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RESEARCH PRODUCT

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

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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 alpha, mercury surface tension gamma, and contact angle theta: e=(-2gamma/P)cos(theta-alpha) if theta-alpha>pi2. 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 alpha value) with opening width, E, distributed over interval [E(0),0], and volume-based distribution of opening width, f(V)(E), is written as where G(X)=(sin(-1)X-X1-X(2))/X(2) and X(E,e)=-cos(theta-alpha)Ee. The exact relation between total internal surface area and integral pressure work is.