Effect of Channel Sidewalls on Joule Heating Induced Sample Dispersion in Rectangular Ducts

In this article, we analyze the effect of channel sidewalls on the broadening of analyte bands resulting from Joule heating during their electrokinetic migration through a rectangular conduit. A method-of-moments formulation has been used to numerically evaluate the Taylor-Aris dispersivity of sample zones under these conditions for thin electrical double layers applicable to a majority of microfluidic assays. Our analysis shows that the larger surface area to volume ratio around the side regions of a rectangular channel causes these corners to stay cooler than the rest of the conduit. While such a thermal profile does not modify the electroosmotic flow in the system for a fixed temperature at the channel walls, it reduces the electrophoretic transport rate by about 10% for small temperature differentials across the channel cross-section (<10°C). The effect of these thermal gradients on the hydrodynamic dispersion of analyte bands is more significant however, increasing such band broadening by nearly an order of magnitude in large aspect ratio designs. Our analyses further show that the trends noted above are magnified when a fixed heat transfer coefficient is assumed at the channel walls, in which case, the temperature along this boundary is no longer constant. The non-isothermal channel walls combined with the temperature dependence of zeta potential and other material properties in this situation leads to a non-uniform electroosmotic slip velocity in the system modifying both fluid and analyte transport rates. Again, while the resulting solute flow profile reduces the migration velocity of sample zones only to a moderate extent, it is found to increase the hydrodynamic dispersion of analyte bands by several orders of magnitude in large aspect ratio rectangular channels.