Helmholtz–Smoluchowski velocity for viscoelastic electroosmotic flows

Many biofluids such as blood and DNA solutions are viscoelastic and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. However, the governing equations for viscoelastic flows are not easily solvable, especially for electroosmotic flows where the streamwise velocity varies rapidly from zero at the wall to a nearly uniform velocity at the outside of the very thin electric double layer. In the present investigation, we have devised a simple method to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels. It is based on the concept of the Helmholtz–Smoluchowski velocity which is widely adopted in the electroosmotic flows of Newtonian fluids. It is shown that the Helmholtz–Smoluchowski velocity for viscoelastic fluids can be found by solving a simple cubic algebraic equation. The volumetric flow rate obtained using this Helmholtz–Smoluchowski velocity is found to be almost the same as that obtained by solving the governing partial differential equations for various viscoelastic fluids.

Graphical abstractA simple method is devised to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels, employing the concept of the Helmholtz–Smoluchowski velocity. (a) Microchannel under consideration, (b) comparison of the Helmholtz–Smoluchowski velocity (UHSUHS) with the solution of the viscoelastic Navier–Stokes equation.Figure optionsDownload full-size imageDownload as PowerPoint slide