In the field of agitation much work has been done to show that the power required by an agitator varies systematically with density of a homogeneous liquid (11 ) or an immiscible liquid pair (8) that is being agitated. The introduction of a gas into a liquid in which a mechanical agitator is rotating, on the other hand, brings about a mixture for which one is unable to calculate an average density significantly related to the power consumption of the impeller. The theory of power requirement of an impeller rotating in a homogeneous fluid is imperfectly developed, consisting mainly of the relatively unrigorous theory of models; that of an impeller handling a gas-liquid mixture has never been treated.Gas-liquid contacting in mixing vessels has been investigated with regard to chemical reactions and mass transfer coefficients by Oldshue ( 9 ) , Bartholomew, Karow, Sfat and Wilhelm (1) and others with no special attention being given correlation of power data. Cooper, Fernstrom, and Miller (4) reported that the agitation power with a high rate of gas feed to the impeller could be as little as 25% of the impeller's no-gas power but declared that the dependence of impeller power on gas rate is erratic and unpredictable. Foust, Mack, and Rushton ( 5 ) presented power data for an arrow-head disperser in the form of a plot of K (horsepower in water with In 1955 Oyama and Endoh (10) attempted to correlate power in gasliquid agitated systems by the K factor of Foust, Mack, and Rushton ( 5 ) and the dimensionless group N , = Q/ ND'. They succeeded in a limited correlation, that of the effect of gas rate on the power of a particular impeller operating at constant speed. Later Calderbank (3) offered the same correlation to data obtained with a flatblade turbine dispersing air in a number of liquids (density ranges 0.74 to 1.6 g./ml., viscosity range 0.5 to 28 centipoises). His plot of P , / P , against N , at constant impeller speed resulted in two intersecting straight line sectors that only approximated the shape of the curve of Oyama and Endoh.Previous to this, in 1955, Kalinske (6) discussed the power required by a flat-blade turbine operating in aerated sewage. He presented the data in the form of a plot of a term directly proportional to K vs. (1 -N , )

We study coordinate-invariance of some asymptotic invariants such as the ADM mass or the Chruściel-Herzlich momentum, given by an integral over a "boundary at infinity". When changing the coordinates at infinity, some terms in the change of integrand do not decay fast enough to have a vanishing integral at infinity; but they may be gathered in a divergence, thus having vanishing integral over any closed hypersurface. This fact could only be checked after direct calculation (and was called a "curious cancellation"). We give a conceptual explanation thereof.

Abstract:This paper focuses on the characterization and modeling of a solid/gas thermochemical reaction between a porous reactive bed and moist air flowing through it. The aim is the optimization of both energy density and permeability of the reactive bed, in order to realize a high density thermochemical system for seasonal thermal storage for house heating application. Several samples with different implementation parameters (density, binder, diffuser, porous bed texture) have been tested. Promising results have been reached: energy densities about 430-460 kWh.m -3 and specific powers between 1.93 and 2.88 W.kg -1 of salt. A model based on the assumption of a sharp reaction front moving through the bed during the reaction was developed. It has been validated by a comparison with experimental results for several reactive bed samples and operating conditions. Keywords:Thermochemical process, seasonal thermal storage, sharp front model, high-density reactive salt, permeability.