This note examines the modeling of non-convective fluxes (e.g., stress, heat flux and others) as they appear in the general, unclosed form of the volume-averaged equations of multiphase flows. By appealing to the difference between slowly and rapidly varying quantities, it is shown that the natural closure of these terms leads to the use of a single, slowly-varying combined average flux, common to both phases, plus rapidly-varying local contributions for each phase. The result is general and only rests on the hypothesis that the spatial variation of the combined average flux is adequately described by a linear function of position within the averaging volume. No further hypotheses on the nature of the flow (e.g., about specific flow regimes) prove necessary. The result agrees with earlier ones obtained by ensemble averaging, is illustrated with the example of disperse flows and discussed in the light of some earlier and current literature. A very concise derivation of the general averaged balance equation is also given.
Toxic effects of petroleum to marine zooplankton have been generally investigated using dissolved petroleum hydrocarbons and in the absence of sunlight. In this study, we determined the influence of natural ultraviolet B (UVB) radiation on the lethal and sublethal toxicity of dispersed crude oil to naupliar stages of the planktonic copepodsAcartia tonsa, Temora turbinata and Pseudodiaptomus pelagicus. Low concentrations of dispersed crude oil (1 μL L−1) caused a significant reduction in survival, growth and swimming activity of copepod nauplii after 48 h of exposure. UVB radiation increased toxicity of dispersed crude oil by 1.3–3.8 times, depending on the experiment and measured variables. Ingestion of crude oil droplets may increase photoenhanced toxicity of crude oil to copepod nauplii by enhancing photosensitization. Photoenhanced sublethal toxicity was significantly higher when T. turbinata nauplii were exposed to dispersant-treated oil than crude oil alone, suggesting that chemical dispersion of crude oil may promote photoenhanced toxicity to marine zooplankton. Our results demonstrate that acute exposure to concentrations of dispersed crude oil and dispersant (Corexit 9500) commonly found in the sea after oil spills are highly toxic to copepod nauplii and that natural levels of UVB radiation substantially increase the toxicity of crude oil to these planktonic organisms. Overall, this study emphasizes the importance of considering sunlight in petroleum toxicological studies and models to better estimate the impact of crude oil spills on marine zooplankton.