Ballistic dispersion in temperature gradient focusing

Molecular dispersion is caused by both molecular diffusion and non-uniform bulk fluid motion. While the Taylor–Aris dispersion regime is the most familiar regime in microfluidic systems, an oft-overlooked regime is that of purely kinematic (or ballistic) dispersion. In most microfluidic systems, this dispersion regime is transient and quickly gives way to Taylor–Aris dispersion. In electrophoretic focusing methods such as temperature gradient focusing (TGF), however, the characteristic time scales for dispersion are fixed, and focused peaks may never reach the Taylor limit. In this situation, generalized Taylor dispersion analysis is not applicable. A heuristic model is developed here which accounts for both molecular diffusion and advective dispersion across all dispersion regimes, from pure diffusion to Taylor dispersion to pure advection. This model is compared to results from TGF experiments and accurately captures both the initial decrease and subsequent increase in peak widths as electric field strength increases. The results of this combined analytical and experimental study provide a useful tool for estimation of dispersion and optimization of TGF systems.