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ARTICLE

A Micromechanical Theory of Flow in Pulmonary Alveolar Sheet

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1 Department of Mechanical Engineering, Hong Kong University of Science and Technology, Hong Kong
2 Department of Engineering Mechanics & Technology, Tongji University, Shanghai 200092, P. R. China
3 Civil Engineering Department, MIT, Cambridge, MA 02139, USA
4 Corresponding author. Tel: +852-2358-7202; fax: +852-2358-1543. E-mail address: pintong@ust.hk

Computer Modeling in Engineering & Sciences 2002, 3(1), 77-86. https://doi.org/10.3970/cmes.2002.003.077

Abstract

In this paper we reexamine the sheet-flow model proposed by Fung and Sobin (1969) for blood flow in capillaries in the pulmonary alveoli from micromechanical point of view. The pulmonary alveolar capillary is assumed to be two parallel membranes connected by periodic tissue posts. Blood is spread out into the very thin layer or sheet between the two membranes. The pulmonary alveolar sheet thus has a microstructure of hexagonal cells. A two-scale theory of homogenization is used to establish the canonical equations for the unit cell. The microscale solution is obtained by means of finite element method and the macroscopic pressure/discharge relationship for the flow in the pulmonary alveolar sheet is found through an average over the unit cell. The influence of cell geometry on the permeability and geometric friction factor of the cell are discussed through numerical examples.
The tissue posts have a significant effect on the flow resistance. Reducing either the post diameter or the vascular space tissue ratio will reduce permeability. For the post configuration considered, with a post volume of 4.5% of the cell, the ratio of permeability to that of Couette flow (K₁₁/K⁰) changes from 0.8 to about 0.3 when the sheet gap to post diameter ratio (h/a) increases from 1 to 5. The reduction in permeability is even more pronounce with denser posts. At h/a = 5, K₁₁/K⁰ is only about 0.3 for the post volume of 4.5% of the cell. When the post volume increases to 20% of the cell, K₁₁/K⁰ drops to 0.05.

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