By William Liou, Yichuan Fang
ISBN-10: 0071443223
ISBN-13: 9780071443227
ISBN-10: 0071588884
ISBN-13: 9780071588881
The quick development in fabricating and using microelectromechanical (MEMS) structures over the past decade isn't really matched by way of corresponding realizing of the radical fluid stream eager about the operation and manufacture of those small units. offering such realizing is essential to designing, optimizing, fabricating and working more suitable MEMS units. Microfluid Mechanics: ideas and Modeling is a rigorous reference that starts with the elemental ideas governing microfluid mechanics and progresses to extra advanced mathematical types, with a purpose to permit examine engineers to higher degree and expect reactions of gaseous and beverages in microenvironments.
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Extra resources for Microfluid Mechanics: Principles and Modeling
Example text
This curve is shown in Fig. 2. Note that the positive value of c1 and the negative value of c1 have equal probability of occurrence. Because the Maxwellian distribution is isotropic and has no directional preference in the velocity space, it then becomes interesting to examine the fraction of particles with certain velocity magnitudes between c and c + dc regardless of the direction. This is equivalent to finding the fraction of particle f 0 dc that lies in a spherical shell centered at the origin of the velocity space and with thickness dc .
3 Transport process. where n is number density. The minus sign is used since a positive c y would carry a momentum deficit at the new location. If one assumes that on an average, a molecule collides with another molecule at the new location with distance λ apart from its original location, say from y = −λ to y = 0 as indicated in Fig. 3, and reaches equilibrium with its new environment. 8) The number of such collisions per unit area per unit time can be estimated by using the average thermal speed and becomes nc .
Let us begin with Eq. 8) Q f dc For example, for Q = c = c¯ + c 1 N 1 = N c¯ = = cdN ∞ cN f dc −∞ ∞ c f dc −∞ where c¯ denotes the average or the mean velocity and c the thermal fluctuation velocity. Therefore, c = ∞ −∞ ¯ f dc (c − c) = c¯ − c¯ =0 The product of dV dc = dx1 dx2 dx3 dc1 dc2 dc3 represents a volume in the combination of physical and velocity space. This is called phase space. 9) 30 Chapter Two Comparing Eq. 9) with Eq. 2), Eq. 10) then represents the number of molecules in the phase space element dV dc.
Microfluid Mechanics: Principles and Modeling by William Liou, Yichuan Fang
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