Electro-osmotic and pressure-driven flow of viscoelastic fluids in microchannels: Analytical and semi-analytical solutions

Abstract

In this work, we present a series of solutions for combined electro-osmotic and pressure-driven flows of viscoelastic fluids in microchannels. The solutions are semi-analytical, a feature made possible by the use of the Debye–Hückel approximation for the electrokinetic fields, thus restricted to cases with small electric double-layers, in which the distance between the microfluidic device walls is at least one order of magnitude larger than the electric double-layer thickness. To describe the complex fluid rheology, several viscoelastic differential constitutive models were used, namely, the simplified Phan-Thien–Tanner model with linear, quadratic or exponential kernel for the stress coefficient function, the Johnson-Segalman model, and the Giesekus model. The results obtained illustrate the effects of the Weissenberg number, the Johnson-Segalman slip parameter, the Giesekus mobility parameter, and the relative strengths of the electro-osmotic and pressure gradient-driven forcings on the dynamics of these viscoelastic flows.

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

“…(16) , we assume the following variable transformation and approximation, = sinh ( ) ≈ 1 2 exp ( ) − 1 2 , but still it will be assessed in the next section. This approximation is usually accurate as in many practical applications the finite electric double layer thickness is very small, about 1-3 orders of magnitude smaller than the thickness of the microfluidic channel [3,4] . Note that in the previous works [3,4] the approximation used was sinh ( ) ≈ 1 2 exp ( ) .…”

“…This approximation is usually accurate as in many practical applications the finite electric double layer thickness is very small, about 1-3 orders of magnitude smaller than the thickness of the microfluidic channel [3,4] . Note that in the previous works [3,4] the approximation used was sinh ( ) ≈ 1 2 exp ( ) . The new approximation proved to be more accurate, avoiding at the same time the break of symmetry, reported in [3,4] .…”

“…Note that in the previous works [3,4] the approximation used was sinh ( ) ≈ 1 2 exp ( ) . The new approximation proved to be more accurate, avoiding at the same time the break of symmetry, reported in [3,4] . With ≈ 1 2 exp ( ) − 1 2 , we have that:…”

“…Of particular interest are viscoelastic fluids, and even though their components may interact in a complex manner with the electric fields and surfaces, leading either to adsorption or walldepletion, as described in the specialized literature [1,5,6] , we are concerned here with the simple fully-developed steady channel flow of homogeneous polymer solutions described by the simplified Phan-Thien and Tanner model with linear stress coefficient function for the polymer contribution plus a Newtonian solvent. This problem is of interest, for instance, to verify numerical methods in more complex situations and it was in this context that this flow was previously addressed in the appendix of Afonso et al [4] , where an analytical solution was originally proposed, but subject to constraints that limited its range of application, such as 3 2 ≤ 2∕27 . In this short communication we present a completely new analytical solution devoid of such restrictions and then briefly discuss the effects of the solvent to polymer viscosity ratio and viscoelasticity upon the flow characteristics, since such an analysis is missing from the literature.…”

Patterned surface charges coupled with thermal gradients may create giant augmentations of solute dispersion in electro-osmosis of viscoelastic fluids

“…In particular, biofluids, like blood plasma, saliva, synovial fluid and vitreous humour [32][33][34][35][36], exhibit viscoelasticity under certain straining conditions. Hence, the use of viscoelastic models to predict their dynamical features remains pertinent [37][38][39][40][41][42]. Accordingly, hydrodynamic dispersion characteristics of viscoelastic fluids have emerged as an important research topic over the recent years.…”