Experimental Study and Turbulence Dissipative Scale Modelling of the Rapid Micromixing of Impinging, Paper-Thin Sheets of Liquids

23 June 2023, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


The impingement of thin liquid sheets produces high energy dissipation rates, which greatly increase the rate of mixing [1,2]. The energy released by the impingement is dissipated within approximately one turnover time of the largest eddies. As a result, micromixing was studied using a simple model that assumes diffusion of species in slabs of fixed thickness (2L), which are generated within the impingement zone. The experimental study followed the progress of an acid-base neutralization containing a fluorophore. A simulation, which included a module for calculating the fluorescence, determined 2L for experimental energy dissipation rates (ϵ) ranging from 5,000 to 7,700,000 W/kg. 2L was found to lie in the range of turbulence dissipative scales less than the Taylor microscale but greater than the Kolmogorov microscale (η). Additionally, the results provided a clear definition of the large eddy Reynolds number (Re) of impinging sheets which previously was uncertain [2]. 2L/v' was found to be a function of Re to the negative 1/4 power and and ν⁄ϵ to the 1/2 power where v' is the velocity associated with the turbulent kinetic energy and ν is the kinematic viscosity. Similar to η/Λ, 2L/Λ is a function of Re to the – 3/4 power, where Λ is the size of the large energy-containing eddies.


Impinging Sheets
Turbulence microscales


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