Flow Rates and Profiles in Micro- and Mesochannels
Friction appears in relative motion between solid bodies, between fluids in a pipe and its wall, but also far from boundaries inside flowing fluids between layers of same velocities (lamina). This has deep implications on the way the fluid behaves. The flow through a pipe or channel can be discriminated in turbulent and laminar flow, which depends on the size of the channel, the flow speed and the properties of the liquid. That means: The larger the size of the channel, the higher the flow speed and the lower the viscosity, the more likely the flow develops turbulence which is described by the Reynolds number (Re):
Re = ū ρ L / η
with the (average) flow speed ū, the channel length L, the density (ρ) and the dynamic viscosity (η) of the fluid. The characteristic dimension is a length scale of the system determining the overall behaviour of the fluid – in our case it can be the lateral or vertical channel size. Re relates flow momentum density ū ⋅ ρ (inertia) to the viscosity. Turbulence starts at Re >2000 … 3000, a number hard to reach in microchannels because of the very small L and ρ, fortunately.
Hence, flow is laminar in our case and friction dominates the flow properties. Friction has averaging smoothing properties, sharp edges in the velocity field vx(x, y, z) get rounded very quickly. Viscosity is the macroscopic consequence of friction. Diffusion in fluids acts in a way to minimise shear stress and large gradients, however, this is less possible near the channel walls, since they do not move a priori.
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