Washburn’s equation

Capillary flow porometry is essentially mercury porosimetry in reverse where the increasing gas pressure required to displace a fluid (not mercury) from a fluid filled scaffold is monitored as a function of time. Higher pressures equate to smaller pore sizes again following Washburn s equation i.e. 

The porosity of solid samples can be quantitatively studied by mercury poro-simetry. The total volume, specific surface area of the pores, bulk density, and particle size can be determined in 1.8 nm-300 pm pore size and 15 nm-3 mm particle size. The principle of the method is that there is a relationship between the pressure of mercury and the size of the pores filled with mercury. The pressure of mercury (p) required for its introduction into the pores of a given radius (r) can be expressed by Washburn s equation ... 

The values generally used are y = 485 dyn cm (1 dyn cm" = 1 m-N m ) and 0 = 140 . As a result of its non wetting properties with regard to numerous solids, mercury was chosen for this operation. It can be noted that Washburn s equation is derived from the more general equation proposed by Young-Laplace relating the pressure difference across a meniscus to its radius via the following expression ... 

Washburn s equation is deduced by assuming that P = 0 (the sample is in vacuum prior to the measurement) and Tp = r cos 6 (cylindrical pores). 

The ability of a system to draw water can be summarized by Washburn s equation ... 

In both methods, Washburn s equation is used, which was derived from the Poiseuille equation to measure viscosity in capillary viscometers. The rate of volume flow (V/t) through a capillary tube with radius, rc, is given by the Poiseuille equation as... 

AC = Yl- This is the case when the solid surface is precovered with the liquid duplex film and the liquid completely wets the solid surface (Fig. 3a). The original form of Washburn s equation. Eq. (16). is used. 

Pore structure of freeze dried PHEMA seafFolds was characterized on a mereuiy poro-simeter Pascal 140 and 440 (Thermo Finigan, Rodano, Italy). It woiks in two pressure intervals, 0-400 kPa and 1-400 MPa, allowing determination of meso- (2-50 nm), macro- (50-1000 nm) and small snperpores (1-116 pm). The pore volnme and most freqnent pore diameter were calculated under the assumption of a cyUndrical pore model by the PASCAL program. It employed Washburn s equation describing capillary flow in porous materials [33]. The volumes of bottle and spherical pores were evaluated as the difference between the end values on the volume/pressure curve. Porosity was calculated according to Equation 2, where cumulative pore volume (meso-, macro- and small supeipores) from mercury porosimetry was used for R. 

The penetration of a liquid within a porous medium can be compared to a first approximation to the phenomenon of capillary rise. We shall derive what is commonly known as Washburn s equation. Consider a capillary tube touching a liquid surface with its axis vertical and internal radius tq. 

When submitted to mercury porosimetry, the structure ofthese materials is compressed under isostatic pressure, before mercury can penetrate by intmsion in the largest pores. The curves obtained show a progressive volume reduction as a function ofpressure and this volume reduction is due to material densification and not to mercury intmsion inside the pore volume. Consequently, Washburn s equation (11-1) should not be used to analyze the... 

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