Mass Balance Relationships Research Articles

Concentrating Engines and the Kidney: I. Central Core Model of the Renal Medulla

Mass balance relations, valid for any counterflow system, are derived and applied to a central core model of the renal medulla, in which descending Henle's limbs (DHL), ascending Henle's limbs (AHL), and collecting ducts (CD) exchange with a central vascular core (VC) formed by vasa recta loops, assumed so highly permeable that the core functions as a single tube open at the cortical end, closed at the papillary. Solute supplied to the VC primarily by the water impermeable AHL may either enter the DHL to be recycled or remain in the core to extract water by osmosis from DHL and CD. If concentrations in core and descending flows are nearly equal, then for all degrees of recycling the ratio of entering DHL concentration to loop concentration is given by r = 1/[1 - f(T)(1 - f(U))], where f(T) is the fractional net solute transport out of AHL and f(U) is the ratio of CD flow to the sum of CD and AHL flows. Differential equations for a single solute are derived for core and AHL concentrations. Explicit analytic solutions are given for solute transport out of the AHL governed by Michaelis-Menten kinetics. Finally the energy requirements for concentration are analyzed.

Velocity Profiles and Dispersion in Estuarine Flow

The dispersion of pollutants in tidal waters is caused by turbulence and the shear effect of oscillatory, density, wind driven and steady flow currents. This investigation examines velocity gradients in an oscillatory system and the effects that these gradients have on the spread of pollutants. Velocity distributions are derived from the equations of motion and a mass balance relationship is used to model the dispersion process. The resulting equations can be used to estimate the spread of pollutants in the uniform density sections of estuaries in which tidal motion is the predominant mechanism of dispersion or combined with equations which represent the influence of density, wind driven or steady flow currents.

Reaction Rate Study of the Dissolution of Cuprite in Sulphuric Acid

The rate of reaction of cuprite was measured in a series of sulphuric acid solutions, from which oxygen had been excluded, at various concentrations and temperatures. The overall reaction Cu2O + H2SO4 → Cu++ + Cuo + H2O + SO4= may be explained quantitatively by two simultaneous rate reactions involving not only H+ but also the hydrolytic adsorption of H2SO4. The results indicate the importance of considering surface mass balance relationships associated with heterogeneous surface reactions.