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A theoretical model for interstitial liquid flow in a stationary or moving foam was devised by relating the physical structure of the foam to the physical properties of the surfactant and the foam movement. This was accomplished through a differential momentum balance within a typical capillary (Plateau border) of noncircular cross section with finite surface viscosity a t its boundaries. Velocity profiles were then calculated and integrated numerically for the randomly oriented capillaries so as to obtain the overall liquid flow through the foam in terms of the pertinent variables. Results are presented in a form suitable for estimating concentrations and flow rates of product and waste streams in foam fractionation.In recent years there has appeared a revival of interest in the potentialities of separating mixtures by foam fractionation. This technique of separation is based on the adsorption of a solute at the surface of bubbles formed by sparging a liquid mixture. These bubbles rise to form a foam which carries solute off overhead. A foam fractionation column can be operated as a refluxing enricher ( 1 6 ) , a stripper (17), or both (11). Applications include water renovation (13, 1 5 ) , radioactive effluent purscation (6, 26), and protein separation ( 2 5 ) . An extensive review of the literature has recently appeared ( 2 4 ) .Some introductory analyses have been presented for the operation of foam fractionation columns (5, 2 4 ) . These analyses show the quantitative role played by surface adsorption. However, they are incomplete in that they do not provide an independent relationship for foam density or for the flow rate of foam overhead. This lack, of course, stems from the complicated nature of foam drainage, especially in a moving column of foam which is constantly being formed at one end and removed at the other.Accordingly, the present investigation was aimed at devising and testing a more complete model which would include the interstitial liquid flow in the foam. The theoretical development is presented here, together with a design procedure. Experimental confirmation is presented in Part I1 of this paper. Part I1 also includes the complete notation for both Parts I and 11. Figure 1 shows a typical foam fractionation column (in this case without external reflux) operating under steady state conditions. By overall balance F = D + W(1)The surfactant passing overhead, namely CDD, can be divided into two parts so as to represent the physical picture more closely (5). The first part is the surfactant adsorbed at the bubble surfaces. This amounts to BGr/d,,. The second part is that in the interstitial liquid CLD. Substitution in Equation (2) yields Also, by material balance for a single surfactantIn a typical situation, F , G, and CF might be the given independent variables. Average bubble diameter d, would Inc., Wilmington, Delaware. r can be measured independently in a standard recirculating separator ( 5 ) or, in certain cases, estimated from surface tension measurements via the Gibbs adsorption equat...

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Runoff and persistence of selected herbicides were studied on four small Piedmont watersheds in Georgia during four growing seasons. This is part of a study designed to provide data for developing and testing mathematical models for agricultural chemical transport. Seasonal runoff losses were determined relative to watershed management, herbicide type and persistence, mode of application, and time of runoff in relation to application timing. Seasonal losses were usually < 2% of the application, unless large runoff volumes were generated shortly after application. Average storm herbicide concentrations in runoff were correlated with herbicide concentrations at the 0‐ to 1‐ cm depth increment of the watershed soils at the time of runoff. Paraquat concentrations in runoff (predominantly sediment associated) were well correlated and positive with the product of soil herbicide concentration and sediment in runoff. Equations describing soilbased herbicide transfer to runoff were power functions with exponents near unity with the form: Y = a xb. Simple relationships such as those developed in this study along with hydrology and erosion/sediment models may he useful in predicting pesticide runoff potential when assessing relative impacts of management decisions. The next step would be to describe key management practices in terms of these coefficients and exponents.