Density functional theory calculations (ωB97X-D) are reported for the reactions of methoxy, tert-butoxy, trichloroethoxy, and trifluoroethoxy radicals with a series of 26 C−H bonds in different environments characteristic of a variety of hydrocarbons and substituted derivatives. The variations in activation barriers are analyzed with modified Evans−Polanyi treatments to account for polarity and unsaturation effects. The treatments by Roberts and Steel and by Mayer have inspired the development of a simple treatment involving the thermodynamics of reactions, the difference between the reactant radical and product radical electronegativities, and the absence or presence of α-unsaturation. The three-parameter equation (ΔH ⧧ = 0.52ΔH rxn (1 − d) − 0.35Δχ AB 2 + 10.0, where d = 0.44 when there is α-unsaturation to the reacting C−H bond), correlates well with quantum mechanically computed barriers and shows the quantitative importance of the thermodynamics of reactions (dictated by the reactant and the product bond dissociation energies) and polar effects.

We have performed two and three-dimensional phase field simulations using the lattice-Boltzmann method of liquid drops rising through a continuous phase liquid under the influence of buoyancy. In their upward motion the drops encounter a knife that is placed with the purpose of slicing the drops in two. A range of scenarios has been observed when the drop hits the knife and it has been investigated how the type of scenario depends on the dimensionless parameters governing the motion and slicing of the drop: the Eötvös number, the Morton number and the ratio of the droplet size and the width of the knife. We studied symmetric and asymmetric encounters between drop and knife and kept track of the size distribution of the resulting fragments.

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