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Electrode-electrolyte interface (Electroosmosis: describe the fluid flow…
Electrode-electrolyte interface
Helmholtz double layer: interface as a capacitor
Gauss law> Gauss theorem>Poisson equation (L6P26)
Use Gauss law to calculate Helmholtz layer capacitance
Did not include ion conc. and app. volt. : :!:
Gouy-Chapman model: infinitive charge surface
Consider ion distribution: Boltzmann distribution
Plug in charge density into Poisson equation
Poisson-Boltzmann equation
Linearlized: Debye Hückel approximation
conc.->infinity, Capacitance-> infinity :red_cross:
nonlinearlized
capacitance correlated by cosh but still the same as the above
Electro displacement :question:
Gouy-Chapman-Stern: Helmholtz and diffusion double layer(two capacitors in series)
Electrophoresis: charge particle in fluid actuated by E-field
velocity= mobility x E-field *use Nernst-Einstein equation to calculate mobility
Nernst-Planck equation: change in concentration= divergence of sum of flux * combine convective and electrokinetic induced ion movement
When considering electrophoresis, the assumption of divergence of the velocity does not hold for every specie.
Electroosmosis: describe the fluid flow when an extrinsic field actuates the electrical double layer * relation of local electric field and outer flow velocity is mobility, function of surface potential, fluid permittivity and viscosity
Inner solution: Near the wall -> extrinsic field is uniform
Navier-Stokes equation with electrostatic term
Assumption: steady isobaric flow in x, and velocity gradient only in y
use Poisson equation > integrate > Poisson Boltzmann equation * boundary condition: u is bounded at infinity, no-slip: u(0)=0
Outer solution: Far from the wall: Net charge density is zero
Use integral analysis of the electrical double layer to solve
Navier-Stokes equation with neglectable electrostatic term due to charge neutrality
Plug in boundary solution of interior solution :question:
Example: apply voltage can drive pump * generate pressure in no-net pressure system