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.

Abstract

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.

Keywords

Impinging Sheets
Micromixing
Turbulence microscales

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