excess volume (at a solid/liquid interface)

Also contains definition of: excess mass (at a solid/liquid interface)
For a pure liquid, despite its low compressibility, the variation of density near a solid surface can be detected and measured. The total volume V of a system consisting of solid and pure liquid is different from (usually less than) that calculated assuming a constant liquid density. If the densities of bulk solid (ρ sol) and liquid (ρ l) are known then an excess volume (usually negative) can be defined as: \[V^{\sigma }=V- V^{\mathrm{sol}}- V^{\,\unicode{x26ac}}=V- \frac{m^{\mathrm{sol}}}{\rho ^{\mathrm{sol}}}- \frac{m^{\text{l}}}{\rho ^{\text{l}}}\] where m sol is the mass of solid, V sol its volume calculated from the bulk density, V° is the initial volume of liquid and m l is the mass of liquid. The excess mass is given by: \[m^{\sigma }=m^{\text{l}}- (V- V^{\mathrm{sol}})\ \rho ^{\text{l}}\]
PAC, 1986, 58, 967. 'Reporting data on adsorption from solution at the solid/solution interface (Recommendations 1986)' on page 972 (https://doi.org/10.1351/pac198658070967)