# 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

I!1

I!’

##### !’.

1 i

l ч  V

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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