Simple model for blending aqueous salt buffers

In preparative chromatography of proteins and other biopolymers, elution is frequently achieved by a stepwise or continuous change of the mobile phase composition, generally denoted as step or linear gradient. The gradient is formed by inline mixing of two aqueous buffers. For prediction of peak profiles, examination of the reliability of blending devices and remote control of chromatography controllers a model would be advantageous. This would be most beneficial for ion-exchange chromatography and hydrophobic interaction chromatography where aqueous buffers must be blended. Here different salt concentrations are commonly blended. The model is able to describe the delay of onset and the transition period for step gradient. We developed a model based on the simple continuously stirred tank reactor model (CSTR) which has been modified to include logistic growth. Two parameters have to be estimated; parameter a is a lumped parameter related to the exponential time constant and Gaussian broadening. The second parameter, denoted b, describes the delay inherent to the system. This novel model is compared to a model based on the convolution of a step input with a Gaussian broadening and an exponential decay. The predicted values of both models are similar, when compared to experimental data obtained from inline mixing of two salt buffers. The logistic growth modified CSTR model exhibited higher residuals than the convolution model. The beginning of the gradient cannot be approximated in a smooth fashion, since the applied equation contains a sharp inflection. The current model's application is limited to the blending of salt buffers; pH is not a consideration of this model.