A complete mathematical model is developed for application to simulate the unsteady two-step on-chip sample injection and separation processes in microfluidic devices. The origin and applicability of the slip-wall velocity boundary condition is discussed. Due to electrophoresis effect, migration influence of every species is considered in the model and then solved for separation analysis. The model is non-dimensionalized in a unique manner to reveal effects of some key fundamental parameters: the Reynolds-Schmidt number, electrophoretic mobility of sample species, applied potentials, etc. In particular, the influence of ReSci is examined over the commonly encountered range and the effect of electrophoretic mobilities on separation is investigated for three different types of samples. Results include center-line concentration profiles as well as concentration contour plots over a range of nondimensional time (less than 400). Resolution is defined and employed to evaluate the separation results. The magnitude of calculated separation resolution (around 2.0) is comparable to experimental results. Through parametric studies, the characteristics of both injection and separation are revealed numerically and well understood for future effective control and innovative chip design.

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