A description of Debye–Hückel theory includes a very detailed discussion of the assumptions and their limitations as well as the mathematical development and applications.
A snapshot of a 2-dimensional section of an idealized electrolyte solution is shown in the picture. The ions are shown as spheres with unit electrical charge. The solvent (pale blue) is shown as a uniform medium, without structure. On average, each ion is surrounded more closely by ions of opposite charge than by ions of like charge. These concepts were developed into a quantitative theory involving ions of charge ze and ze, where z can be any integer. The principal assumption is that departure from ideality is due to electrostatic interactions between ions, mediated by Coulombs law: the force of interaction between two electric charges, separated by a distance, r' in a medium of relative permittivity ε is given by
It is also assumed that
*The solute is completely dissociated; it is a strong electrolyte.
*Ions are spherical and are not polarized by the surrounding electric field. Solvation of ions is ignored except insofar as it determines the effective sizes of the ions.
*The solvent plays no role other than providing a medium of constant relative permittivity (dielectric constant).
*There is no electrostriction.
*Individual ions surrounding a "central" ion can be represented by a statistically averaged cloud of continuous charge density, with a minimum distance of closest approach.
The last assumption means that each cation is surrounded by a spherically symmetric cloud of other ions. The cloud has a net negative charge. Similarly each anion is surrounded by a cloud with net positive charge.