Investigation of slip effects on electroosmotic mixing in heterogeneous microchannels based on entropy index

Abstract

In this article electrokinetic mixing through heterogeneous microchannels has been studied and the effects of slip coefficient, zeta-potential, Debye-Hückel parameter and Reynolds number on mixing efficiency have been investigated. The microchannels studied here, have non-homogenous zeta-potential distribution at the wall, while other surface properties are considered to be homogenous. In order to investigate the electro-osmotic mixing, the Navier-Stokes, Nernst-Planck, Laplace and convection-diffusion equations have been solved numerically for velocity field, ions distribution, electrical potential and concentration field, respectively. The entropy of concentration distribution has been used as a quantitative index to evaluate the mixing performance. The results show that the behavior of electro-osmotic micromixers strongly depends on the amount and distribution of wall zeta-potential and in most cases the mixing efficiency increases with reduction of slip coefficient or Debye-Hückel or Reynolds number. It is found that in presence of slip, mixing efficiency decreases at low Reynolds numbers, while increases at high Reynolds numbers. Also, the accuracy of Helmholtz-Smoluchowski approximate model is investigated and it is found that the performance of the Helmholtz-Smoluchowski model in predicting the mixing efficiencies deteriorates for high wall zeta-potential or low values of Debye-Hückel parameter.

Numerical Analysis of the Heterogeneity Effect on Electroosmotic Micromixers Based on the Standard Deviation of Concentration and Mixing Entropy Index

“…The H–S condition is applied to the boundaries with this simplification, and the velocity field within the flow domain is then solved using this boundary condition. The H–S model’s validity has been well studied for investigating the fluid flow field [ 33 ], and determining concentration field and mixing efficiency has shown that this model can have high accuracy for predicting mixing under suitable conditions and that the maximum error is negligible [ 34 ].…”

“…The slip presence led to a significant enhancement of energy conversion efficiency in a similar study [ 46 ]. Other studies in this field include the investigation of surface slip phenomenon in the electroosmotic flow of non-Newtonian fluids in porous media [ 47 ], the surface slip examination in microfluidic equipment [ 48 ], the analytical and numerical study of slip flow of Newtonian fluids inside flat microchannels [ 34 , 49 ], and analytical study of electroosmotic slip flow of viscoelastic fluids with pressure gradient in flat [ 50 ] and annular microchannels [ 51 ].…”

“…The most common mixing criterion is the concentration-based index applied in both homogeneous and heterogeneous zeta-potential channels and provides acceptable results [ 18 , 52 ]. Another criterion used to study the mixing of microchannels is the mixing entropy criterion [ 34 , 53 , 54 ]. Unlike the previously introduced criterion, this criterion is mainly employed in channels without heterogeneity on the wall.…”

“…Figure 3. The velocity changes in a homogeneous microchannel through the full numerical solution model and analytical solution of electroosmotic velocity field with and without the slip boundary condition[34,62].…”

Numerical analysis of a microfluidic mixer and the effects of different cross-sections and various input angles on its mixing performance

“…The most remarkable benefit of the above microfluidic devices, compared to the conventional devices, comes from the unique feature, i.e., the large surface area-to-volume ratio, which significantly improves the mass, heat, and energy transfer rates. This feature can result in not only better proficiency and performance but also greater yield [25,26]. Besides, other positive points such as low reagent consumption, less computational time (time-efficient), low cost (cost-efficient), portability, and high throughput expand their utilization in the domains of microsystems, micro-total analysis systems (µTAS), and lab-on-a-chip (LoC) systems [25,27,28].…”