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Metachronal propulsion of non-Newtonian viscoelastic mucus in an axisymmetric tube with ciliated walls

Communications in Theoretical Physics 2021年第3期73卷 43-54页

作者： S Shaheen K Maqbool R Ellahi Sadiq M Sait Department of Mathematics and Statistics International Islamic UniversityIslamabadPakistan Fulbright Fellow Department of Mechanical EngineeringUniversity of California RiversideCAUnited States of America Center for Communications and IT Research Research InstituteKing Fahd University of Petroleum&MineralsDhahran-31261Saudi Arabia

Cilia-induced flow of viscoelastic mucus through an idealized two-dimensional model of the human trachea is presented.The cilia motion is simulated by a metachronal wave pattern which enables the mobilization of highly viscous mucus even at nonzero Reynolds numbers.The viscoelastic mucus is analyzed with the upper convected Maxwell viscoelastic formulation which features a relaxation time and accurately captures normal stress generation in shear flows.The governing equations are transformed from fixed to wave(laboratory)frame with appropriate variables and resulting differential equations are perturbed about wave number.The trachea is treated as an axisymmetric ciliated tube.Radial and axial distributions in axial velocity are calculated via the regular perturbation method and pressure rise is computed with numerical integration using symbolic software MATHEMATICA^(‘TM’).The influence of selected parameters which is cilia length,and Maxwell viscoelastic material parameter i.***.relaxation time for prescribed values of wave number are visualized graphically.Pressure rise is observed to increase considerably with elevation in both cilia length and relaxation time whereas the axial velocity is markedly decelerated.The simulations provide some insight into viscous-dominated cilia propulsion of rheological mucus and also serve as a benchmark for more advanced modeling.

关键词： viscoelastic mucus ciliated surface trachea inertial flow axisymmetric tube rheology flow

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Mathematical model for the ciliary-induced transport of seminal liquids through the ductuli efferentes

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International Journal of Biomathematics 2017年第3期10卷 1-17页

作者： A. A. Farooq A. M. Siddiqui Department of Mathematics COMSATS Institute of Information Technology Tobe Camp Abbottabad Pakistan Department of Mathematics Pennsylvania State University York Campus York PA 17403-3398 USA

This study describes the consequences of the ciliary motion on the transport of seminal liquid through the ductus efferentes of the male reproductive tract. By assuming the seminal liquid as a couple stress fluid, we have formulated a mathematical model for a two-dimensional flow through an axially symmetric tube whose inner surface is ciliated in the form of a metachronal wave. The governing system consists of nonlinear coupled partial differential equations which is reduced to a system of ordinary differential equations by utilizing the long wavelength approximation in an environment of the inertia free flow. Exact solutions for the velocity distribution, the pressure gradient and the stream function are obtained in terms of the couple stress parameters and the ciliary metachronism. Special attention is given to the pumping and the trapping characteristics due to the cilia motility. The study reveals that the ciliary pumping has to be more efficient to transport a couple stress fluid as compared to a Newtonian fluid. Moreover, the theoretical results for the couple stress fluid are found to be in good agreement with those reported by [T. J. Lardner and W. J. Shack, Cilia transport, Bull. Math. Biophys. 34 (1972) 325–335]. The analytical results are also displayed in graphical form.

关键词： Ciliary-induced flow metachronal wave couple stress fluid axisymmetric tube

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