© Cambridge University Press 2010 Brian J. Kirby, PhD Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY Powerpoint.

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Presentation transcript:

© Cambridge University Press 2010 Brian J. Kirby, PhD Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY Powerpoint Slides to Accompany Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices Chapter 9

© Cambridge University Press 2010 Solid-liquid interfaces acquire charge because there is a Gibbs free energy change associated with adsorption or reaction at surfaces Surface charge is coincident with a diffuse countercharge in the fluid The equilibrium structure of this diffuse countercharge is described using the Poisson and Boltzmann equations Ch 9: The Diffuse Structure of the Electrical Double Layer

© Cambridge University Press 2010 The Poisson-Boltzmann equation describes the potential and species concentration distributions in the EDL Poisson equation: electrostatics Boltzmann equation: equilibrium electrodynamics Sec 9.1: The Gouy-Chapman EDL

© Cambridge University Press 2010 The Poisson-Boltzmann equation describes the potential and species concentration distributions in the EDL Sec 9.1: The Gouy-Chapman EDL

© Cambridge University Press 2010 nondimensionalization of the Poisson-Boltzmann equation defines the thermal voltage and the Debye length the thermal voltage normalizes the potential and the normalized potential describes the magnitude of electromigratory forces with respect to random thermal forces the Debye length normalizes the coordinate system and describes to what extent the EDL can be considered a thin boundary layer near the wall Sec 9.1: The Gouy-Chapman EDL

© Cambridge University Press 2010 the Poisson-Boltzmann equation has many commonly used, simplified forms Sec 9.1: The Gouy-Chapman EDL

© Cambridge University Press D, Debye-Huckel approximation: exponential potential decay Sec 9.1: The Gouy-Chapman EDL

© Cambridge University Press D, Debye-Huckel approximation: exponential potential decay Sec 9.1: The Gouy-Chapman EDL

© Cambridge University Press 2010 solving for the potential distribution in a geometry allows prediction of the electroosmotic flow velocity Sec 9.1: The Gouy-Chapman EDL