Peristaltic activity for electro-kinetic complex driven cilia transportation through a non-uniform channel

Now-a-days in medical science, the transport study of biological fluids through non-uniform vessels are going to increase due to their close relation to the reality. Motivated through such type of complex transportation, the current study is presented of cilia hydro-dynamics of an aqueous electrolytic viscous fluid through a non-uniform channel under an applied axial electric field. Mathematical Formulations: Because of the complexity shape and nature of flow channel, we have used curvilinear coordinates in the derivation of continuity and momentum equationsin a fixed frame of reference. A linear transformation is used to renovate the flow system of equations from fixed (laboratory) to moving (wave) frame. For further simplification, the dimensionless variables are introduced to make the flow system of equations into the dimensionless form and at last convert these equations in term of stream function by using the mathematical terminologies of streamlines. The whole analysis is performed under (low Reynolds number) creeping phenomena and long wavelength approximation, respectively. Additionally, small ionic Peclet number and Debye-Huckel linearization are used to simplify the Nernst-Planck and Poisson-Boltzmann equations. The BVP4C technique is used to obtain the numerical solution for velocity distribution, pressure gradient, pressure rise and stream function through MATLAB.

The amplitude of velocity distribution is increased (decreased) at larger values of non-uniform parameter (cilia length). The non-uniform parameter played a vital role not only in the enhancement of circulation at the upper half of the channel but also the length of bolus increased. Results of straight channel are gained for larger value of the dimensionless radius of curvature parameter as well as cilia length.