Non-Newtonian Solute Mixing via Protonic Exchange of a Polyelectrolyte Layer: Unveiling Formation of Electroosmotic Vortices

Biochemical and medical diagnostics are two main fields in which vortex generation in microfluidic devices has several applications. Therefore, the aim of the present endeavor is to investigate the characteristics of a non-Newtonian vortex under the influence of a pH-sensitive polyelectrolyte layer (PEL)-modulated electroosmotic effect in a microchannel. Additionally, it is considered that the bulk solution pH (pH_b₀) and ionic concentration of the solution influence the zeta potential. Accordingly, the corresponding mathematical framework is constructed by using a numerical solver based on the finite element method and is subsequently verified against available experimental data in limiting conditions. Within the range of pH_b₀ and rheological parameters─Carreau number and flow behavior index─we critically analyze the PEL space charge density, net body force, and flow pattern. The current findings indicate that the existence of discrete net electrical body force patterns yields specific flow structures that enable substantial variation in the flow rate and mixing efficiency. The dominance of the basic PEL group protonic exchange at lower pH_b₀ and acidic PEL group protonic exchange at higher pH_b₀, respectively, permits positive and negative PEL space charge densities. Consequently, it is evident that the net electrical body force in PEL is extremely pH_b₀-dependent. Therefore, with smaller pH_b₀, the anticlockwise vortex with a negative flow rate is identified, whereas the clockwise vortex with a positive flow rate is predicted for larger pH_b₀. In turn, five distinct flow pattern regimes appear when the bulk solution pH pivots from 3 to 11. Remarkably, mixing efficiency exceeds 90% for greater diffusive Peclet numbers in highly acidic liquids. Overall, the outcomes of this study may significantly impact the design of microfluidic devices that mix and transport non-Newtonian liquids at particular pH_b₀ values.