On the Eulerian–Lagrangian formulation of balance equations in porous media

The article presents a general approach to modeling the transport of extensive quantities in the case of flow of multiple multicomponent fluid phases in a deformable porous medium domain under nonisothermal conditions. The models are written in a modified Eulerian–Lagrangian formulation. In this modified formulation, the material derivatives are written in terms of modified velocities. These are the velocities at which the various phase and component variables propagate in the domain, along their respective characteristic curves. It is shown that these velocities depend on the heterogeneity of various solid matrix and fluid properties. The advantage of this formulation, with respect to the usually employed Eulerian one, is that numerical dispersion, associated with the advective fluxes of extensive quantities, are eliminated. The methodology presented in the article shows how the Eulerian–Lagrangian formulation is written in terms of the relatively small number of primary variables of a transport problem. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 505–530, 1997     

Directly Bound Deuterons Increase X-Nuclei Hyperpolarization using Dynamic Nuclear Polarization

Deuterated ¹³C sites in sugars (D-glucose and 2-deoxy-D-glucose) showed 6.3-to-17.5-fold higher solid-state dynamic nuclear polarization (DNP) levels than their respective protonated sites at 3.35T. This effect was found to be unrelated to the protonation of the bath. Deuterated ¹⁵N in sites bound to exchangeable protons ([¹⁵N₂]urea) showed a 1.3-fold higher polarization than their respective protonated sites at the same magnetic field. This relatively smaller effect was attributed to incomplete deuteration of the ¹⁵N sites due to the solvent mixture. For a ¹⁵N site that is not bound to protons or deuterons ([¹⁵N]nitrate), deuteration of the bath did not affect the polarization level. These findings suggest a phenomenon related to DNP of X-nuclei directly bound to deuteron(s) as opposed to proton(s). It appears that direct binding to deuterons increases the solid-state DNP polarization level of X-nuclei which are otherwise bound to protons.