Modeling of surface-fluid electrokinetic coupling on the laminar flow friction factor in microtubes

The present work's originality lies in the evidence of a non-negligible effect of the fluid ions' and co-ions' interaction with the wall surface in a microtube. This study is based on the EDL theory (electrical double layer), which is developed here for a circular geometry. High electrical surface potentials are taken into account for the present study, they induce the nonlinearity of the problem's main equation (Poisson-Boltzmann equation). The electrical field is determined, then the velocity profile, and, finally, the Poiseuille number, which is the product between the friction factor and Reynolds number. We show that even with the EDL effect taken into account, the Poiseuille number does not depend on the mean velocity. Our model for high surface potentials (>25 mV) agrees with previous experimental results carried out with microtubes ranging from 530 to 50 mum [1].