MIT10_626S11_assn05

# MIT10_626S11_assn05 - 10.626 Electrochemical Energy Systems...

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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 0 be the potential of the no-slip plane y = 0 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 (0) = η b . Show that ε b ζ ψ 0 ε = η b 0 η (b) Derive

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