  The free volume comprised between rough surfaces in contact governs the
fluid/gas transport properties across networks of cracks and the
leakage/percolation phenomena in seals. In this study, a fundamental insight
into the evolution of the free volume depending on the mean plane separation,
on the real contact area and on the applied pressure is gained in reference to
fractal surfaces whose contact response is solved using the boundary element
method. Particular attention is paid to the effect of the surface fractal
dimension and of the surface resolution on the predicted results. The free
volume domains corresponding to different threshold levels are found to display
fractal spatial distributions whose bounds to their fractal dimensions are
theoretically derived. A synthetic formula based on the probability
distribution function of the free volumes is proposed to synthetically
interpret the numerically observed trends.
