Electric double layers around finite-size clay particles

The electric double layer of co- and counterions around a finite, disc-shaped, uniformly charged clay platelet in a spherical or cylindrical Wigner-Seitz cell is studied within the linearized Poisson-Boltzmann theory. Explicit expressions are obtained for the density profiles, in the form of series in Legendre or Bessel functions. The quadrupole moment and the free energy of the charge distribution are calculated as functions of clay and salt concentrations. In cylindrical geometry, swelling is shown to be restricted under the action of electrostatic forces alone.