Isotropic-nematic density inversion in a binary mixture of thin and thick hard platelets

We study the phase behavior of a binary mixture of thin and thick hard platelets, using Onsager’s second virial theory for binary mixtures in the Gaussian approximation. Higher virial terms are included by rescaling the excluded volume part of the Onsager free energy using a modified form of the Carnahan-Starling free energy for hard spheres (Parsons’ approach). Our calculations provide a simple explanation for the isotropicnematic (I-N) density inversion, as experimentally observed in systems of polydisperse gibbsite platelets by Van der Kooij et al. (J. Phys. Chem. B 2001, 105, 1696). In these systems, a nematic upper phase was found to coexist with an isotropic bottom phase. We confirm the original conjecture of the authors, which states that the phenomenon originates from a pronounced fractionation in thickness between the phases, such that the thick platelets are largely expelled from the nematic phase and preferentially occupy the isotropic phase. Our calculations show that the inverted state is found in a major part of the I-N coexistence region. In addition, a nematic-nematic demixing transition is located at sufficiently high osmotic pressures for any thickness ratio L2/L1 > 1. The N-N coexistence region is bounded by a lower critical point which shifts toward lower values as the thickness ratio is increased. At high thickness ratios (L2/L1 > 3.3), a triphasic coexistence is found at which two nematic phases coexist with an isotropic phase. We show that the demixing transition is driven by a small Φ(L/D) contribution to the excluded volume entropy

Mapping submarine sand waves with multiband imaging radar - 2. Experimental results and model comparison

On August 16, 1989, and on July 12, 1991, experiments were performed to study the mapping of submarine sand waves with the airborne imaging radar, a polarimetric (and, in 1991, interferometric) airborne P, L, and C band synthetic aperture radar system. The experiments took place in an area 30 km off the coast of the Netherlands, where the bottom topography is dominated by sand waves with a height between 2 and 6 m and a crest-to-crest distance of about 400 m at an average depth of 22 m. Ground measurements were recorded on a nearby platform and on a ship in the test area, which also acted as a position fix. On August 16, 1989, the wind was 5 m/s directed toward the northeast, while the surface current velocity was around 0.5 m/s directed toward the southwest. One overflight was made, with the flight direction parallel to the sand wave crests and the radar looking upwind. At P band, the sand waves are clearly visible as dark bands, as predicted by theory, while at L band the sand waves show up as sawtooth-shaped modulations. On July 12, 1991, wind and surface current had the same (opposite)-directions as in 1989, though the wind was much higher (10 m/s). Three flights were made, with the radar pointing upwind, cross wind, and downwind. The upwind and downwind images are very similar. Despite the high wind speed, the sand waves are clearly visible as sawtooth-shaped modulations at P band and vaguely visible at L band. At C band, only wind streaks can be seen. All cross wind images show the sand waves as dark bands, now with the highest modulations at C band. The wind streaks that dominated the upwind and downwind images at C band are much less pronounced in the cross wind images. The images are compared with predictions from a new model of the imaging mechanism which includes contribution to the radar cross section of waves moving both from and to the radar. Wave blocking or wave reflection is treated in an approximate manner. For the radar looking upwind or downwind, the predicted modulations at P and L band agree well with the observations, while those at C band are too high. For the radar looking cross wind, the model severely underestimates the modulations. It is questioned whether a local relaxation source term can describe such a situation. The interferogram shows some structure caused by bottom-induced surface current variations