# Interdisciplinary Applied Mathematics

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4. As a final remark, interfacial interactions between the gas and surface molecules may result in inelastic reflections, due to the long-range interaction forces between the gas and surface molecules. Consequently, the gas molecules may condense and then evaporate after a certain time. This results in deposition of a thin layer of gas molecules on the surface. Using Langmuir’s theory of adsorption, Myong (2004) explained the accommodation coefficient concept, and studied velocity slip for both monatomic and diatomic molecules. He has shown that the Langmuir model recovers Maxwell’s first-order slip conditions, and he also described equation (2.43) in the context of the Langmuir model (Myong, 2004).

(2.20a)

(2.20b)

Us — Uw Ts — Tw

## 3

### Shear-Driven Flows

In this chapter we consider shear-driven gas microflows with the objective of modeling a certain class of flows encountered in microsystems. For example, the flow between the rotor and base plate of a micromotor and the flow between the stationary and movable arms of a comb-drive mechanism are shear-driven microflows (see Figures 1.1 and 1.2, respectively). In order to circumvent the difficulty of understanding the flow physics for complex engineering geometries, we concentrate on prototype flows such as the linear Couette flow, and flow in shear-driven microcavities and grooved microchannels. First, we present analytical and numerical results for steady Couette flow in the slip flow regime. This is followed in Section 3.2 by the development and validation of an empirical model for steady Couette flow in the transition and free-molecular flow regimes. In Section 3.3, we present simulation results and analysis for oscillatory shear-driven flows in the entire Knudsen regime. The last two sections include flows in prototype complex geometries, such as the microcavity, and grooved microchannel flows.

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