| Flow through an annular geometry has many applications in chemical, environmental, mechanical and bio-medical engineering. A number of researchers have proposed combining electroosmotic flow (EOF) and pressure-driven flow as a means of controlling the motion and separation of bioparticles in a variety of microfluidic devices, including those with an annular geometry to sort particles using electrophoresis, dielectrophoresis, and electrokinetics techniques.;In order to obtain a reliable model for predicting performance of such micro-based devices, the EOF calculations are studied. A vital aspect of these calculations is based on the electrostatic potential in the device. We present here a systematic investigation of the electrostatic potential distribution in an annular geometry. Our objective in this contribution is to present a mathematical model for the electrostatic potential distribution in a straight annular geometry. The analytical solutions for the electric potential profile in the annulus are obtained by solving the 2D Poisson--Boltzmann equation with both long channel and Debye--Huckel approximations.;The ultimate goal of this research has been to conduct analyses that can be used towards a better understanding of the role of capillary geometry in determining biomolecular separations or, alternatively, mixing. As a result of this investigation, one can assess the behavior of the electrostatic potential inside an annular channel. Two key parameters have been identified to describe the electrostatic potential behavior: 1) the ratio (R) of an imposed upper wall potential to the linear combination of both upper and lower wall potentials, a parameter which handles the symmetrical/non-symmetrical aspects of the electrostatic potential and 2) the inverse Debye length (k) that controls the "shape" of the channel section. Results of this study are illustrated by using a series of portraits that capture the key behaviors of the electrostatic potential with respect to these parameters described above. |
