Interdisciplinary Applied Mathematics

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is presented as a    function    of    x    f°r    several    a    values.    We    observe    that    the


electroosmotic potential decays to zero with increased x for all these cases. The decay rate can be quantified by presenting a logarithmic plot of the electroosmotic potential in the near-wall region as a function of x, as shown in Figure 7.3 (right). A careful examination of Figure 7.3 (right) shows exponential decay of the electroosmotic potential with slope —1 for x > 2. This result can be easily verified by expanding equation (7.10) for x > 2, where tanh (a/4) < 1, and exp(—x) ^ 1. Under these conditions


Ф*{х) ~ a tanh (4) exp(“*7    (7Л1)


In analogy to the 99% boundary layer thickness in traditional fluid mechanics, an effective EDL thickness 99) can be defined as the distance from the wall (in terms of Ad) at which the electroosmotic potential decays to 1% of its original value (Dutta and Beskok, 2001a). The effective EDL thickness as a function of the ionic energy parameter a is presented in Table 7.2. We can calculate the value of S99 in terms of the щ* coordinates by dividing the value of S99 given in Table 7.2 by


TABLE 7.2. Variation of the effective EDL thickness Sgg and the EDL displacement thickness S*    as    a    function    of the ionic    energy    parameter    a.    The    values    of


Sgg and S* are given in terms of the Debye length Ad .


a


i


3


5


7


10


699


4.5846


4.439


4.2175


3.9852


3.6756


s*


0.98635


0.891567

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