Graduate Thesis Or Dissertation
 

A model of ciliary streaming in the respiratory system

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  • The respiratory tract is lined with a mucous blanket which is motivated by a ciliated epithelium. This blanket includes a lower serous layer of fluid through which the cilia beat and an upper viscid layer into which particulates from the inhaled air are deposited. The movement of the mucous blanket comprises the ciliary stream and is the primary mechanism responsible for clearance of particulates from the respiratory system. A mathematical model was developed representing a small segment of the ciliary stream and describing the movement of the upper viscid layer of mucus and the tips of the cilia which project through the serous fluid into the upper viscid layer. The cilia tips are represented as a continuous surface which oscillates along the lower edge of the viscid mucous layer. The mucus was assumed to behave as a Bingham plastic. An analytical solution is presented for the steady-state component of the mucous velocity and both numerical and analytical solutions are presented for the time-dependent component, which is a parabolic differential equation with a moving boundary. Conclusions indicated that in order to obtain a mucous flow in the positive direction, the tips of the cilia cannot be in constant contact with the upper fluid layer. The serous layer, which has been almost completely neglected in previous research, appears to be at least as important to the system as the upper viscid layer. Furthermore, the thickness of the serous layer may be the most important single parameter of the system.
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