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Phase separation and criticality are analyzed in $z$:1 charge-asymmetricionic fluids of equisized hard spheres by generalizing the Debye-H\"{u}ckelapproach combined with ionic association, cluster solvation by charged ions,and hard-core interactions, following lines developed by Fisher and Levin(1993, 1996) for the 1:1 case (i.e., the restricted primitive model). Explicitanalytical calculations for 2:1 and 3:1 systems account for ionic associationinto dimers, trimers, and tetramers and subsequent multipolar clustersolvation. The reduced critical temperatures, $T_c^*$ (normalized by $z$),\textit{decrease} with charge asymmetry, while the critical densities\textit{increase} rapidly with $z$. The results compare favorably withsimulations and represent a distinct improvement over all current theories suchas the MSA, SPB, etc. For $z$$\ne$1, the interphase Galvani (or absoluteelectrostatic) potential difference, $\Delta \phi(T)$, between coexistingliquid and vapor phases is calculated and found to vanish as $|T-T_c|^\beta$when $T\to T_c-$ with, since our approximations are classical, $\beta={1/2}$.Above $T_c$, the compressibility maxima and so-called $k$-inflection loci(which aid the fast and accurate determination of the critical parameters) arefound to exhibit a strong $z$-dependence.Comment: 25 pages, 14 figures; last update with typos corrected and some added  reference

Criticality in charge-asymmetric hard-sphere ionic fluids