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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. Brian J. Kirby, PhD Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY. Ch 9: The Diffuse Structure of the Electrical Double Layer.

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Brian J. Kirby, PhD Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY

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  1. Powerpoint Slides to AccompanyMicro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices Chapter 9 Brian J. Kirby, PhD Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY

  2. Ch 9: The Diffuse Structure of the Electrical Double Layer • 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

  3. Sec 9.1: The Gouy-Chapman EDL • The Poisson-Boltzmann equation describes the potential and species concentration distributions in the EDL • Poisson equation: electrostatics • Boltzmann equation: equilibrium electrodynamics

  4. Sec 9.1: The Gouy-Chapman EDL • The Poisson-Boltzmann equation describes the potential and species concentration distributions in the EDL

  5. Sec 9.1: The Gouy-Chapman EDL • 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

  6. Sec 9.1: The Gouy-Chapman EDL • the Poisson-Boltzmann equation has many commonly used, simplified forms

  7. Sec 9.1: The Gouy-Chapman EDL • 1D, Debye-Huckel approximation: exponential potential decay

  8. Sec 9.1: The Gouy-Chapman EDL • 1D, Debye-Huckel approximation: exponential potential decay

  9. Sec 9.1: The Gouy-Chapman EDL • solving for the potential distribution in a geometry allows prediction of the electroosmotic flow velocity

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