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Unformatted text preview: 10.626 Electrochemical Energy Systems Spring 2011 MIT, M. Z. Bazant Problem Set 5 – Electrokinetics and Electrochemical Kinetics Due: Lecture 35 1. General electro-osmotic slip formula. Consider a thin, ﬂat, uniformly charged double layer subject to a tangential electric field E = Ex ˆ, which results in an effective electro- osmotic slip velocity, u s = u x ( y = ∞ ), outside the double layer. Define the zeta potential ζ as a measure of the slip velocity per field in units of voltage via, ε b ζ u s = − E η b where ε b and η b are the permittivity and viscosity of the bulk solution. Let ψ be the potential of the no-slip plane y = relative to the neutral bulk solution y = ∞ . (a) For a quasi-equilibrium double layer, we can express dielectric saturation (reduced pemit- tivity in large fields due to aligning solvent dipoles) as ε ( ψ ) and the viscoelectric effect (thickening of the ﬂuid in large fields or large charge density) as η ( ψ ), where ε (0) = ε b and η...
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.
- Spring '03