# Interdisciplinary Applied Mathematics

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von Smoluchowski, 57 vorticity, 273 vorticity flux, 73 vorticity-streamfunction, 54

wall atoms

structure, 369 thermal motion, 369 wall registry index, 377 water

bond angle, 405 bond length, 405 first coordination shell, 423 PPC model, 412 properties, 406, 414 six-site model, 413 SPC model, 409 SPC/E model, 410 SSD model, 407 ST2 model, 410 TIPnP model, 410 WCA potential, 626 Weeks-Chandler-Andersen potential, 369

wet electronic circuit, 305 wetting, 31

contact angle, 32 hydrophobic, 32 hysteresis, 32

Winchester hard disk drive, 2

How small    should    a sample    size be    so    that    we    can assign    it    mean

properties?

The case of av = 1 is called diffuse reflection.

3

Steady plane Couette flows have linear velocity profiles, which result in d2U/dn2 = 0. Therefore, the high-order slip effects in equations (2.42) and (2.43) diminish for plane Couette flows. In Section 3.2, we demonstrate a generalized slip model for linear Couette flows that is valid for Kn    12.

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P5 + 12^^ Kn0(l -P) + 12^—^ Kill loge(P)

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nv    nv

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= B(L — x),

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Even    at    very    low    Mach    numbers,    where the    flow is    often assumed to

be isothermal, the temperature variations can be nonnegligible. For example, the simulation results predict that at Ma = 0.12, Kn = 0.2, the temperature variation can be as large as 7 K within a distance of

8

What are the effects of the finite slider length (L) for high Kn transport?

What are the finite length and width effects on Knudsen’s minimum?

We can identify multiple operation conditions in the transition and free-molecular regimes using the relative ratios of X to h, W, and L. However, such studies require extensive analysis of the finite length slider problem using the Boltzmann equation or DSMC. Data for internal rarefied gas flows through finite-length channels and orifices can provide guidance in determining these finite-length scale effects (see Section 15.4 and also (Sharipov and Sleznev, 1998)).

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