Modelling sub-micron particle slip flow in liquid chromatography

The profoundly fast flow rates, observed at unexpectedly low column back-pressures, of capillaries packed with colloidal silica-based stationary phases is explained using slip flow theory applied to the particles themselves rather than the capillary walls. An equation is proposed that leverages nanoscale thermodynamics, geometrical considerations and Hagen-Poiseuille flow without the traditional no-slip boundary condition. It is found that the proposed model successfully fits/predicts real-world data taken from the literature, presented in a plot of the observed flow (enhancement) as a function of the (diminishing) mean particle size, so long as the particles do not exceed ~1 μm. This finding lends support to the continued use of colloidal silica packings in liquid chromatographic applications to achieve efficient separations of molecules on the smallest scale.