This paper establishes the mathematical formalism for the modeling of the mucus layer in the human trachea as a viscoelastic multiphase fluid system with surface tension with a view toward study of instability properties of the air-mucus system aimed at improving the design of new bioaerosol suppressing medication. The effects of surface tension, previously only conjectured and very poorly understood, are clearly established with quantitative relationships. Several very important physiological conclusions are obtained supporting one method of potential treatment and prevention of disease transmission by alteration of the mucus layer properties over other potential methods.
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