A new non-dimensional parameter to obtain the minimum mixing length in tree-like concentration gradient generators

Microfluidic-based concentration gradient generators (CGGs) have a number of applications in chemical, biological and pharmaceutical studies. Thus, precise design of the microfluidic system is crucial to maintaining the desired concentration gradient in microchannels. One of the design considerations is the length of microchannels in the structure of a CGG. A CGG with a short length fails to provide the complete diffusive mixing, while the size of the microchip would unfavorably increase by incorporating a long CGG. Considering a CGG as a tree-like structure consisting of T-shaped micromixers, the mixing process of the species at a straight microchannel has been solved analytically. Herein, we define a new non-dimensional parameter (psi) as the ratio of the minimum length of the microchannel required for the desired fluid mixing to the product of the channel width and Peclet number. The numerically obtained values of psi (i.e., 0.22 and 0.17 for 95% mixing in straight and serpentine micromixers, respectively) are in good agreement with the experimental results. The numerical simulation also shows that the value of psi is the same for all micromixers in a CGG with the similar microchannel structure (e.g., straight or serpentine) and is independent of the channel size (width-to-depth ratio) and fluid velocity. Therefore, psi can be computed only once for any micromixer with different structures (e.g., zigzag, square wave, and so forth) and then considering this constant value of psi, the minimum required length of all other micromixers in a CGG with similar repetitive structures and dimensions at the specified flow rates could be designed quickly and precisely. (C) 2018 Elsevier Ltd. All rights reserved.