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We investigate the suitability of the local compressibility chi(z) as ameasure of the solvophobicity or hydrophobicity of a substrate. Defining thelocal compressibility as the derivative of the local one-body density w.r.t.the chemical potential at fixed temperature, we use density functional theory(DFT) to calculate chi(z) for a model fluid, close to bulk liquid-gascoexistence, at various planar substrates. These range from a `neutral'substrate with a contact angle of approximately 90 degrees, which favoursneither the liquid nor the gas phase, to a very solvophobic, purely repulsivesubstrate which exhibits complete drying (i.e. contact angle 180 degrees). Wefind that the maximum in the local compressibility, which occurs within one-twomolecular diameters of the substrate, and the integrated quantity chi_ex (thesurface excess compressibility, defined below) both increase rapidly as thecontact angle increases and the substrate becomes more solvophobic. The localcompressibility provides a more pronounced indicator of solvophobicity than thedensity depletion in the vicinity of the surface which increases only weaklywith increasing contact angle. When the fluid is confined in a parallel slitwith two identical solvophobic walls, or with competing solvophobic andsolvophilic walls, chi(z) close to the solvophobic wall is altered little fromthat at the single substrate. We connect our results with simulation studies ofwater near to hydrophobic surfaces exploring the relationship between chi(z)and fluctuations in the local density and between chi_ex and the mean-squarefluctuation in the number of adsorbed molecules.

The Local Compressibility of Liquids near Non-Adsorbing Substrates: A Useful Measure of Solvophobicity and Hydrophobicity?