Total electric potential

Now the total electric potential at any point is taken equal to the sum of the potential due to the applied electric field plus the potential in the double layer, and this sum must satisfy Poisson s equation. Denoting the potential in the double layer by i/f, we see that... 

As is apparent from Eq. 1, evaluation of the momentum equation requires a description of the net charge density, pe, and the total electrical potential, O. The latter of these comprises of the summation of the electrical double layer, /, and the apphed electric potential, cj), as per Eq. 3 ... 

The dependence of the total electric potential on the charge distribution is shown by Poisson s equation ... 

Figure 3. IM NaCl solution at 30°C and -4e electrode charge. Top. Probability distribution profiles across the cell for H atom, water, and ions and Cl Bottom. Total electric potential and component (monopole, dipole, combined monopole plus dipole, quadnipole and octopole) electric multipole potentials. The total potential was calculated from the total electric charge distribution. Note that though the monopole and dipole components go off scale their sum is finite and weaker than the quadnipole component of the potential for the SPCE water.

Figure 7. 3M NaCl solution at 30 C and -4c electrode charge. Top. Probability density distribution profiles across the cell for H atoms, water, Na and Cr ions. Bottom. Total electric potential and component multipole potentials. Total potential was calculated by atom method (see text). Note that monopole and dipole potentials are flat across most of the cell because the screening zone is narrow for 3M NaCl solution. Octopole potential not displayed for clarity.

In this presentation, the total electrical potential at R is the sum of two contributions— the direct potential due to a at the center and an effective screening potential, having the opposite sign to that of the first term—which arise from the ionic atmosphere. The latter may be viewed as the constant potential within a sphere of radius k due to a net charge of - Za6 on its surface. This is another interpretation of the effective radius of the ionic atmosphere. 

When a pressure gradient is imposed across a membrane, the solution close to the solid surface at the pore wall remains immobile while the rest of the solution filling the pores moves past. This movement creates an electrical potential drop across the membrane, Ap. The flow-induced potential drop leads to a dynamical contribution to the total electric potential profile, q)( z). Under stationary conditions the electric potential within a pore, F(r), varies only radially. Both contributions to the total potential inside a pore can be written as... 

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