We show how nuclear magnetic spin-lattice relaxation dispersion of 1H water can provide a direct reliable value of the specific surface area of a cement-based material. The remarkable features of the relaxation dispersion support an interpretation in terms of coupled solid-liquid relaxation at pore interfaces, surface diffusion, and nuclear paramagnetic relaxation. The measurement is sufficiently fast to be applied continuously during the progressive hydration and setting of the material. This method is relevant to other chemically reactive porous media in chemical engineering and oil recovery.

We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions. We show that the nature of the bifurcation, which can be either supercritical or subcritical or even take the form of isola (or detached lobes) strongly depends on the parameters. This dependence is described in a range of parameters numerically accessible (which unfortunately remains remote from geophysical application), and we show how the magnetic Prandtl number and the Ekman number control these transitions.

A quasi-geostrophic, or ␤, model of nonlinear thermal convection in rapidly rotating spherical fluid shells is investigated. We study time dependent instabilities for a range of Rayleigh number and Ekman number with a Prandtl number set to the unity. Above the onset of convection, increasing the Rayleigh number for a given Ekman number, we reproduce the sequence of bifurcations described by Busse ͓Phys. Fluids 14, 1301 ͑2002͔͒ for the three-dimensional case: A first transition results in vacillating flow; a second transition gives rise to chaotic oscillations in time and localized convection in space; then a third leads to quasi-periodic relaxation oscillations. This study shows that the quasigeostrophic model encompasses the desired bifurcation sequence. It allows the investigation of a range of Ekman numbers unavailable to three-dimensional models with present computing resources. Decreasing the Ekman number, we unexpectedly found that all three transitions occur for marginally supercritical Rayleigh number. The range of Rayleigh number for which the amplitude of convection is steady vanishes in the asymptotic limit of small Ekman numbers. This effect could significantly alter the nature of the instability characterizing the onset of convection in particular whether it is a supercritical or subcritical bifurcation.

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