Rheological fluid motion in tube by metachronal waves of cilia

This paper presents a theoretical study of a non-linear rheological fluid transport in an axisymmetric tube by cilia. An attempt has been made to explain the role of cilia motion in the transport of fluid through the ductus efferent of the male reproductive tract. The Ostwald-de Waele power-law viscous fluid is considered to represent the rheological fluid. We analyze pumping by means of a sequence of cilia beats from rowto-row of cilia in a given row of cells and from one row of cells to the next(metachronal wave movement). For this purpose, we consider the conditions that the corresponding Reynolds number is small enough for inertial effects to be negligible, and the wavelengthto-diameter ratio is large enough so that the pressure can be considered uniform over the cross section. Analyses and computations of the fluid motion reveal that the time-average flow rate depends on ε, a non-dimensional measure involving the mean radius a of the tube and the cilia length. Thus, the flow rate significantly varies with the cilia length.Moreover, the flow rate has been reported to be close to the estimated value 6 × 10ml/h for human efferent ducts if ε is near 0.4. The estimated value was suggested by Lardner and Shack(Lardner, T. J. and Shack, W. J. Cilia transport. Bulletin of Mathematical Biology, 34, 325–335(1972)) for human based on the experimental observations of flow rates in efferent ducts of other animals, e.g., rat, ram, and bull. In addition, the nature of the rheological fluid, i.e., the value of the fluid index n strongly influences various flow-governed characteristics. An interesting feature of this paper is that the pumping improves the thickening behavior for small values of ε or in free pumping(?P = 0) and pumping(?P > 0) regions.

Analytical approach to entropy generation and heat transfer in CNT-nanofluid dynamics through a ciliated porous medium

The transportation of biological and industrial nanofluids by natural propulsion like cilia movement and self-generated contraction-relaxation of flexible walls has significant applications in numerous emerging technologies. Inspired by multi-disciplinary progress and innovation in this direction, a thermo-fluid mechanical model is proposed to study the entropy generation and convective heat transfer of nanofluids fabricated by the dispersion of single-wall carbon nanotubes（SWCNT） nanoparticles in water as the base fluid. The regime studied comprises heat transfer and steady, viscous, incompressible flow, induced by metachronal wave propulsion due to beating cilia, through a cylindrical tube containing a sparse（i.e., high permeability） homogenous porous medium. The flow is of the creeping type and is restricted under the low Reynolds number and long wavelength approximations. Slip effects at the wall are incorporated and the generalized Darcy drag-force model is utilized to mimic porous media effects. Cilia boundary conditions for velocity components are employed to determine analytical solutions to the resulting non-dimensionalized boundary value problem. The influence of pertinent physical parameters on temperature, axial velocity, pressure rise and pressure gradient, entropy generation function, Bejan number and stream-line distributions are computed numerically. A comparative study between SWCNT-nanofluids and pure water is also computed. The computations demonstrate that axial flow is accelerated with increasing slip parameter and Darcy number and is greater for SWCNT-nanofluids than for pure water. Furthermore the size of the bolus for SWCNT-nanofluids is larger than that of the pure water. The study is applicable in designing and fabricating nanoscale and microfluidics devices, artificial cilia and biomimetic micro-pumps.

Cilia-assisted hydromagnetic pumping of biorheological couple stress fluids

A theoretical study is conducted for magnetohydrodynamic pumping of electroconductive couple stress physiological liquids(e.g.blood)through a two-dimensional ciliated channel.A geometric model is employed for the cilia which are distributed at equal intervals and produce a whip-like motion under fluid interaction which obeys an elliptic trajectory.A metachronal wave is mobilized by the synchronous beating of cilia and the direction of wave propagation is parallel to the direction of fluid flow.A transverse static magnetic field is imposed transverse to the channel length.The Stokes’couple stress(polar)rheological model is utilized to characterize the liquid.The normalized two-dimensional conservation equations for mass,longitudinal and transverse momentum are reduced with lubrication approximations(long wavelength and low Reynolds number assumptions)and feature a fourth order linear derivative in axial velocity representing couple stress contribution.A coordinate transformation is employed to map the unsteady problem from the wave laboratory frame to a steady problem in the wave frame.No slip conditions are imposed at the channel walls.The emerging linearized boundary value problem is solved analytically and expressions presented for axial(longitudinal)velocity,volumetric flow rate,shear stress function and pressure rise.The flow is effectively controlled by three geometric parameters,viz cilia eccentricity parameter,wave number and cilia length and two physical parameters,namely magnetohydrodynamic(MHD)body force parameter and couple stress non-Newtonian parameter.Analytical solutions are numerically evaluated with MATLAB software.Axial velocity is observed to be enhanced in the core region with greater wave number whereas it is suppressed markedly with increasing cilia length,couple stress and magnetic parameters,with significant flattening of profiles with the latter two parameters.Axial pressure gradient is decreased with eccentricity parameter whereas it is elevated with cilia length,in the channel core region.Increasing couple stress and magnetic field parameter respectively enhance and suppress pressure gradient across the entire channel width.The pressure-flow rate relationship is confirmed to be inversely linear and pumping,free pumping and augmented pumping zones are all examined.Bolus trapping is also analyzed.The study is relevant to MHD biomimetic blood pumps.