Mathematical Modeling of Two-Stage Extraction Kinetics using the Single Drop Technique

This paper focuses on the mathematical modeling of the two-stage extraction using the single drop technique. Two stages of extraction are being considered: the drop formation step, where dimensions of the drop are highly dependent on time, and the drop travel step, during which the drops size and dimensions are assumed constant. Models for both extraction steps are derived and the combined model is proposed. Two-stage and one-stage models of extraction are compared. Errors occuring when considering only the travel stage of the single drop extraction have been calculated and their dependencies on various extraction parameters have been determined. The analysis of the combined two-stage model has proven that the travel-stage-only model generates significant errors during the determination of reaction rate constants when the drop formation time is significant in relation to the whole extraction time. Thus, the two-stage model should be used to reduce originating errors.