What is the interaction between dissolved ions of opposite valence in a solution at rest? NaCl is dissolved in water. Ions sodium and chloride are sufficiently free from each other so that they may occupy different regions of the solution after an active transport process through a membrane, or a mere electric field is in place.

They still act upon each other, and a membrane voltage is set by oppositely charged ions lining its interior and exterior surfaces.

So my question is this: how free are those ions in a uniform solution at equilibrium? Aren't they actually forming pairs of watered ions, although weakly bound? Can they form even bigger clusters, be them of short lifetime?

Note: I originally asked this on Physics SE but after several weeks I have received no answer nor any other kind of reaction, so I am trying Chemistry SE now.
The answer is: it depends. Dissolution of a salt implies that the entropy gained exceeds the cost of breaking lattice interactions (the solution enthalpy, assuming it is positive). Electrostatic interactions compete with kT (thermal jostling). Under physiological conditions, long range interactions are strongly screened by intervening solvent molecules and other ions. At best ions are subject to an effective potential due to distant ions, in particular between segregated charges as in the cases you present (e.g. on opposite sides of a membrane).

However, ionic solutions are generally regarded as "non-ideal". This means that interactions between the ions and with the solvent cannot be dismissed. At high salt concentration ion pairing will be encouraged. Above the solubility limit salt precipitation will occur, preceded by formation of clusters (seeds). If an ion has multiple charges, then electrostatic interactions will be stronger and pairing will be encouraged. Some metal ions form permanent ligand complexes that can attenuate the overall charge or distribute it over the complex, and the ligands can form a "cage" about the central ion, altering the interaction potential with solvent and other ions. The effect of temperature is complex. The entropic cost of association increases with T, but the dielectric constant of the solvent tends to decrease also.

If you are interested in reading on ion-pairing in NaCl solutions you may want to start with Ref. 1. It explains that association is negligible in dilute solutions:


  For dilute NaCl, we predict a coordination number of 5.3 with only waters in the solvation sphere for Na+ at 25 °C, 1 bar. With increasing NaCl molality, we find increased Cl complexation of Na. At 25 °C and 1 bar the Na+ ions in an 8 m solution of NaCl have 4.3 waters and 1.0 Cl ligands in their first coordination shell. There is some evidence of solvent-separated Na–Cl ion pairs from the peak in the Na–Cl pair distribution function at 5 Å. However, this disappears with increasing temperature. 


There is more on formation of NaCl complexes and clusters in that article.

References


Sherman, DM Collings, MD. Geochem. Trans., 2002, 3(11), 102–107