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<p>Fitting the Langmuir-Like Equation to adsorption isotherms provides capacity and affinity constants which allow fundamental understanding of adsorption but are not helpful for large-scale processes where the relation to the initial concentrations is most needed. In this paper, a novel equation is derived that allows the achievable final concentrations to be predicted based on any user-defined starting concentration, adsorbent loading, or solution volume. The equation accounts for both site-specific bonding and hydrophobic bonding and provides versatile plots while being simple to use in a spreadsheet format. The adsorption of barbituric acid, fluoxetine, phenobarbital, and procaine to 4 types of commercial activated carbons at different pH values, temperatures, buffers, and cosolvents is studied as an example. For instance, it was shown that for a 0.8&#xa0;mg/mL initial solution of phenobarbital, a 20% increase of carbon mass will only result in a 5% decrease in final concentration. At 0.2&#xa0;mg/mL initial phenobarbital concentration, no considerable improvement in adsorption can be observed for a loading mass to solution ratio &gt; 0.75&#xa0;mg adsorbent /mL solution. For adsorbates with a high extent of hydrophobic bonding, great reductions in concentrations, approaching zero, can be achieved even at high initial concentrations. The derived equation is free of assumptions, and is not specific to the systems studied.</p> Graphical Abstract <p></p>

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Prediction of Large-Scale Adsorption Process Parameters Using Two-Mechanism Langmuir Constants

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Zaid Assaf,
  • Dale Eric Wurster

摘要

Fitting the Langmuir-Like Equation to adsorption isotherms provides capacity and affinity constants which allow fundamental understanding of adsorption but are not helpful for large-scale processes where the relation to the initial concentrations is most needed. In this paper, a novel equation is derived that allows the achievable final concentrations to be predicted based on any user-defined starting concentration, adsorbent loading, or solution volume. The equation accounts for both site-specific bonding and hydrophobic bonding and provides versatile plots while being simple to use in a spreadsheet format. The adsorption of barbituric acid, fluoxetine, phenobarbital, and procaine to 4 types of commercial activated carbons at different pH values, temperatures, buffers, and cosolvents is studied as an example. For instance, it was shown that for a 0.8 mg/mL initial solution of phenobarbital, a 20% increase of carbon mass will only result in a 5% decrease in final concentration. At 0.2 mg/mL initial phenobarbital concentration, no considerable improvement in adsorption can be observed for a loading mass to solution ratio > 0.75 mg adsorbent /mL solution. For adsorbates with a high extent of hydrophobic bonding, great reductions in concentrations, approaching zero, can be achieved even at high initial concentrations. The derived equation is free of assumptions, and is not specific to the systems studied.

Graphical Abstract