Figure P2.9 shows the layout of a microfluidic device with both series and parallel channels. The first segment has a length L₁ = 1 mm and the relative lengths of the others are as indicated. Suppose that each channel has a square cross-section with side length 100 μm and that all flow is horizontal. The overall pressure drop for water is P_A – P_D = 3000 Pa. You may assume that the channels are long enough that the extra resistances associated with the bends and junctions are negligible.

(a) Evaluate the flow-rate ratios Q₂/Q₁, Q₃/Q₁, Q₄/Q₁, and Q₅/Q₁.

(b) Calculate Q₁.

Transcribed Image Text:

PA Q₁ 4 PB Q₂ L₂ = 4L₁ Q3 L3=24₁ Q4 Pc Q5 45=4 PD 44 = 44₁ Figure P2.9 Microfluidic device, adapted from Oh et al. (2012). The channel lengths and widths are not to scale.