Abstract
In this paper we present an in-depth analysis and analytical solution for time periodic hydrodynamic flow (driven by a time-dependent pressure gradient and electric field) of viscoelastic fluid through cylindrical micro- and nanochannels. Particularly, we solve the linearized Poisson–Boltzmann equation, together with the incompressible Cauchy momentum equation under no-slip boundary conditions for viscoelastic fluid in the case of a combination of time periodic pressure-driven and electro-osmotic flow. The resulting solutions allow us to predict the electrical current and solution flow rate. As expected from the assumption of linear viscoelasticity, the results satisfy the Onsager reciprocal relation, which is important since it enables an analogy between fluidic networks in this flow configuration and electric circuits. The results especially are of interest for micro- and nanofluidic energy conversion applications. We also found that time periodic electro-osmotic flow in many cases is much stronger enhanced than time periodic pressure-driven flow when comparing the flow profiles of oscillating PDF and EOF in micro- and nanochannels. The findings advance our understanding of time periodic electrokinetic phenomena of viscoelastic fluids and provide insight into flow characteristic as well as assist the design of devices for lab-on-chip applications.
Highlights
Micro- and nanofluidic applications require the transportation of fluids to be driven by an external driving force, which can be either a pressure gradient [pressuredriven flow (PDF)] or an external electric field [electroosmotic flow (EOF)] or the combination of these two driving forces
Our work aims to fill this gap by attempting to investigate the theoretical relations between fluxes and forces for time periodic electrokinetic flow of viscoelastic fluid in narrow confinement
It is important to note that knowing the relationships between driving forces and conjugate fluxes in electrokinetics [which for simple Newtonian fluid and steady mixed PDF–EOF can be described by transport equations and the Onsager relations of non-equilibrium thermodynamics (Masliyah and Bhattacharjee 2006)] is a crucial aspect for miniaturization and integration
Summary
National Food Institute, Technical University of Denmark (DTU-Food), Mørkhøj Bygade 19, Søborg 2860, Denmark insight into flow characteristic as well as assist the design of devices for lab-on-chip applications.
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