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

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=(−2γ/P)cos(θ−α) if θ−α>π2. The equations relating the volume of mercury in a single slit to hydrostatic pressure are established. The total volume of mercury VHgtot(E0,e) intruded in a set of unconnected isomorphous slits (same α value) with opening width, E, distributed over interval [E0,0], and volume-based distribution of opening width, fV(E), is written as VHgtot(E0,e)=−∫E0efV(E)dE+(1−b)e2∫E0efV(E)dEE2−tanα∫E=e0G(X(E,e))fV(E)dE, where G(X)=(sin−1X−X1−X2)/X2 and X(E,e)=−cos(θ−α)Ee. The exact relation between total internal surface area and integral pressure work is Stot=−1γHg(cosθ+sinα)∫0VHgtotPdVHgtot.