This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and diffusion. Expanding upon analysis originally developed for non-reactive transport in the context of Taylor dispersion of scalars, this work extends the modified gradient diffusion model explicated by Peters (Turbulent Combustion, 2000) and based on work by Corrsin (JFM, vol. 11, beyond single-component transport phenomena and involving nonlinear reactions. The presented model forms, from this weakly-nonlinear extension of the original dispersion theory, lead to an analytic expression for the eddy diffusivity matrix that explicitly captures the influence of the reaction kinetics on the closure operators. Furthermore, we demonstrate that the derived model form directly translates between flow topologies through a priori and a posteriori testing of a binary species system subject to homogeneous isotropic turbulence. Using two-and three-dimensional direct numerical simulations involving laminar and turbulent flows, it is shown that this framework improves prediction of mean quantities compared to previous results. Lastly, the presented model form, collapses to the earlier gradient diffusion and its modified version derived by Corrsin in the limits of non-reactive species and linear reactions, respectively.

We have examined the evolution of irradiation-induced Ga nanoparticle (NP) arrays on GaAs surfaces. Focused-ion-beam irradiation of pre-patterned GaAs surfaces induces monotonic increases in the NP volume and aspect ratio up to a saturation ion dose, independent of NP location within the array. Beyond the saturation ion dose, the NP volume continues to increase monotonically while the NP aspect ratio decreases monotonically. In addition, the NP volumes (aspect ratios) are highest (lowest) for the corner NPs. We discuss the relative influences of bulk and surface diffusion on the evolution of Ga NP arrays.

Nonlocal algebraic closure models associated with both unresolved advective transport and nonlinear reaction terms in a Reynolds-averaged Navier-Stokes context are presented in this work. In particular, a system of species subject to binary reactions and transport by advection and diffusion are examined by expanding upon analysis originally developed for binary reactions in the context of Taylor dispersion of scalars. This work extends model forms from weakly-nonlinear extensions of that dispersion theory and the role of nonlocality in the presence of reactions is studied and captured by analytic algebraic expressions. These expressions can be incorporated into an eddy diffusivity matrix that explicitly capture the influence of chemical kinetics on the closure operators. Furthermore, we demonstrate that the model form derived in a laminar context directly translates to an analogous setup in homogeneous isotropic turbulence. We show that this framework improves prediction of mean quantities compared to previous results.

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