Experimental study and turbulence dissipative scale modelling of the rapid micromixing of impinging thin sheets of liquids

Abstract

Previous studies have shown that the impingement of thin liquid sheets produces high energy dissipation rates due to the release of kinetic energy in a very small mass of liquid (0.0001–0.01 g), even though flowrates are on the order of L/min. Rapid micromixing occurs because the dissipated energy leads to a substantial reduction in the initial segregation size scale of the liquids, which is the single-sheet thickness at impingement (~ 100 μm). In the present study, the micromixing was investigated by following the progress of an acid-base neutralization accompanied by a change in fluorescence intensity of a fluorophore. Micromixing was modeled using a framework that assumes diffusion and reaction of species occur within slabs of fixed thickness (2L). The slabs are fixed in size because the released kinetic energy is dissipated within one turnover time of the large energy-containing eddies produced in the turbulent impingement zone. A simulation, which included a module for calculating the fluorescence intensity, determined 2L for experimental energy dissipation rates (ϵ) ranging from 4×104 to 7.7×106 W/kg. 2L was found to lie in the range of turbulent dissipative scales less than the Taylor microscale but greater than the Kolmogorov microscale. 2L/v′ was found to be a function of ReΛ−1/4 and ν/ϵ1/2, where v′ is the velocity associated with the turbulent kinetic energy, ReΛ is the large-eddy Reynolds number and ν is the kinematic viscosity. Similar to η/Λ, 2L/Λ is a function of ReΛ−3/4, where ηis the Kolmogorov microscale and Λ is the size of the large energy-containing eddies.