In Forward Osmosis the diffusion of the solute is counter to that of the solvent i.e. there is so-called “reverse salt diffusion”. Furthermore, the ratio of the two fluxes is generally taken to be a constant because of the assumption of ideal semi-permeability. However with the Spiegler-Kedem (S-K) model there is an allowance for a minor deviation from ideal semi-permeability and the ratio of the solute flux and solvent flux is no longer constant. The theoretical variation of the solute flux with increasing draw solution concentration is illustrated for various degrees of deviation from ideal semi-permeability. A novel variant of the S-K model is also introduced and predictions compared with those obtained using the standard form. With the acceptance that the form of “breakthrough” involving co-current flow is impossible, a limitation is imposed upon the S-K model but even with this limitation the theoretically predicted variation of solvent flux with increasing draw concentration is for certain sets of parameters of an unexpected form for minor deviation from ideal semi-permeability. That intriguing counter-intuitive outcomes can result from application of the S-K model indicates a need to rethink its formulation of the equations and the expressions for the coefficients. This will have implications for forward osmosis and possibly reverse osmosis modelling.

中文翻译：

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Spiegler-Kedem模型在正向渗透中的应用

在正向渗透中，溶质的扩散与溶剂的扩散相反，即存在所谓的“反向盐扩散”。此外，由于理想的半渗透率的假设，通常认为两个通量的比率是恒定的。但是，使用Spiegler-Kedem（SK）模型时，与理想的半渗透率之间的偏差很小，并且溶质通量和溶剂通量之比不再恒定。说明了相对于理想半渗透率的各种偏离程度，溶质通量随汲取溶液浓度的增加而发生的理论变化。还介绍了SK模型的新型变体，并将预测结果与使用标准形式获得的预测结果进行了比较。接受了并流的“突破”形式是不可能的，对SK模型施加了一个限制，但是即使有这个限制，理论上预测的溶剂通量随拉伸浓度的增加而变化的情况，也适用于某些形式的参数，这些参数具有意想不到的形式，与理想的半渗透性存在较小的偏差。SK模型的应用可能会产生令人反感的结果，这表明有必要重新考虑其方程式和系数表达式的表述。这将对正向渗透和可能的反渗透建模产生影响。SK模型的应用可能会产生令人反感的结果，这表明有必要重新考虑其方程式和系数表达式的表述。这将对正向渗透和可能的反渗透建模产生影响。SK模型的应用可能会产生令人反感的结果，这表明有必要重新考虑其方程式和系数表达式的表述。这将对正向渗透和可能的反渗透建模产生影响。