Cos velocity u, Im/s) Liquid tood i^lmWhl tension increases as liquid goes down the column, surface tension neg ative (o—) when surface tension drops as liquid goes down the columr and surface tension neutral when surface tension does not chang along the column. As outlined earlier (Sec. 6.4.4), the tendency of) liquid film to break up is higher for a negative than for a positive syi tem. MacDougall (58) estimates that for a negative system the MWR is approximately twice as high as for a positive system.

Schmidt (102) observed that flooding and minimum wetting are caused by two different mechanisms. A low-liquid-rate column may therefore flood even when it operates below the MWR. This is most likely to occur in vacuum systems (where liquid rates are low and vapor velocities are high) and in high-surface-tension, low-viscosity systems.

Prediction by correlation. Schmidt (102) developed the following correlation from his fundamental model which describes minimum wetting for random packings.

(1 - Tl)°* <e where CL is the liquid falling film number, and TL is the shear stress number, given by Eqs. (8.36) and (8.37), respectively.

The angle <J> in Eq. (8.35) is the contact angle, discussed in more detail in Sec. 8.2.16. Contact angles are difficult to estimate; a chart useful for preliminary estimates was presented by Mersmann and Deixler (926). For systems that do not experience underletting (Sec. 8.2.16), the (1 - coa<t>)2/3 term in Eq. (8.35) can be approximated by assuming <|> * 10°, giving Eq. (8.38):

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