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Abstract:A numerical model was developed for flows involving an interface between a homogenous fluid and a porous medium. The numerical model is based on the finite volume method with body-fitted and multi-block grids. The Darcy-Forchheimer extended model is used to govern the flow in the porous medium region. At its interface, a shear stress jump was imposed, together with a continuity of normal stress. Furthermore, the effect of the jump condition on the diffusive flux is considered, additional to that on the convective part which has been usually considered. Numerical results of three flow configurations are presented. The modeling is suitable for problems which have complex interface boundary conditions coupling between two flow domains.

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An asymmetric unactivated alkene/C-H bond difunctionalization reaction for the concomitant construction of C-CF3 and C-O bonds was realized by using a Cu/Brønsted acid cooperative catalytic system, thus providing facile access to valuable chiral CF3-containing N,O-aminals with excellent regio-, chemo-, and enantioselectivity. Mechanistic studies revealed that this reaction may proceed by an unprecedented 1,5-hydride shift involving activation of unactivated alkenes and a radical trifluoromethylation to initiate subsequent enantioselective functionalization of C-H bonds. Control experiments also suggested that chiral Brønsted acid plays multiple roles and not only controls the stereoselectivity but also increases the reaction rate through activation of Togni's reagent.