# A Review of Passive Constant Flow Regulators for Microfluidic Applications
## 3 Mechanical Passive Constant Flow Regulators
### Device with a Thin Flexible Flap  
The final category of passive flow control devices to be considered in this section refers to microfluidic devices comprising a thin flexible flap and stiff stopper that form a flow constriction in a microchannel. [PERSON] et al. considered a planar flap/stopper configuration, as illustrated in Figure 13[65]. The flap deflects towards the stopper with the applied pressure and narrows the fluid constriction. The resulting increase of the hydraulic resistance compensates for the pressure variations to maintain the forward flow rate constant. For reverse flow, the device exhibits a small hydraulic resistance and diodicity (the ratio of the backward pressure drop to the forward pressure drop [66]) up to \(10^{5}\) was measured experimentally [67].  
This microfluidic variable resistor was fabricated in PDMS using standard replica molding techniques. The channel was formed by bonding the structured PDMS layer to flat PDMS or glass substrate(s) [65; 67; 68]. [PERSON] et al. designed four different stopper/flap configurations: (a) basic design, as depicted in Figure 13, (b) centered stopper channel, (c) centered stopper channel with centered flap, and (d) double-flapped design [65]. All devices had a microchannel 300 \(\upmu\)m wide and 275 \(\upmu\)m high, a stopper channel 1000 \(\upmu\)m long and 40 \(\upmu\)m wide, and a flap-free end 33 \(\upmu\)m away from the channel sidewall. The designs a, b, c, and d have a flap 60, 50, 60, and 50 \(\upmu\)m wide and 36, 40, 45, and 50 \(\upmu\)m away from the stopper, respectively. Flow rate measurements were performed with water. Constant flow rates of 1.2, 0.16, 2.2, and 0.15 mL/min at \(\pm\)3.5% in the pressure range \([1000;2000]\) mbar were measured for the designs a, b, c, and d, respectively [65]. Two other configurations designed using 3D fluid-structure interaction simulations were fabricated and tested later by [PERSON] et al. [67; 68],  
Figure 12: Schematic drawings of a constant flow regulating spring valve. (**a**) Device at rest. A small part of the piston groove is engaged into the narrow part of the cylinder to form a fluidic channel. (**b**) Device submitted to a large pressure \(P_{\text{in}}\gg P_{\text{out}}\). As the inlet pressure increases, the piston moves along the cylinder and the channel length increases as well. At large pressure, the piston is stopped and the hydraulic resistance of the device becomes constant.  
the designs A and B with a flap 60 and 75 \(\upmu\)m wide and 36 and 25 \(\upmu\)m away from the stopper, respectively. Both designs had a microchannel 300 \(\upmu\)m wide and 275 \(\upmu\)m high, a flap 266 \(\upmu\)m wide and 275 \(\upmu\)m high, and a stopper channel 500 \(\upmu\)m long, 40 \(\upmu\)m wide, and 275 \(\upmu\)m high. The measured saturation threshold pressures are 900 mbar for design A and 600 mbar for design B. Constant flow rates of 0.21 and 1.2 mL/min at \(\pm\)3% at pressure up to 2000 mbar were reported for designs A and B, respectively.  
[PERSON] et al. recently investigated a 3D-printed flap valve made of a photocurable resin [69]. The pressure-induced flap deflection narrows the flow restriction between the flap end and the microchannel sidewall. A theoretical model was developed to define the design rules. Using a flap with a tilt angle of 40\({}^{\circ}\), a thickness of 300 \(\upmu\)m, and an initial gap of 300 \(\upmu\)m, [PERSON] et al. measured, with water, a large constant flow rate of 111 mL/min \(\pm\) 5.8% in the pressure range [200; 600] mbar.