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In a recent article, we showed how the properties of the density-densitycorrelation function and its integral, the local structure factor, in the fluidinterfacial region, in systems with short-ranged forces, can be understoodmicroscopically by considering the resonances of the local structure factor[Nat.Phys.~{\bf 15}, 287 (2019)]. Here we illustrate, using mean-fieldsquare-gradient theory and the more microscopic Sullivan density functionalmodel, how this approach generalises when there is liquid-gas asymmetry, i.e.when the bulk correlation lengths of the coexisting liquid and gas phases aredifferent. In particular, we are able to express the correlation function\textit{exactly} as a simple average of contributions arising from twoeffective Ising-symmetric systems referred to as the symmetric gas andsymmetric liquid. When combined with our earlier results, this generatesanalytical approximations for the correlation function and the local structurefactor, which are near indistinguishable from the numerical solution to theOrnstein-Zernike equations over the whole range of wave-vectors. Our resultshighlight how asymmetry affects the correlation function structure, anddescribes the crossover from a long-ranged Goldstone mode to short-rangedproperties determined by the local density, as the wave-vector increases.

Microscopic determination of correlations in the fluid interfacial region in the presence of liquid-gas asymmetry