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260   Principles and Methods



           1.0


           0.8


          1-n/n o  0.6  Nanoparticles
                    dp < 100 nm
           0.4


           0.2
                     α = 1.0
                     α = 0.5
           0.0
             0.01              0.1                1                 10
                                       dp (µm)
        Figure 7.17  Particle removal assuming two different attachment efficiencies as a
        function of particle size calculated using equation 4.4 (v   0.14cm/sec, 	   0.43, a c
        355 m, L   9.25 cm)



        they comprise. In Figure 7.17, particle removal, represented as the mass
        concentration of particles removed, 1-n/n , is plotted as a function of par-
                                             0
        ticle size on a semi-log scale. Increasing the fluid flow rate or flow veloc-
        ity serves to increase particle mobility. Particles in the nano-size range
        (d   1 to 100 nm) are relatively immobile, which is indicated by their
          p
        high removal values. As particle size increases, mobility increases until
        a relative maximum in mobility is reached at around 1.5  m. For parti-
        cles larger than approximately 1.5  m mobility begins to decrease as the
        collector efficiency increases due to a larger contribution by interception
        and gravity. Holding all other variables constant, nanoparticles should
        be relatively immobile under a given set of conditions in comparison to
        other micron-sized particles of similar surface chemistry.


        Quantifying nanoparticle
        deposition and mobility
        It is somewhat nonintuitive that the very small size of nanoparticles may
        actually lead to less mobility (a higher deposition rate) in a porous
        medium such as a groundwater aquifer or a filter in comparison with
        larger particles. Observations of particle deposition in porous media
        over a wide range of particle sizes suggest that the current description
        of particle transport to collectors is reasonably complete [59–61].
        However, when particle attachment is not favorable only a fraction of
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