Shear stress at the cilia wall is considered as an imperative factor that affects the efficiency of cilia beatings as it describes the momentum transfer between the fluid and the cilia. We consider a visco-inelastic Prandtl fluid in a ciliated channel under electro-osmotic pumping and the slippage effect at cilia surface. Cilia beating is responsible for the stimulation of the flow in the channel. Evenly distributed cilia tend to move in a coordinated rhythm to mobilize propulsive metachronal waves along the channel surface by achieving elliptic trajectory movements in the flow direction. After using lubrication approximations, the governing equations are solved by the perturbation method. The pressure rise per metachronal wavelength is obtained by numerically integrating the expression. The effects of the physical parameters of interest on various flow quantities, such as velocity, pressure gradient, pressure rise, stream function, and shear stress at the ciliated wall, are discussed through graphs. The analysis reveals that the axial velocity is enhanced by escalating the Helmholtz–Smoluchowski velocity and the electro-osmosis effects near the elastic wall. The shear stress at the ciliated boundary elevates with an increase in the cilia length and the eccentricity of the cilia structure.
Broadband, slow sound on a glide-symmetric meander-channel surface
