Tham khảo tài liệu 'the mems handbook introduction & fundamentals (2nd ed) - m. gad el hak part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Molecular-Based Microfluidic Simulation Models 6-5 and liquids go through multiple collisions at a given instant making the treatment of the intermolecular collision process more difficult. The dilute gas approximations along with molecular chaos and equipartition of energy principles lead us to the well established kinetic theory of gases and formulation of the Boltzmann transport equation starting from the Liouville equation. The assumptions and simplifications of this derivation are given in Vincenti and Kruger 1977 and Bird 1994 . Momentum and energy transport in the bulk of the fluid happen with intermolecular collisions as does settling to a thermodynamic equilibrium state. Hence the time and length scales associated with the intermolecular collisions are important parameters for many applications. The distance traveled by the molecules between the intermolecular collisions is known as the mean free path. For a simple gas of hard-sphere molecules in thermodynamic equilibrium the mean free path is given in the following form Bird 1994 Ả Wm n -1 The gas molecules are traveling with high speeds proportional to the speed of sound. By simple considerations the mean-square molecular speed of the gas molecules is given by Vincenti and Kruger 1977 ĨP VỠ2 J- fiRT V p where R is the specific gas constant. For air under standard conditions this corresponds to 486 m sec. This value is about i to 5 orders of magnitude larger than the typical average speeds obtained in gas microflows. The importance of this discrepancy will be discussed in Section . In regard to the time scales of intermolecular collisions we can obtain an average value by taking the ratio of the mean free path to the mean-square molecular speed. This results in tc 10 101 for air under standard conditions. This time scale should be compared to a typical microscale process time scale to determine the validity of the thermodynamic equilibrium assumption. So far we have identified the vast number
