Screening in Yukawa fluid mixtures

The effective pair potential between mesoscopic charged particles in a neutralising background medium takes a Yukawa form $\exp (-\lambda r)\mathrm{/}r$ with screening length ${\lambda }^{-1}$. We consider a dilute suspension of such Yukawa particles dispersed in a solvent with correlation length $\xi <{\lambda }^{-1}$ and show that the Yukawa interaction is screened' if the pair potentials between solvent particles exhibit Yukawa decay with the same screening length $\lambda^{-1}$. However, if the solvent pair potentials are shorter ranged than the solute Yukawa potentials, then the effective potential between pairs of solute particles is unscreened’, i.e. the effective potential between the solute particles is equal to the bare potential at large particle separations.