Abstract
Cilia-induced flow of fractional Burgers fluid is studied in an inclined tube for both symplectic and antiplectic wave patterns. The solution of the problem is persued under the long wave length limitation. The fractional Adomian decomposition method is employed to evaluate the pressure gradient. Mathematical expressions for the axial velocity, frictional force, pressure gradient, and stream function are obtained and the influence of the main operating parameters is discussed in detail. It is noted that the velocity profile is more dominant in the case of antiplectic metachronal waves compared to symplectic ones, which confirms former results on the better capability of antiplectic waves to transport mucus, obtained with more complex numerical solvers.
Highlights
Dutch light microscopist Antoni was the first to discover cilia in 1675 and Sharpey was the first to discuss cilia in English language in 1835
Dauptain et al (2008) used the immersed boundary (IB) method to examine the motion of fluid due to one row of cilia on a ctenophore Pleurobrachia pileus, which is commonly known as a sea gooseberry for Reynolds numbers Re within the range [50 − 200]
Frictional force, pressure rise, pressure gradient and streamlines are plotted for different values of the main operating parameters and the main results can be summarized as follows:
Summary
Dutch light microscopist Antoni was the first to discover cilia in 1675 and Sharpey was the first to discuss cilia in English language in 1835. Dauptain et al (2008) used the IB method to examine the motion of fluid due to one row of cilia on a ctenophore Pleurobrachia pileus, which is commonly known as a sea gooseberry for Reynolds numbers Re within the range [50 − 200] They found that as the beating of cilia increases, it spreads more power to the interacting fluid and this work may be considered as a guideline for solving the fluid-structure interaction problem. All reported studies (Barton and Raynor, 1967; Ross and Corrsin, 1974; Fulford and Blake, 1986; Dillon et al, 2007; Smith et al, 2008; Vélez-Cordero and Lauga, 2013; Maqbool et al, 2016) confirmed the fact that more efforts are still required in terms of scientific research to better understand the internal flow structure due to cilia motion and their interaction with the surrounding fluid. Another motivation of the present paper is that the literature is scarce on fractional fluid models (see the monograph of Oldham and Spanier, 1974 for example)
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