Interdisciplinary Applied Mathematics

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For the larger nanotube, the volume of the liquid inclusion is about 10~18 liters, and    the    pressure    difference across    the    liquid    is in    the    range    of    1


3 MPa. The double meniscus bounding the liquid in the larger nanotube shows good wettability of the inner carbon walls by the water-based fluid; it can be possibly described by continuum-based simulations, see Chapter 14. However, on the smaller nanotube the noncontinuum behavior requires atomistic simulations, see Chapter 16. The closed-end tube is typical of samples made through a hydrothermal process (Libera and Gogotsi, 2001; Ye et al., 2004). These nanotube samples were frequently found to contain a high-pressure multicomponent fluid showing curved interfaces separating the liquid from the gas phase. The heating experiments performed in (Megaridis et al., 2002), reported an array of dynamic interface phenomena visualized in real time in the nanotube interior.


Another very interesting multiphase flow at nanoscales is shown in Figure 1.24. The cross-flow device is a T-junction consisting of two nanochannels, one containing water and the other hexadecane plus 2% Span80. Because the two fluids are immiscible, an instability is formed. The pictures show the resulting patterns of water in oil emulsions in the outlet channel. The complexity varies dramatically as a function of the pressure applied to the input channels, as indicated in Figure 1.24. Each of these streams is generated spontaneously and is continuously moving as more droplets are formed. This regime too can be described by quasi-continuum approximation.


Electrokinetic effects are important in microfluidics; they provide a means


of maintaining a certain level of flowrate with practically uniform profiles; see Chapter 7. They were first discovered in experiments with porous clay (Reuss, 1809; Wiedmann, 1852). The basic mechanism is based on the interaction of an ionized solution with static charges on dielectric surfaces such as    glass.    A high    concentration    of    ions    is present    next    to    the    wall

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