(394c) Electrostatics Potential in Annular Geometry

Flow through an annular geometry has many applications in chemical, environmental, mechanical and bio-mechanical engineering [1]. 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 an annular geometry to sort particles using electrophoresis [2-3]. We present here a systematic investigation of the electrostatic potential distribution in an annular geometry. Our objective in this contribution is present a mathematical model for the electrostatic potential distribution in both straight and divergent 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. This result is in preparation to the derivation of the Electrohydrodynamic Velocity profile. The ultimate goal of this research is to understand the role of capillary geometry in determining biomolecular separations.  As a result of this investigation, one can assess the behavior of the electrostatic potential inside of annular channel. Three key parameters have been identified to describe the electrostatic potential behavior: the angle (∝), ratio of up wall potential to the linear combination of both wall potentials, R, which handles the symmetrical/non-symmetrical aspects of the electrostatic potential, and the ratio of the width to the length (γ) 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 the three parameters described above.

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2. Xuan X., Xu B., Li D., 2005 Accelerated particle electrophoretic motion and separation in converging–diverging microchannels. Anal Chem. 77, 4323–4328.
3. Ai Y., Joo S. W., Jiang Y., Xuan X., Qian S., 2009 Transient electrophoretic motion of a charged particle through a converging–diverging microchannel: effect of direct current-dielectrophoretic force. Electrophoresis. 30, 2499–2506.