Effect of the solvent viscosity on pure electro-osmotic flow of viscoelastic fluids

Abstract

In this work the fully-developed steady channel flow of the homogeneous polymer solution studied in [4] is revisited and a completely new analytical solution is proposed which is devoid of the limitations of the previous solution (3 2 ≤ 2∕27), i.e., it is valid for the complete range of the rheological parameters. The viscoelastic fluid is described by the simplified Phan-Thien and Tanner model with linear stress coefficient function for the polymer contribution plus a Newtonian solvent. The solution is also valid if the polymer contribution is described by the finitely extensive non-linear elastic model with the Peterlin approximation for the average spring force (FENE-P model).

Analytical Solution of Mixed Electroosmotic/Pressure Driven Flow of Viscoelastic Fluids between a Parallel Flat Plates Micro-Channel: The Maxwell Model Using the Oldroyd and Jaumann Time Derivatives

“…In the channel central region, the shear and normal stresses are practically zero; the presence of both stresses is only close to the wall, being higher for lower De 2 sh for α = 0. Ferras et al [51] found the same behavior using the simplified Phan-Thien-Tanner model with a linear stress coefficient function for the polymer contribution plus a Newtonian solvent. For the codeformational time derivative (α = 0), both the shear and normal stresses are higher with increasing viscoelasticity.…”

“…Afonso et al [23] obtained analytical solutions for the flow of viscoelastic fluids using the PTT model, They mentioned that theκ effects on the velocity profile is restricted to a narrow region, the effective EDL thickness: higher values ofκ lead to thinner EDL and consequently higher velocity gradients. The internal micro-structure of viscoelastic fluids interact in a complex process with electric fields and surfaces, leading either to adsorption or wall-depletion, as described in [51,57]. In Figure 7, the effect of the viscoelasticity on the dimensionless velocity withκ = 20 and Γ = 1 is exhibited.…”

“…When the De 2 sh increases, the velocity plateau also increases significantly; the same results were reported by Afonso et al [23] using the simplified PTT model. Ferras et al [51] analyzed the effects of the solvent to polymer viscosity ratio and viscoelasticity using the simplified Phan-Thien-Tanner model with linear stress coefficient function; in their work, the Debye-Hückel approximation and the electrokinetic parameter of (κ = 20) were used. They reported that increasing the viscoelasticity leads to an increase of the dimensionless velocity, which is more intense for intermediate values of viscosity ratio (Newtonian viscosity/(Newtonian viscosity + polymer viscosity)).…”

“…Another time derivative is the Jaumann derivative (also called corotational derivative), which gives their components, in fixed coordinates, of the time derivative as observed in a coordinate system which translates and rotates with the local rotation [38,40]. The former is one of the most used in the electroosmotic flows [23,28,47,49,51].…”

Manipulation of micro‐ and nanoparticles in viscoelastic fluid flows within microfluid systems

“…Scientists have also explored different features of VEF flows for bioengineering applications using microfluidics devices. Various lab‐on‐chip microfluidic platforms have been developed for particle manipulation in VEF electroosmotic flow (EOF) within microchannels (Afonso, Alves, & Pinho, ; Ferrás, Cavadas, Resende, Afonso, & Pinho, ; Sadeghi, Saidi, & Mozafari, ) for micromixing of liquids as well as washing, stretching, sorting, focusing, and separation of particles of interest (D'Avino, Greco, & Maffettone, ; Gan, Lam, Nguyen, Tam, & Yang, ; Lu, Liu, Hu, & Xuan, ; Ramsay, Simmons, Ingram, & Stitt, ; Yuan et al ).…”