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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 10

Tham khảo tài liệu 'the mems handbook introduction & fundamentals (2nd ed) - m. gad el hak part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Lubrication in MEMS 11-3 microfabricated rotor a cylinder of density p diameter D and length L compared to the pressure p acting on its projected surface area. This can be expressed as a non-dimensional load parameter pnLD2 4 D z ---- z pLD p 11.1 from which it can be seen that the load parameter decreases linearly as the device shrinks. For example the load parameter due to the rotor mass for the MIT Microengine which is a relatively large MEMS devices measuring 4 mm in diameter and 300 microns deep is approximately 10 3. The benefits of this scaling are that orientation or the freely suspended part becomes effectively irrelevant and that unloaded operation is easy to accomplish. In addition since the gravity loading is negligible the primary forces that one needs to support are pressure-induced loads and in a rotating device loads due to rotational imbalance. This last load is very important and will be discussed in more detail in connection to rotating lubrication requirements. The chief disadvantage of the low natural loading is that unloaded operation is often undesirable in hydrodynamic lubrication where a minimum eccentricity is required for journal bearing stability and in practice gravity loading is often used to advantage. Therefore a scheme for applying an artificial load needs to be developed. This is discussed in more detail later in the chapter. 11.2.2 Applicability of the Continuum Hypothesis A common concern in microfluidic devices is the appropriateness of the continuum hypothesis as the device scale continues to fall. At some scale the typical inter-molecular distances will be comparable to the device scales and the use of continuum fluid equations becomes suspect. For gases this is measured by the Knudsen number Kn the ratio of the mean free path to the typical device scale. Numerous experiments Arkilic et al. 1997 1993 Breuer et al. 2001 have determined that non-continuum effects become observable when Kn reaches approximately 0.1 and that .