In the pressure infiltration of metal matrix composites, molten metal is injected under external pressure into a porous preform of the reinforcing material. Equilibrium capillary parameters characterizing wetting for this process are summarized in plots of metal saturation versus applied pressure, also known as drainage curves. Such curves can be measured in our laboratory during a single experiment with an infiltration apparatus designed to track the rate of metal penetration into porous preforms under conditions characteristic of metal matrix composite processing (temperatures in excess of 1000 A degrees C and pressures in the order of 10 MPa). For such measurements to be valid, infiltration of the preform with molten metal must be mechanically quasi-static, i.e., the metal must flow at a rate sufficiently low for the metal pressure to be essentially uniform across the preform at all times. We examine this requirement quantitatively, using a finite-difference model that simulates the unsaturated unidirectional ingress of molten metal into a ceramic particle preform of finite width. We furthermore present improvements in the experimental apparatus developed in our laboratory to measure the entire drainage curve in a single experiment. We compare numerical results with new experimental data for the copper/alumina system to show (i) that pressurization rates sufficiently low for quasi-static infiltration can be produced with this apparatus, and (ii) that taking the relative permeability equal to the saturation yields better agreement with experiment than does the expression originally proposed by Brooks and Corey.