Application of the Washburn equation

The experimental method employed in mercury porosimetry, discussed more extensively in Chapter 20, involves the evacuation of all gas from the volume containing the sample. Mercury is then transferred into the sample container while under vacuum. Finally, pressure is applied to force mercury into the interparticle voids and intraparticle pores. A means of monitoring both the applied pressure and the intruded volume are integral parts of all mercury porosimeters. 

---

Szekely J, Neumann A, Chuang Y. (1971) The rate of capillary penetration and the applicability of the Washburn equation. ] Colloid Interface Sci 35 273-278. 

Mercury porosimetry is featured in many of the contributions to this volume. Indeed, it is now one of the most popular methods available for the characterization of a wide range of porous materials and the derived pore sizes are often quoted in the patent and technical literature. The method is based on the non-wetting nature of mercury and the application of the Washburn equation. The volume of mercury penetrating into a porous solid is determined as a function of the applied pressure, which is assumed to be directly related to the pore width. 

Inspection of Fig. 2 reveals that the applicability of the Washburn equation (eq. 6) is limited to data points with 10 s < t < 100 s. The correct solution of the imbibition equation (eq. 10) fits the measured data points perfectly. 

The applied pressure is related to the desired pore size via the Washburn Equation [1] which implies a cylindrical pore shape assumption. Mercury porosimetry is widely applied for catalyst characterization in both QC and research applications for several reasons including rapid reproducible analysis, a wide pore size range ( 2 nm to >100 / m, depending on the pressure range of the instrument), and the ability to obtain specific surface area and pore size distribution information from the same measurement. Accuracy of the method suffers from several factors including contact angle and surface tension uncertainty, pore shape effects, and sample compression. However, the largest discrepancy between a mercury porosimetry-derived pore size distribution (PSD) and the actual PSD usually... 

We now consider application of percolation theory to describing mercury intrusion into porous solids. First we briefly recall the main physical principles of mercury porosimetry (in particular, the Washburn equation). These principles are treated in detail in many textbooks [e.g., Lowell and Shields 49)]. The following discussions (Sections IV,B and IV,C) introduce general equations describing mercury penetration and demonstrate the effect of various factors characterizing the pore structure on this process. Mercury extrusion from porous solids is briefly discussed in Section IV,D. 

The method of mercury porosimetry requires evacuation of the sample and subsequent pressurization to force mercury into the pores 49). This technique was originally developed to enable pore sizes to be determined in the macropore range, where the gas adsorption method breaks down for practical reasons (6). Application of mercury porosimetry is based on the Washburn equation 62,63),... 

In many cases, it has been found experimentally that for liquids penetrating a porous medium, the Washburn law is dimensionally applicable (h r ). Therefore, the simplest approach toward modelling and understanding the kinetics of penetration into a porous medium is to treat it as a capillary with an effective radius . However, the model of an effective radius may be insufficient, especially when a significant distribution of pore sizes exists. It was concluded that the effective pore radius of a network of interconnected capillaries of varying radius, calculated by using the Washburn equation, may be very different from the radius calculated by other measurements, such as mercury porosimetry (39). A more sophisticated approach is based on the idea to model a porous medium as a group of capillaries of various sizes (16). 

The contact angle of liquids on solid powders can be measured by application of the Rideal-Washbum equation. For horizontal capillaries (gravity neglected), the depth of penetration 1 in time t is given by the Rideal-Washburn equation [11]... 

In spite of the growing popularity of mercury porosimetry and the ready availability of excellent automated equipment, the interpretation of the mercury intrusion-extrusion data is still far from clear. The values of surface tension and contact angle which must be inserted in the Washburn equation are still uncertain - as are the limits of applicability of the equation itself. Other problems include the reversible or irreversible deformation of the pore structure, which undoubtedly occurs with some corpuscular or weakly agglomerated systems. 

Inert polymer matrices, studied for use in possible controlled release applications, have used porosimetry to investigate a number of properties [54-56]. The kinetics of liquid capillary penetration into these matrices was explored using a modified Washburn equation [54]. It was shown that water... 

---