Interdisciplinary Applied Mathematics

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distance from the wall, and ш is the Debye-Huckel parameter given by equation (7.1). Since uih = л/оф, the near-wall scaling parameter (y) and the nondimensional distance from the wall (nc = 1 — n) can be represented in terms of each other (i.e., у = фсфг]*). Based on this, equation (7.9) can be simplified to


Фс



tanh


a



1 tanh



a


4



exp (—у)



(7.10)


It is clear that the inner layer scaling of the potential distribution is independent of в for Ad ^ h. In Figure 7.3 the near-wall potential distribution


I


0.9′


0.8′


0.7′


0.6′


*5.0.5′


0.4′


0.3′


0.2′


0.1′


0′



•0.75



-0.5



-0.25



-1



-0.75



-0.5



-0.25



4N


i N


i



I l


I


I



1 -0.75′



—-а=1,р=1


——-а=1,в=10


__________ а=1,в= 100


—-а=1,в= 1000


— а=1,в= 10000



‘ -0.5 ‘


n



‘-0I25′



—    0.5 3


; D


—    0.6


■ 0.7 : 0.8 0.9 — 1



1


0.9′


0.8′


0.7′


0.6′


> 0.5^| 0.4′ 0.3′ 0.2′ 0.1 0′



а=10, в=1 а=10, в=10 а=10, (3=100 а=10, (3=1000 а=10, (3=10000






FIGURE 7.2. Variation of normalized electroosmotic potential ф* across half of a channel for various values of a and в.

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