Washbume

Deshaies, R.J., Koch, B.D., Wemer-Washbume, M., Craig, E.A., Schekman, R. (1988). kA subfamily of stress proteins facilitates translocation of secretory and mitochondrial precursor polypeptides. Nature 332,800-805. 

Rowley, A., Johnston, G.C., Butler, B., Werner-Washbume, M., Singer, R.A. (1993). Heat shock-mediated cell cycle blockage and G1 cyclin expression in the yeast saccomyces cerevisiae. Mol. Cell. Biol. 13, 1034-1041. 

The pore shape affects the pressure of mercury intrusion in ways not contemplated by the usual Washbum-Laplace or Kloubek-Rigby-Edler models. These models have been developed for cylindrical pores and correctly account for the penetration of mercury in the cylindrical pores of MCM-41. The uneven surface of the cylindrical pores of SBA-15 is responsible for a significant increase of the pressure of mercury intrusion and, thereby, for a corresponding underevaluation of the pore size if the classical pressure-size correlations are applied. 

The comparison between pore sizes evaluated by Hg intrusion and N2 volumetry for MCM-41 and SBA-15 samples are reported in Fig. 3. The data obtained from the two techniques coincide for MCM-41, while Hg intrusion underevaluates the pore size of the SBA-15 samples. The Washbum-Laplace model (Fig. la) [1] does not account for the cavitation effects in the retraction of Fig [9], which are taken into account by the Kloubek-Rigby-Edler model (Fig. lb) [2], The pore size evaluated by N2 adsorption is not affected by the defects of the pore walls of SBA-15, as these defects have already been filled when capillary condensation takes place [10]. 

Figure 3. Pore size from Fig porosimetry data calculated by the (a) Washbum-Laplace equation or the (b) Kloubek-Rigby-Edler equations vs. the pore size from N2 volumetry. Triangle MCM-41 lozenges SBA-15 samples empty symbols intrusion filled symbols retraction. The solid lines correspond to equal diameters from Fig porosimetry and N2 volumetry.

The penetration of mercury in MCM-41, a material with smooth cylindrical pores, takes place at the pressure indicated by the Washbum-Laplace model, indicating that this model is still valid at the scale of a few nanometers. When the pore surface is pitted with micropores or when the pores are interconnected, like in the case of SBA-15, the Washbum-Laplace model underevaluates the size of the pores, due to the excess energy needed for advancement of the meniscus beyond the surface defects. 

It is interesting to observe that a fair correlation can be found between the pore size evaluated by the Washbum-Laplace model and the pore size evaluated by the BJH model of nitrogen adsorption in the case of SBA-15 [12] and other materials with interconnected pores [13], In the case of gas adsorption, the surface defects are filled at a lower pressure and do not affect the pressure of capillary condensation [10]. However, the BJH model does not take into account the effects of curvature on condensation and systematically underevaluates the size of the mesopores [7, 14]. 

Martinez, M.J., Aragon, A.D., Rodriguez, A.L., Weber, J.M., Timlin, J.A., Sinclair, M.B., Haaland, D.M., and Werner-Washbume, M., Identification and removal of contaminating fluorescence from commercial and in-house printed DNA microarrays, Nucleic Acid Res., 31(4), 1-8, 2003. 

The left-hand side of the latter equation is related to the liquid inertia, whereas both terms in the right-hand side are related to capillarity (the driving force), and viscous resistance, respectively. Under steady conditions, capillarity is balanced by the viscous drag of the liquid, and the famous Lucas-Washbum s equation can be derived (De Geimes et al., 2002) ... 

In the last decade, a variety of microporous and mesoporous materials have been developed for applications in catalysis, chromatography and adsorption. Great attention has been paid to the control of (i) pore surface chemistry and (ii) textural properties such as pore size distribution, pore size and shape. Recently, a new field of applications for these materials has been highlighted [1-3] by forcing a non-wetting liquid to invade a porous solid by means of an external pressure, mechanical energy can be converted to interfacial energy. The capillary pressure, Pc p, required for pore intrusion can be written from the Laplace-Washbum relation,... 

The rate of liquid penetration has been investigated by Rideal and Washburn [7, 8]. For horizontal capillaries (gravity-neglected), the depth of penetration I in time t is given by the Rideal-Washbum equation [7, 8] ... 

Thus, a plot of f- versus t gives a straight line, from the slope of which 0 can be obtained. The Rideal-Washbum [7, 8] equation can be appUed to obtain the... 

The rate of penetration of a liquid by a distance I through capillaries with radius r has been described by the Rideal-Washbum equation,... 

Penetration of a liquid flowing under its own capillary pressure in a horizontal capillary, or in general, where gravity can be neglected, is theoretically described (4) by the Lucas-Washbum equation... 

The Lucas-Washbum equation is the simplest equation to model the rate of capillary penetration into a porous material. It is derived from Poiseuille s iaw (4) for laminar flow of a Newtonian liquid through capillaries of circular cross-section by assuming that the pressure drop (AP) across the liquid-vapor interface is given by the Laplace-Young (6) equation. In practice, depending... 

Finally increase in n shown by several systems during postdrying (3) (see Table I) stems from subterranean absorption processes e.g. interconnection of partially filled pores and localized surface fibre wicking. The values of n which in several cases are close to the theoretical value, 0.5, for a Lucas-Washbum type capillary model, suggest that the condition of flow through completely filled and interconnected capillaries to supply the spreading front, is ultimately attained. This final stage reflects lag in the equilibration of bulk and surface capillary forces. 

Deviations between the experimental results and the modified Lucas-Washbum capillary models demonstrate the limitations of these theories for paper structures. Moreover, as discussed above, concentration gradients will likely exist within the penetration zone during ink jet printing so that AP, the capillary pressure, is no longer constant and hence [l] loses its validity. The inapplicability of [l] thus makes derivation of an effective pore radius, on the basis of [4] and Figure 4, dubious. 

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