Transient electro-osmotic flow of generalized second-grade fluids under slip boundary conditions

Abstract

This work investigates the transient slip flow of viscoelastic fluids in a slit micro-channel under the combined influences of electro-osmotic and pressure gradient forcings. We adopt the generalized second-grade fluid model with fractional derivative as the constitutive equation and the Navier linear slip model as the boundary conditions. The analytical solution for velocity distribution of the electro-osmotic flow is determined by employing the Debye–Hückel approximation and the integral transform methods. The corresponding expressions of classical Newtonian and second-grade fluids are obtained as the limiting cases of our general results. These solutions are presented as a sum of steady-state and transient parts. The combined effects of slip boundary conditions, fluid rheology, electro-osmotic, and pressure gradient forcings on the fluid velocity distribution are also discussed graphically in terms of the pertinent dimensionless parameters. By comparison with the two cases corresponding to the Newtonian fluid and the classical second-grade fluid, it is found that the fractional derivative parameter β has a significant effect on the fluid velocity distribution and the time when the fluid flow reaches the steady state. Additionally, the slip velocity at the wall increases in a noticeable manner the flow rate in an electro-osmotic flow.

Analysis of Transient Buoyancy/Electroosmotic Driven Flow in a Vertical Microannulus with Velocity-Slip and Temperature-Jump

“…Their results clearly show that realistic values of the wall zeta potential produce thermal transport behavior which differs significantly from that predicted by an analysis employing the Debye-Hückel approximation [14]. Other related contributions where the combined pressure and electroosmotic flow are considered both in cylindrical and rectangular geometries are due to [15]- [20]. Usually, the EDL effects can be neglected for flows in microchannels since the EDL thickness is relatively small compared to the characteristic channel length.…”

Assorted kerosene-based nanofluid across a dual-zone vertical annulus with electroosmosis

“…Taking into account the application of the external electric field, the mobile ions in the EDL have a tendency to migrate and generate a fluid body force, which enables a bulk liquid to move through a viscous effect. Numerous experimental, theoretical and numerical studies on the EOF for different kinds of fluids have been published in the literature [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] . Modern technology has increased interest in flow and heat transfer research, which encompass heat exchangers, fluid transport, chemical processing equipment, and micro-electronic cooling.…”

Numerical study of electroosmotic slip flow of fractional Oldroyd‐B fluids at high zeta potentials

“…Wang et al. analytically and numerically investigated the electroosmotic slip flow of a fractional second‐grade fluid. In their works, the slip boundary condition and the asymmetric zeta potential at the walls were also considered.…”

“…In most of the research on the electroosmotic flow, the analytical expression of electrostatic potential distribution in electric double layer (EDL) can be obtained by using the Debye–Hückel linear approximation, which was proposed by Debye‐Hückel in 1923, to linearize the Poisson–Boltzmann equation . It is worthy of mentioning here that their analysis is valid only for a low surface potential (ζ < 25 mV).…”