Mathematical and numerical model to study two-dimensional free flow isoelectric focusing.

Even though isoelectric focusing (IEF) is a very useful technique for sample concentration and separation, it is challenging to extract separated samples for further processing. Moreover, the continuous sample concentration and separation are not possible in the conventional IEF. To overcome these challenges, free flow IEF (FFIEF) is introduced in which a flow field is applied in the direction perpendicular to the applied electric field. In this study, a mathematical model is developed for FFIEF to understand the roles of flow and electric fields for efficient design of microfluidic chip for continuous separation of proteins from an initial well mixed solution. A finite volume based numerical scheme is implemented to simulate two dimensional FFIEF in a microfluidic chip. Simulation results indicate that a pH gradient forms as samples flow downstream and this pH profile agrees well with experimental results validating our model. In addition, our simulation results predict the experimental behavior of pI markers in a FFIEF microchip. This numerical model is used to predict the separation behavior of two proteins (serum albumin and cardiac troponin I) in a two-dimensional straight microchip. The effect of electric field is investigated for continuous separation of proteins. Moreover, a new channel design is presented to increase the separation resolution by introducing cross-stream flow velocity. Numerical results indicate that the separation resolution can be improved by three folds in this new design compare to the conventional straight channel design.