MIT10_626S11_lec30

MIT10_626S11_lec30 - VI Electrokinetics Lecture 30 Linear...

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Unformatted text preview: VI. Electrokinetics Lecture 30 Linear Electrokinetic Phenomena MIT Student 1 Linear Electrokinetic Resonse of a Nanochannel We start with the system in equilibrium Q = 0 I = 0 ε ∇ 2 ψ = ρ ( ψ ) ∇ p E =- ρ eq ∇ ψ Where p e is the electrostatic pressure. Now, consider applyig a small perturbationΔ P, Δ V and calculate linear response, and assume diffuse charge does not change: φ ( x, y,z ) = ψ ( x, y ) E zz ˆ- equilibrium potential profile small perturbation: axial electric field p ( x, y,z ) = p E ( x, y )- G zz ˆ z ∇ p =-∇ ⊥ p E + G ˆ small 1 Lecture 31: Linear electrokinetic phenomena 10.626 (2011) Bazant The transverse gradient ∇ = ∂ ∂ x y ⊥ ∂x...
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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.

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MIT10_626S11_lec30 - VI Electrokinetics Lecture 30 Linear...

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