Mixing and reaction in turbulent plumes: the limits of slow and instantaneous chemical kinetics

Abstract

We investigate the behaviour of a reactive plume in the two limiting cases of slow and instantaneous chemical reactions. New laboratory measurements show that, whereas the slow reaction between the source and entrained chemical species takes place within the whole volume of each eddy in the plume, the fast reaction develops preferentially at the periphery of the eddies. We develop a new model that quantifies the mixing of the reactive buoyant fluids at the Batchelor scale and thereby the progress of the fast reaction. We present a series of new experimental results that suggest that a critical distance from the source, $z_{crit}$, exists at which the volume of fluid that is entrained from the ambient is equal to that which is mixed within the plume at the Batchelor scale. For $z>z_{crit}$, only a fraction of the entrained fluid is rapidly mixed and reacts with the plume fluid. The results of the new experiments enable us to quantify the distance from the source at which an instantaneous reaction reaches completion, and show that it can be significantly larger than the distance $L_{s}$ at which the stoichiometric dilution of the plume fluid is achieved. In the limit of an instantaneous reaction, the longitudinal profiles of source chemical concentration in the plume depend on $(z_{crit}/L_{s})^{5/6}$. The predictions of the model are validated against the experimental results, and the profiles of source chemical concentration in the plume for slow and fast reactions are compared.

Micro-droplet nucleation through solvent exchange in a turbulent buoyant jet

“…As entrainment is the only mechanism we include in the model, the significant deviation from the experimental results unveils that additional factors must contribute to the observed phenomenon. Mingotti & Cardoso (2019) considered mixing as the bottleneck for the fast reactive plume, which led to the prolonged depletion of the injected liquid before reaching stoichiometric level. Mingotti & Cardoso (2019) pointed out that mixing was constrained within the Batchelor scale located at the rim of the eddies in the reactive plume, causing incomplete reaction for those entrained fluids.…”

“…We therefore use a light attenuation technique to measure the local concentration. This technique has been widely adapted in turbulent jet and plume studies based on the pioneering work of Cenedese & Dalziel (1998), from single phase cases with dye as in Kikkert, Davidson & Nokes (2007), Allgayer & Hunt (2012), Van Sommeren, Caulfield & Woods (2012) and Mingotti & Cardoso (2019), to multiphase ones as in Leppinen & Dalziel (2001) and Mingotti & Woods (2015). The method is based on the Lambert–Beer law, relating the recorded depth-integrated intensity to the concentration field, namely where is the recorded intensity of the averaged images, the reference intensity of the background, the light absorption property of the dye determined from calibration, the depth of the substance in the line of sight and the desired line-of-sight average concentration.…”

“…We compare the ouzo case with the nucleation-free case of injecting only dyed ethanol, revealing the distinct features of the ouzo case in the radial concentration profile, the centreline evolution and the oversaturation flow rate. Adapting the mixing-limited arguments for the prolonged depletion of the reacting plume of Mingotti & Cardoso (2019), the extended lifetime of the droplet-laden respiratory puff of Chong et al. (2021) and of the evaporating spray of de Rivas & Villermaux (2016) and Villermaux et al.…”

“…Their experimental findings show that the reactions only occurred preferentially in part of the thermals for the instantaneous case, while for the slow reactions the thermals were homogeneous in composition. Mingotti & Cardoso (2019) experimentally compared the slow and instantaneous reactions in turbulent plumes, discovering preferential reaction for the instantaneous case as well, which appeared on the edge of the eddies. They formulated a theoretical prediction for the concentration evolution in reacting plumes using scale analysis of entrainment, mixing and reactions.…”

Chemical reaction for mixing studies

“…There is, however, a constant need to have at one's disposal a chemical signal, produced via a proper chemical reaction, reflecting the intrinsic dynamics of any system having its own kinetics, may it be biological [19][20][21] or not [22,23].…”