Diffusion without shear forces

Following Kerkhof and Geboers (2005), an approximation of the Boltzmann equation for a multicomponent monatomic 

Acceleration force = converted momentum change partial pressure gradient + external forces - thermal diffusion force + shearing force + intermolecular friction force 

For a fixed coordinate system, we consider steady transport and have 

the first term represents the change of the convection flow, which is small compared with the other forces, so that Eq. (6.211) becomes 

When external force is absent, and using the flows defined by N, = v,c we find 

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Microfluidics handles and analyzes fluids in structures of micrometer scale. At the microscale, different forces become dominant over those experienced in everyday life [161], Inertia means nothing on these small sizes the viscosity rears its head and becomes a very important player. The random and chaotic behavior of flows is reduced to much more smooth (laminar) flow in the smaller device. Typically, a fluid can be defined as a material that deforms continuously under shear stress. In other words, a fluid flows without three-dimensional structure. Three important parameters characterizing a fluid are its density, p, the pressure, P, and its viscosity, r. Since the pressure in a fluid is dependent only on the depth, pressure difference of a few pm to a few hundred pm in a microsystem can be neglected. However, any pressure difference induced externally at the openings of a microsystem is transmitted to every point in the fluid. Generally, the effects that become dominant in microfluidics include laminar flow, diffusion, fluidic resistance, surface area to volume ratio, and surface tension [162]. 

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