Theory of mercury intrusion in a distribution of unconnected wedge-shaped slits

Abstract Effective mercury intrusion in a wedge-shaped slit is gradual, the intruded depth increasing with applied pressure. The Washburn equation must be modified accordingly. It relates the distance, e , separating the three-phase contact lines on the wedge faces to the hydrostatic pressure, P , wedge half-opening angle α , mercury surface tension γ , and contact angle θ : e = ( − 2 γ / P ) cos ( θ − α ) if θ − α > π 2 . The equations relating the volume of mercury in a single slit to hydrostatic pressure are established. The total volume of mercury V Hg tot ( E 0 , e ) intruded in a set of unconnected isomorphous slits (same α value) with opening width, E , distributed over interval [ E 0 , 0 ], and volume-based distribution of opening width, f V ( E ) , is written as V Hg tot ( E 0 , e ) = − ∫ E 0 e f V ( E ) d E + ( 1 − b ) e 2 ∫ E 0 e f V ( E ) d E E 2 − tan α ∫ E = e 0 G ( X ( E , e ) ) f V ( E ) d E , where G ( X ) = ( sin −1 X − X 1 − X 2 ) / X 2 and X ( E , e ) = − cos ( θ − α ) E e . The exact relation between total internal surface area and integral pressure work is S tot = − 1 γ Hg ( cos θ + sin α ) ∫ 0 V Hg tot P d V Hg tot .