Analysis of Electroosmotically Modulated Peristaltic Transport of Third Grade Fluid in a Microtube Considering Slip-Dependent Zeta Potential

The present study investigates electroosmotically modulated peristaltic transport of third-grade fluid through a microtube taking into consideration the intricate coupling of zeta potential and hydrodynamic slippage. The analytical results encompass the mathematical expressions for dimensionless electrical potential distribution as well as series solutions for stream function and axial pressure gradient up to first order utilizing the perturbation technique for small Deborah number coupled with the Cauchy product for infinite series. Critical values and ranges of wavelength have been obtained where the axial pressure gradient vanishes. Moreover, pivotal values and ranges of wavelength have also been noted for the invariance of pressure gradient with respect to Deborah number as well as Debye-Hückel parameter. Trapping phenomenon has also been investigated by contours of streamlines wherein the zones of recirculation or trapped boluses are formed predominantly near the microtube walls. Additionally, the relative enhancement in hydrodynamic slippage amplifies the trapped bolus size, whereas, a diminishing behavior on bolus size is observed by the electroosmotic parameter.