High energy dissipation rates from the impingement of free paper-thin sheets of liquids: Determination of the volume of the energy dissipation zone

08 May 2023, Version 2
This content is a preprint and has not undergone peer review at the time of posting.


The micromixing time of impinging thin liquid sheets depends upon the energy dissipation rate (ϵ). Earlier work studied the coefficient of restitution of the collision, which sets the amount of energy released [1]. The purpose of this study was to determine the volume of the energy dissipation zone. High-speed video was used to measure the velocity of features, generated in the front single sheet, as they passed through the impingement zone (IZ) and into the mixed sheet. The experimental results show that the released kinetic energy is dissipated within the residence time of the impingement zone (t_r). A new equation for ϵ_IZ (ϵ calculated based on a volume equal to the IZ volume) was developed and compared with ϵ derived from turbulence energy cascade theory: ϵ = C_ϵ{U_Λ}^2/t_Λ where C_ϵ is the dimensionless dissipation rate coefficient, {U_Λ}^2 is the turbulent kinetic energy and t_Λ is the large eddy turnover time. When the minimum value of C_ϵ (C_{ϵA} ) ≈ 0.5, t_Λ ≈ t_r. These results agree with the notion from turbulence energy cascade theory that large, energy-containing eddies lose their energy within t_Λ. For ϵ_IZ > 3x10^4 W/kg, C_ϵ/C_{ϵA} ≈ 1. At lower values of ϵ_IZ, C_ϵ > C_{ϵA}, and ϵ > ϵ_IZ (ϵ = ϵ_IZ C_ϵ/C_{ϵA}). For impinging sheets, C_ϵ was found to impact the rate at which kinetic energy is lost from the large eddies and not the amount of kinetic energy that is released by the collision.


Impinging Sheets
Energy Dissipation Rate


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