Interdisciplinary Applied Mathematics

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Adsorption is important in interactions of liquids with nanoporous materials such as glasses. The boundary conditions for fluid flow are very sensitive to    the    type    and amount    of    adsorption    on    the walls    of a    MEMS

device. Liquids confined in microgeometries exhibit a supercooling of the liquid-solid phase transition, which can be quite substantial and depends strongly on the geometry of the pores (Tell and Maris, 1983). Anomalous diffusion has been observed experimentally, and it is manifested as either suppression of    the    diffusion    coefficient    by    two    orders    of    magnitude    at    the

boundary    (Dozier    et    al.,    1986),    or    an enhancement    by    an    order    of    magnitude over    the    bulk    (D’Orazio    et    al.,    1989).    The    key    parameter    in    such surface-bulk interactions is the degree of pore filling.

An intriguing flow regime has been discovered by Megaridis and his collaborators, see (Megaridis et al., 2002; Ye et al., 2004; Naguib et al., 2004), in nanotubes containing multiphase flow at high pressure, see Figure 1.23. The left figure shows a transmission electron microscope image of a fluid-filled multi-walled closed carbon nanotube synthesized using a hydrothermal procedure. The nanotube contains a stable liquid membrane bordered by two gas bubbles. Note the well-defined menisci separating the gas and liquid phases. On the right a much smaller nanotube is shown, about ten time less in diameter. This three-walled carbon nanotube, which was produced using arc evaporation, has been subsequently filled with water via high-temperature high-pressure treatment in an autoclave. The fluid interfaces are no longer smooth, as in the larger nanotube. The liquid molecules appear to form a long chain, with dry areas visible close to the wall. Amorphous carbon is present on the nanotube wall exterior. The graphene sheets seen in the lower portion of the micrograph belong to larger carbon nanotubes, which, however, are void of fluids. The walls of the nanotubes are made of carbon (graphene) layers, but the gaps in between the carbon atoms do not allow water to seep through. Only hydrogen can escape through these very fine pores. This explains why these multilayered walls can contain    the    fluid    contents    at    such    high pressures    for    quite    some time.

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