Analytical and numerical investigations of mixing fluids in microchannel systems of different geometrical configurations

This work presents theoretical and numerical studies related to micromixing phenomena using two different shapes of microchannel systems (i.e., X‐ and Y‐shaped, respectively). In this study, we consider a system that consists of a primary fluid, an aqueous phase (Fluid A), and a secondary fluid (distributed phase), Rhodamine B, in water (Fluid B). In this study, a two‐dimensional closed‐form generalized analytical model is developed and solved using the method of separation variables to understand the fluid flow mixing behaviour under the influence of a convective–diffusive mass transport process. In addition, numerical simulations are also performed by solving the continuity, momentum, and mass transport equations for the two proposed microchannel systems under different flow conditions to understand the relative effects on micromixing phenomena resulting from the convection and diffusion mass transport. Results obtained from the numerical simulations evaluate the mixing performance by varying the inlet flow velocity of the secondary fluid stream (Fluid B: Rhodamine B in water). The numerical result in terms of the radial concentration distribution profile as a function of channel width based on the operating Reynolds number by varying inlet feed flow velocity (Fluid B) shows that more effective mixing has been carried out by the X‐shaped microchannel compared to the Y‐shaped microchannel. Moreover, the proposed generalized analytical model was validated with the obtained numerical results in terms of the normalized concentration distribution as a function of the normalized channel width. A good agreement between the analytical and obtained numerical results (±9%) for both shapes of microchannel systems has been observed. Concentration profile as a function of channel width for two proposed microchannel systems (i.e, X‐shaped and Y‐shaped)