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2.2 Fluidics and microfluidics 9
in mind are listed below, with brief comments on the importance and
influence on microfluidic flows.
• Viscosity. The first parameter to be introduced is the viscosity
η,which is a measure of the internal friction in a liquid. It is defined
as the ratio between the shear stress and the shear rate:
η = F/A
dv/dy
(2.1)
where F is the applied force, A is the area on which the force is
applied, and dv/dy is the velocity gradient perpendicular to the
shear direction.
The viscosity is usually temperature dependent. Often viscosity
is independent of the applied shear stress, like in the case of e.g.
water. These liquids are called Newtonian. In non-Newtonian
liquids the viscosity changes with the shear stress. Examples of
such liquids are shampoo and paint, which are shear-thinning, or
a mixture of corn starch and water, which is shear-thickening.
• Reynolds number. The second important parameter of a liquid
flow is the dimension-less Reynolds number Re. Is is defined as
the ratio of the inertial forces to the viscous forces, and is defined
as
Re = ρdv
η
(2.2)
where ρ is the density, d is a length scale of the system (for microfluidic
channels typically the channel cross sectional dimension),
and v is the flow velocity. If the inertial forces dominate, the
Reynolds number is high, and the flow is said to be turbulent. In
this regime, the behavior of the flow is chaotic and stochastic,
meaning that a complete description is difficult, and possible only
on a statistical scale.
If the viscous forces dominate, the Reynolds number is low, and the
flow is called laminar. Streamlines of the flow are regular and can
(mostly) be calculated. Empirical observations (in macroscopic
systems) have yielded a Re value of ∼2000 – 3000 as the transition
between the two flow regimes.