Evidence of deviations between experimental and empirical mixing lengths: Multi-discharge field tests in an arid...

Despite advances in wastewater treatment plant (WWTP) efficiencies, multiple contaminants of concern, such as microplastics, pharmaceuticals, and per- and poly-fluoroalkyl substances (PFAS) remain largely untreated near discharge points and can be highly concentrated before they are fully mixed within the receiving river. Environmental agencies enforce mixing zone permits for the temporary exceedance of water quality parameters beyond targeted control levels under the assumption that contaminants are well-mixed and diluted downstream of mixing lengths, which are typically quantified using empirical equations derived from one-dimensional transport models. Most of these equations were developed in the 1970s and have been assumed to be standard practice since then. However, their development and validation lacked the technological advances required to test them in the field and under changing flow conditions. While new monitoring techniques such as remote sensing and infrared imaging have been employed to visualize mixing lengths and test the validity of empirical equations, those methods cannot be easily repeated due to high costs or flight restrictions. We investigated the application of Lagrangian and Eulerian monitoring approaches to experimentally quantify mixing lengths downstream of a WWTP discharging into the Rio Grande near Albuquerque, New Mexico (USA). Our data spans river to WWTP discharges ranging between 2-22x, thus providing a unique dataset to test long-standing empirical equations in the field. Our results consistently show empirical equations could not describe our experimental mixing lengths. Specifically, while our experimental data revealed "bell-shaped" mixing lengths as a function of increasing river discharges, all empirical equations predicted monotonically increasing mixing lengths. Those mismatches between experimental and empirical mixing lengths are likely due to the existence of threshold processes defining mixing at different flow regimes, i.e., jet diffusion at low flows, the Coanda effect at intermediate flows, and turbulent mixing at higher flows, which are unaccounted for by the one-dimensional empirical formulas. Our results call for a review of the use of empirical mixing lengths in streams and rivers to avoid widespread exposures to emerging contaminants.