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A theoretical study of multicomponent chromatography is here presented in which the system is considered to be one-dimensional, isothermal, locally at equilibrium and to have negligible diffusion effects. The discussion starts with constant initial and entry conditions and goes on to stepwise constant data with an arbitrary number of discontinuities. The Langmuir adsorption isotherm is perfectly fitted to the exposition of the mathematical theory of quasilinear equations for it leads to explicit forms for the Riemann invariants and characteristic parameters. This paper develops the theory of simple waves and of shock waves on an independent basis and illustrates this theory by the construction of solutions and the analysis of the interaction of waves. It is shown incidentally that the entropy change across a shock is consistent with the second law of thermodynamics. The separation of solutes is discussed and brief consideration is given to the problems associated with non-uniform geometry and non-isothermal adsorption.

A simplified model for diffusion and reaction in the boundary layer surrounding a burning carbon particle is considered. The model accounts for the homogeneous combustion of carbon monoxide and the heterogeneous reaction of carbon with oxygen and with carbon dioxide, the latter two reactions appearing in the model as nonlinear boundary conditions. It provides an insight into the double and single film models, proposed by others, as well as of the distribution of the products in the combustion of carbon.

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The object of this study was to derive a model which would accurately describe the evaporation of a multicomponent droplet, especially near its boiling point. The model is derived and is shown to have the following properties: the transport of one component can be augmented by the bulk (Stefan) flow of the other components, and the droplet can never exceed its boiling point, a property not realized by previous models. The ordinary differential equations which constitute the model were integrated numerically, and results are given for both two-and three-component droplets. SCOPEThe object of this study was to derive a mathematical model which would give an improved description of the evaporation of a multicomponent droplet in a stagnant gas, especially near the droplet boiling point. A large number of processes, such as spray drying, spray humidification, and combustion of liquid fuels in furnaces and in various types of engines, involve the evaporation of droplets. In addition, many of these processes operate at high temperatures where the droplet approaches a wet-bulb temperature very near its boiling point. Attempts to model such processes usually rely on a fairly simple model for the evaporation of a single-component droplet. Models exist which give an adequate description of evaporation under these conditions. However, in the multicomponent case it was found that the only model available was an adaptation of the single-component expression. Furthermore, this model gives erroneous results near the boiling point of the droplet and even permits the droplet to exceed its boiling point by a substantial amount. Hence, an improved droplet model is required if high-temperature, multicomponent spray processes are to be described with any accuracy. CONCLUSIONS AND SIGNIFICANCEA model was derived which gives an improved description of the evaporation of a multicomponent droplet. It was discovered that the augmentation of diffusive mass transfer by Stefan (bulk) flow from the drodet days an essential part in the improved model. The importance of Stefan flow in single-component evaporation has been known for some time. However, it was found to play an even greater role in the multicomponent case, where the transport of one component can be augmented by the transport of another. The inclusion in the model of this coupling of the transfer rates leads to the correct description of evaporation near the boiling point, and, in particular, keeps the droplet temperature from exceeding the boiling point. The remaining features of the droplet model were readily deduced from an analysis of the ordinary differential equations in the temperature-concentration phase plane. The behavior of evaporating droplets was further illustrated with the results of numerical calculations carried out for two-and three-component droplets. The model presented here represents a definite improvement over models previously available, notwithstanding its failure to include the effects of intraDarticle diffusion. Moreover, it agrees with results observed ...