Small-angle neutron scattering (SANS) data for the tri-n-butyl phosphate (TBP)-n-dodecane, HNO3-UO2(NO3)(2) solvent extraction system have been interpreted using the Baxter model for hard spheres with surface adhesion. The increase in the scattering intensity in the low Q range observed when increasing amounts of HNO3 or UO2(NO3)(2) are transferred into the organic phase has been interpreted as arising from interactions between solute particles. The SANS data have been reproduced using a 12-16 Angstrom diameter of the hard sphere, d(hs), and a 5.6k(B)T-7.1k(B)T stickiness parameter, tau(-1). When in contact with an aqueous phase, TBP in n-dodecane forms small reverse micelles containing three TBP molecules. Upon extraction of water, HNO3, and UO2(NO3)(2), the swollen micelles interact through attractive forces between their polar cores with a potential energy of about 2k(B)T and an effective Hamaker constant of about 4k(B)T. The intermicellar attraction, under suitable conditions, leads to third-phase formation. Upon phase splitting, most of the solutes in the original organic phase (water, TBP, HNO3, and UO2(NO3)(2)) separate in a continuous phase containing interspersed layers of n-dodecane.