Interdisciplinary Applied Mathematics

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1.3 The Pioneers

A systematic research effort in micromechanics in the context of MEMS devices, i.e., fabrication and operation, began in the late 1980s. Richard Feynman, in his prophetic lecture in 1959 “There’s plenty of room at the bottom,” described new vistas and novel new applications in microscale science and engineering. In a follow-up lecture in 1983 at the Jet Propulsion Laboratory, Feynman revisited this subject, anticipating some of today’s standard MEMS technologies such as the sacrificial-layer method of making silicon micromotors, the use of electrostatic actuation, and the importance of friction and contact sticking in such devices. Both lectures are included in (Trimmer, 1997), where other classical and seminal papers in MEMS and micromechanics up to 1990 can be found.

Fundamental work in microflows started much earlier. In 1846, Poiseuille published the first paper describing flow in tubes with diameters ranging from 30 рш to 150 pm (Poiseuille, 1846). His studies with liquids led to the well-known relationship between flowrate, pressure drop, and tube geometry, although he seemed to be unaware of the viscosity concept at that time. In 1909, Knudsen studied gas flows through glass capillary tubes in the transition and free molecular flow regimes (Knudsen, 1909). In these experiments, the volumetric flowrate normalized with the inlet to exit pressure difference (Q/(Pi — Po) showed a minimum at Kn « 1, when plotted against the average pressure in the capillary. This counter intuitive behavior is known as the Knudsen’s paradox or Knudsen’s minimum. The first known experiment of flow in a microchannel was performed by Gaede in 1913, who placed two parallel plates 4 pm apart (Gaede, 1913). Gaede found that the flowrate of hydrogen decreases about 50% from the free-molecular value while passing through a minimum and then rising with increasing pressure levels. In long capillaries, the difference between the minimum and the free-molecular value is only 5 to 8%, as also seen in Figure 1.17. Although Knudsen’s minimum is measured in smooth capillaries, crimped tubes do not exhibit this behavior (Tison, 1993). Therefore, rarefied flows behave differently in pipes and channels, and the surface conditions can be important in gas transport in the transitional and free-molecular flow regimes.

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