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Question: Suppose a dilute solution flows through a circular microchannel with the diameter d = 20 μm. The mean velocity of the flow is measured to be U = 300 μm/s. If we also know the density of the solution is ρ = 1000 kg/m3 , the viscosity of the solution is μ = 5 × 10-3 Pa·s, and the diffusion coefficient of the solute in the flow is D = 2 × 10-8 cm2 /s, please compute the following quantities and answer corresponding questions.
(a) The Reynolds number Re of the flow.
(b) Based on the value of Reynolds number and associated criteria (please specify the criteria), determine the type of flow, and whether viscous force or inertial force is dominant for the flow.
(c) The Péclet number Pe of the flow.
(d) Based on the value of Péclet number and associated criteria (please specify the criteria), determine whether advection or diffusion is dominant for the flow.
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