Capillary electrophoresis heat-dissipation tradeoff

The capillary electrophoresis heat-dissipation tradeoff is the balance between rapid electrically driven separation and the temperature rise caused by Joule heating. Narrow capillaries offer a large wall area per liquid volume, while high electric fields increase migration speed and electrical heat production. The 1981 primary experiment demonstrated efficient separations in a 75-micrometre-bore, one-metre glass capillary at 30 kV; it does not imply that arbitrarily high fields are thermally harmless.^[ref]

A simple model makes the competing scalings explicit. For a cylindrical liquid column of radius $a$, uniform electrical conductivity $\sigma$ and axial field $E$, current and heat production per unit length areAt fixed conductivity and bore, doubling the field doubles drift speed for constant electrophoretic mobility but quadruples generated heat. Halving the bore radius reduces heat per length by four at fixed field.

For steady radial heat conduction, let the liquid's thermal conductivity be $\kappa$ and impose a fixed wall temperature $T_w$. With uniform volumetric heating $q^{\prime \prime \prime }=\sigma E^2$, the cylindrical heat equation givesRegularity at the axis and the wall condition fix the integration constants. The center-to-wall rise is $\Delta T_{\max }=\sigma E^2{a}^2/(4\kappa )$. The symbol $\kappa$ here denotes thermal conductivity, not an optical decay constant.

For stipulated $\sigma =0.1S/m$, $E=30kV/m$, $a=25\mu \mathrm{m}$ and $\kappa =0.6W/(\mathrm{m}\mathrm{K})$, the model gives $P^{\prime }=0.1767$ W/m and center-to-wall rise 0.02344 K. Doubling the radius or field multiplies that rise by four. This ideal calculation holds the wall temperature fixed; it does not include heating through the capillary wall, instrument housing or cooling system.

Temperature gradients can change liquid viscosity, migration and band dispersion. Conversely, reducing bore size also reduces sample volume and optical path through the sample. A useful instrument experiment therefore records current and separation behavior while controlling cooling conditions, rather than judging success only by reduced migration time. The thermal model predicts what to test; it is not a measured temperature profile from the cited experiment.