中的质量传输。传输由四个无量纲参数决定：λ，管道纵横比；d，末端浓度的相对差异；γ，径向传输系数；以及Pe，佩克莱数。该问题针对任意γ进行了公式化表述，但对于臭氧和一氧化氮的情况，γ值较小。给出了Pe远小于1且γ远小于1时的渐近分析，由此得出了我们所寻求的浓度场和传输特性。它还为质量和传热共轭问题提供了低佩克莱数分析，这在现有文献中尚无。讨论了该模型在肺小气道传输中的应用，特别是吸气和呼气过程中的径向吸收差异。根据γ和Pe的相对大小，吸气过程中分数摄取量随Pe增大而减小，但呼气过程中可能增大。
