# Interdisciplinary Applied Mathematics

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Modeling of liquids in microdomains, see Chapters 7-9, requires a different approach. In mesoscopic scales a continuum description suffices (see Chapter 14), whereas in submicron dimensions atomistic modeling is required (see Chapter 16). We have already discussed slip phenomena in liquids in Section 1.2; however, other phenomena may be present, for example:

wetting,

adsorption, and electrokinetics.

FIGURE 1.23. Transmission electron micrographs showing continuum behavior in a nanotube of large-diameter (left) and non-continuum behavior in a nanotube of diameter about ten times smaller (right). These two images demonstrate a dramatically different degree of interaction between fluid/wall for the two cases. (Courtesy of C.M. Megaridis, A.G. Yazicioglu and Y. Gogotsi.)

The wetting of the solid surfaces by liquids can be exploited in microfluidics to determine precisely defined routes based on surface tension gradients and different types of surfaces, i.e., hydrophobic or hydrophilic. Control can be accomplished via active contaminants or thermally; see Chapter 8. Wetting may also affect flow and performance of a MEMS device by altering its mechanical response or even blocking flow channels. While there exist macroscopic descriptions of wetting, they do not fully incorporate effects such as hysteresis (Dussan, 1979; deGennes, 1985), layering, and monolayer spreading (Heslot et al., 1989; Jin et al., 1997). Hysteretic effects can have a dramatic    effect    on    the    value    of    the    contact    angle    and the

strength of surface tension. In modeling wetting phenomena it is important to incorporate the possible deformation of the solid in wetting processes, since local regions of high stress can produce distortions of the elastic solid (Shanahan, 1988), e.g., the elastomeric walls used in some patterned drug delivery applications.

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