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

• Published in: Canadian journal of physics Vol. 95; no. 12; pp. 1313 - 1320
• Main Authors: Wang, Xiaoping, Qi, Haitao, Xu, Huanying
• Format: Journal Article
• Language: English
• Published: Ottawa NRC Research Press 01.12.2017; Canadian Science Publishing NRC Research Press
• Subjects: analytical solutions; Approximation; Boundary conditions; Boundary value problems; calcul fractionnaire; Computational fluid dynamics; Constitutive equations; Constitutive relationships; Derivatives; Derivatives (Mathematics); electro-osmotic flow; Electroosmosis; Equilibrium flow; Exact solutions; Flow rates; Flow velocity; Fluid flow; fluide généralisé de grade deux; Fluids; fractional calculus; generalized second-grade fluid; Integral transforms; Integrals; Mathematical models; Microchannels; Newtonian fluids; Parameters; Pressure effects; Rheological properties; Rheology; Slip flow; Slip velocity; solutions analytiques; Steady state; Stress concentration; Velocity; Velocity distribution; Viscoelastic fluids; Viscoelasticity; vitesse de glissement; écoulement électro-osmotique
• ISSN: 0008-4204; 1208-6045
• DOI: 10.1139/cjp-2017-0179

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.