ES potential two parallel plates

AI Thread Summary
The discussion focuses on deriving the electrostatic potential between two flat plates in an electrolyte solution, emphasizing the low surface potential at the plate surfaces. Participants mention the use of the Poisson equation for electrostatic potential, noting that previous attempts to solve the problem were incorrect, particularly involving hyperbolic cosine functions. The Poisson-Boltzmann equation is referenced, indicating a relationship between the potential and charge density. The interaction between the plates is described mathematically, but participants express frustration with the complexity of the derivation. Overall, the conversation highlights the challenges in accurately modeling the electrostatic potential in this scenario.
Knot Head
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Derive the electrostatic potential between two flat plates in electrolyte solution. The surface potential at the plate surfaces is low.

I think this problem uses the Poisson equation for electostatic potential, but the one I came up with was wrong. It involves the hyperbolic cos. (cosh)
 
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Knot Head said:
Derive the electrostatic potential between two flat plates in electrolyte solution. The surface potential at the plate surfaces is low.

I think this problem uses the Poisson equation for electostatic potential, but the one I came up with was wrong. It involves the hyperbolic cos. (cosh)

\Phi'(\(pmR)=\pm2S_{R}/\lambda_{GC}
S_{R}=sgn(\sigma_{R}
\Phi'(0)=0

and Poisson-Boltzman
\Psi=\betaq\phi for two identical charged plates is given by
-\Psi''(z)+sinh \Psi(z)=0
the first integral= cosh \Psi
the interaction between the two plates is:
P=2nT(\alpha-1)=T\delta\alpha/4\pil\lambda

I keep going around and around but I'm not even close. Any advice would be greatly appreciated.
 
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