A reliable experimental protocol to quantify the mixing of liquids in microchannels

Mixing of liquids in a microchannel is critical for many applications of microfluidics. However, experimental quantification of mixing is a challenge, and a number of methods have been proposed. A typical approach to quantifying mixing involves measuring the mixing index (MI), which is a function of the standard deviation of pixel intensity distribution across the channel cross section. In calculating MI, usually, the measured pixel intensities are stretched/normalized and rescaled such that the smallest and largest intensities are assigned as 0 and 1. Consequently, the fully mixed and unmixed states are identified and assigned the average intensity (⟨I⟩) of 0.5. This artificial scaling makes comparison of MI found across studies with varied geometry and mixing mechanisms difficult. In this study, it is shown that precise measurement of ⟨I⟩ is crucial for determining the MI. A new experimental protocol to measure MI is proposed, and the efficacy of this approach is demonstrated by determining the MI for two passive configurations; in one, the mixing is purely diffusive, and in another, both diffusive and advective mixing occurs. It is found that MI values from experiments and numerical simulations agree to within 5% when both advective and diffusive mixing occurs. By incorporating the data from this study in prominent formulas in the literature for calculating MI, it is illustrated that our experimentally determined MI values have the closest agreement with results from simulation.