Our first objective focuses on investigating the flow of Newtonian fluids through a narrow cylindrical fluidic channel. This involves solving the Navier-Stokes (NS) equation to derive analytical expressions for both axial and tangential (or swirl) velocities. To address the numerical solution of the scalar species transport equation, we integrate the analytically derived velocity fields. Following this, we conduct a thorough analysis of the effectiveness of solute mixing, considering the inlet swirl responsible for the bulk rotation of the fluid in the tangential direction. This analysis involves a comprehensive evaluation that includes both qualitative and quantitative assessments. It explores a defined set of parameters, such as Reynolds number and Peclet number, with a specific emphasis on practical applications.

The second objective extends the initial investigation to encompass non Newtonian fluids. This entails solving the Navier-Stokes (NS) equation with a focus on deriving analytical expressions for axial and tangential (or swirl) velocities using the power-law scheme. Additionally, we incorporate the derived velocity field expressions into the scalar species transport equation and solve it numerically. Subsequently, a comprehensive examination of the effectiveness of solute mixing is carried out, encompassing both qualitative and quantitative assessments. In this analysis, the prominent role of inlet swirl becomes evident in achieving efficient mixing, attributed to the bulk rotation of fluid in the tangential direction. This effect is particularly pronounced with an increase in shear-thinning fluid compared to shear-thickening fluid. The assessment covers a specific set of parameters, emphasizing their practical applications, which include considerations of Reynolds number and the power-law index.

In the third objective, we employed numerical methods to explore the transport and mixing behavior of biofluids exhibiting non-Newtonian characteristics. This study investigates the impact of polyelectrolyte layer (PEL)-modulated electrostatics, fluid rheology, and frictional drag on biofluids. The expectation is a notable rise in flow velocity due to electroosmotic actuation, counteracted by increased frictional drag potentially reducing flow velocity. The research specifically examines the influence of patterned PEL structures on vortical flow and associated mixing phenomena. The study conducts various analyses with different patterns under the same set of parameters, focusing on practical applications and interpreting the implications of each configuration. Furthermore, the research investigates how the PEL affects mixing length and the initiation of recirculation zones to achieve better mixing within a short length scale in the given problem.

The fourth objective investigated here extends the third by introducing a pH dependent soft polyelectrolyte layer (PEL) structure within the narrow fluidic channel while maintaining the effects of fluid rheology. This investigation delves into the combined impact of pH-dependent PEL-modulated electrostatics, fluid rheology, and solution bulk pH on biofluids. The primary goal is to explore the characteristics of a non-Newtonian vortex influenced by a pH-sensitive PEL modulated electroosmotic effect in a microchannel. The study specifically focuses on the influence of pH-sensitive PEL structures on vortical flow and associated mixing phenomena. Utilizing various analyses with different patterns under consistent parameters, the research emphasizes practical applications and interprets the implications of each configuration. Ultimately, the study's findings may significantly influence the design of microfluidic devices tailored for mixing and transporting non-Newtonian liquids at specific bulk pH values.

Our objective is to obtained the droplet based efficient mixing in a crossflow T-junction with Mineral oil as continuous phase and DI Water based ferrofluid as dispersed phase under the uniform magnetic field.