The Law of Capillary Rise

Interestingly, the impregnation criterion (/ 0) is much less restrictive than the spreading criterion (5 0) since 7 = 5 + 7. This explains why we see most liquids spontaneously soak sponges and other porous materials, whereas complete spreading is far less prevalent. In the first case, one surface is replaced by another, while in the second it is replaced by two others, which is a priori less favorable. 

The energy of a liquid column can be written in terms of its height h and the radius R of the capillary  

Finally, note that equation (2.30) was derived under the condition R H, which implies that tube diameters are small compared to the capillary length (R k ). In practice, this means that diameters are in the submillimeter range. When this condition is not met, correction terms must be introduced in equation (2.31) [the first such correction term for H(R) is of order R]. These correction terms were worked out in detailed mathematical developments first by Laplace, and subsequently by Poisson, Gauss, and Rayleigh in the 19th century. 

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Microporous membranes will fill their pores with wetting fluids by imbibing that fluid in accordance with the laws of capillary rise. The retained fluid can be forced from the filter pores by air pressure applied from the upstream side. The pressure is increased gradually in increments. At a certain pressure level, liquid will be forced first from the set of largest pores, in keeping with the inverse relationship of the applied air pressure P and the diameter of the pore, d, described in the bubble point equation ... 

The law of capillary rise (2.31) flows directly from equation (2.33). 

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