# A Review of Passive Constant Flow Regulators for Microfluidic Applications
## 3 Mechanical Passive Constant Flow Regulators
### Flow Regulator with Passive Membrane Valve in PDMS
Finally, the device made of photopolymer, a silicone film, and PDMS exhibits a four-layer structure with bottom and cover layers in photopolymer (structured using 3D printing technology), a seal layer in silicone, and the membrane in PDMS [46]. The working principle of this latter device, which furthermore comprises a check valve, is illustrated in Figure 9.  
[PERSON] et al. manufactured and tested four different types of five-layer-stacked PDMS flow regulators noted \((\text{W}200,\text{ L},\text{ H}75)\) with different membrane lengths L (from 100 to 400 \(\upmu\)m) to study the influence of the flexible membrane length on the flow rate (see Table 1 in Appendix A) [43]. W and H are respectively the width and the height of the contraction channel (i.e., valve) in \(\upmu\)m, while L represents the width of the two aligned control channels (i.e., valve length). All flow-rate characteristics were measured using water. When the length of the membrane increases from 100 to 400 \(\upmu\)m, the threshold  
Figure 8: Schematic drawing of a passive flow regulator using autonomous deflection of parallel membrane valves. The increase \(\delta p\) of the inlet pressure induces a deflection of two membranes and thus an increase \(\delta R_{h}\) of the hydraulic resistance of the device (adapted from Reference [42]). pressure and regulated flow rate decrease from 250 to 150 mbar and 2.55 to 1.12 mL/min, respectively. Six other PDMS flow regulators were characterized to study the influence of the cross-sectional dimensions on the flow rate: three samples (W100, L, H75) and three samples (W200, L, H130) with L = 200, 300, 400 \(\upmu\)m, respectively. The measured regulated flow rates and threshold pressures are summarized in Table 15 in Appendix A. All results supported theoretical expectations: the stiffer the membrane, the higher the regulated flow rate and threshold pressure. As an example, increasing the height from 75 \(\upmu\)m (sample (W200, L400, H75)) to 130 \(\upmu\)m (sample (W200, L400, H130)) leads to a decrease of the threshold pressure from 150 to 100 mbar and an increase of the regulated flow rate from 1.12 to 2.79 mL/min [43]. Additional tests performed on a sample (W150, L300, H70) which exhibits, in static pressure conditions, a pressure threshold of 250 mbar and a regulated flow rate of \(1.49\pm 0.018\) mL/min, showed that the autoregulation performances are maintained under sinusoidal varied pressures in the range \([250;500]\) mbar [44]. Another version of this passive flow regulator with a seven-layer-bond architecture for improved manufacturing capabilities was characterized by [PERSON] et al. [45]. In the pressure range \([200;700]\) mbar, the devices with channel heights of 90 and 145 \(\upmu\)m showed a regulated flow rate of respectively 1.36 and 0.29 mL/min. The four-layer structure made using 3D printing and UV laser cutting technologies was finally considered for prototyping a passive flow regulator, using a PDMS membrane of 50 \(\upmu\)m in thickness, an obstacle in the seal-layer of \(500\times 800\)\(\upmu\)m, and channel height and width of respectively 250 and 600 \(\upmu\)m. The device, dedicated to low-cost and portable lab-on-a-chip (LOC) applications, showed a constant flow rate of \(25.2\pm 1.2\) mL/min in the pressure range \([700;1300]\) mbar. Device with a Notched Pin and a Moving Elastomeric Membrane with a Central Through-Hole  
The first mention of a flow-controlled hydrocephalus shunt was made, to the best of the author's knowledge, by [PERSON], who mentioned in 1982 that according to neurosurgeons' comments, the ideal valve should be flow-controlled such as to only remove the excess of cerebrospinal fluid (CSF) [50]. The first valve based on this principle, that the flow through the shunt shall not exceed the CSF production rate throughout the range of physiological intracranial pressures (ICP), was designed  
Figure 9: The working principle of the microfluidic device with a check valve and a flow regulating valve in PDMS.