Flow in tubules due to ciliary activity

Mathematical modelling of ciliary propulsion of an electrically-conducting Johnson-Segalman physiological fluid in a channel with slip

Bionic systems frequently feature electromagnetic pumping and offer significant advantages over conventional designs via intelligent bio-inspired properties. Complex wall features observed in nature also provide efficient mechanisms which can be utilized in biomimetic designs. The characteristics of biological fluids are frequently non-Newtonian in nature. In many natural systems super-hydrophobic slip is witnessed. Motivated by these phenomena, in this paper, we discussed a mathematical model for the cilia-generated propulsion of an electrically-conducting viscoelastic physiological fluid in a ciliated channel under the action of magnetic field. The rheological behavior of the fluid is simulated with the Johnson-Segalman constitutive model which allows internal wall slip. The regular or coordinated movement of the ciliated edges (which line the internal walls of the channel) is represented by a metachronal wave motion in the horizontal direction which generates a two-dimensional velocity profile. This mechanism is imposed by a periodic boundary condition which generates propulsion in the channel flow. Under the classical lubrication approximation, the boundary value problem is non-dimensionalized and solved analytically with a perturbation technique. The influence of the geometric, rheological (slip and Weissenberg number) and magnetic parameters on velocity, pressure gradient and the pressure rise (evaluated via the stream function in symbolic software) are presented graphically and interpreted at length.

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

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.

Study of heat transfer on physiological driven movement with CNT nanofluids and variable viscosity

BACKGROUND AND OBJECTIVES

With ongoing interest in CNT nanofluids and materials in biotechnology, energy and environment, microelectronics, composite materials etc., the current investigation is carried out to analyze the effects of variable viscosity and thermal conductivity of CNT nanofluids flow driven by cilia induced movement through a circular cylindrical tube. Metachronal wave is generated by the beating of cilia and mathematically modeled as elliptical wave propagation by Blake (1971).

METHODS, RESULTS AND CONCLUSIONS

The problem is formulated in the form of nonlinear partial differential equations, which are simplified by using the dimensional analysis to avoid the complicacy of dimensional homogeneity. Lubrication theory is employed to linearize the governing equations and it is also physically appropriate for cilia movement. Analytical solutions for velocity, temperature and pressure gradient and stream function are obtained. The analytical results are numerically simulated by using the Mathematica Software and plotted the graphs for velocity profile, temperature profile, pressure gradient and stream lines for better discussion and visualization. This model is applicable in physiological transport phenomena to explore the nanotechnology in engineering the artificial cilia and ciliated tube/pipe.

An investigation of non-Newtonian fluid flow due to metachronal beating of cilia in a tube

The aim of this study is to explain theoretically the role of ciliary motion on the transport of epididymal fluid through the ductus efferentes of the male reproductive track. For this purpose, a mathematical model has been developed for the flow of a non-Newtonian fluid in an axisymmetric tube due to metachronal wave of cilia motion for the more realistic consequences. Carreau viscous fluid model is considered to see the rheological effects on the pumping characteristics of the flow. Regular perturbation method has been employed to obtain the analytical expressions for the stream function, the velocity field and a relation between the pressure difference and the volume flow rate. It is found that the volume flow rate is influenced significantly by Weissenberg number We and the cilia length parameter ε. The computational results are presented graphically to see the effects of various physical parameters. Finally, the analysis is applied and compared with the observed value of the flow rate of spermatic fluid in the ductus efferentes of the male reproductive track. The volume flow rate is reported closed to the estimated value 6 × 10-3 ml/h in the human ductus efferentes when We = 0.5 and ε is near by 0.25.

Heat transfer analysis of bi-viscous ciliary motion fluid

The impulsion system of cilia motion is deliberated by biviscosity fluid model. The problem of two-dimensional motion of biviscosity fluid privileged in a symmetric channel with ciliated walls is considered. The features of ciliary structures are resolute by the supremacy of viscous effects above inertial possessions by the long-wavelength and low Reynolds approximation. Closed-form solutions for the longitudinal pressure gradient, temperature and velocities are obtained. The pressure gradient and volume flow rate for different values of the biviscosity are also premeditated. The flow possessions for the biviscosity fluid resolute as a function of the cilia and metachronal wave velocity.

A mathematical model for the flow of a Casson fluid due to metachronal beating of cilia in a tube

A mathematical model is developed to study the transport mechanism of a Casson fluid flow inspired by the metachronal coordination between the beating cilia in a cylindrical tube. A two-dimensional system of nonlinear equations governing the flow problem is formulated by using axisymmetric cylindrical coordinates and then simplified by employing the long wavelength and low Reynolds number assumptions. Exact solutions are derived for the velocity components, the axial pressure gradient, and the stream function. However, the expressions for the pressure rise and the volume flow rate are evaluated numerically. The features of the flow characteristics such as pumping and trapping are illustrated and discussed with the help of graphs. It is observed that the volume flow rate is influenced significantly by the width of plug flow region H p as well as the cilia length parameter ε. The analysis is also applied and compared with the estimated value of the volume flow rate of epididymal fluid in the ductus efferentes of the human male reproductive tract.

Swimming like algae: biomimetic soft artificial cilia

Cilia are used effectively in a wide variety of biological systems from fluid transport to thrust generation. Here, we present the design and implementation of artificial cilia, based on a biomimetic planar actuator using soft-smart materials. This actuator is modelled on the cilia movement of the alga Volvox, and represents the cilium as a piecewise constant-curvature robotic actuator that enables the subsequent direct translation of natural articulation into a multi-segment ionic polymer metal composite actuator. It is demonstrated how the combination of optimal segmentation pattern and biologically derived per-segment driving signals reproduce natural ciliary motion. The amenability of the artificial cilia to scaling is also demonstrated through the comparison of the Reynolds number achieved with that of natural cilia.