# A Review of Passive Constant Flow Regulators for Microfluidic Applications
## 3 Mechanical Passive Constant Flow Regulators
### Flow Regulator with Passive Membrane Valve in PDMS  
Contrary to the detour autoregulators, the hydraulic resistance of the devices considered in this sub-section occurs mainly in the part of the main channel where the compliant valve is positioned. In 2009, [PERSON] et al. developed a passive flow regulator in PDMS using parallel membrane valves [42]. A schematic cross-section of the device is shown in Figure 8. The increase \(\delta p\) of both inlet and sub-channel (or control channel) pressures induces a deflection of the two membranes. The narrowing of the fluid path leads to an increase \(\delta R_{h}\) of the main channel hydraulic resistance. Both analytical and 3D FEM simulations were carried out to design the passive constant flow regulators. The working principle is thus similar to the detour autoregulator made by [PERSON]'s group [37; 39], except the fact that the pressure drop occurs here only in the space between the two thin membranes. The structure of the device is also simplified, and the minimum pressure to achieve flow regulation was lowered for better integration with micropumps. Figure 7: Schematic drawing of a microfluidic current source in PDMS comprising a main channel, a detour channel, and a pushup valve. The flow direction is indicated by the arrow (forward bias). The main and detour channel lengths are noted L and L\({}_{2}\), respectively. The increase of the inlet pressure generates a larger pressure drop along the main channel and thus the pushup valve will progressively obstruct the main channel and lead, beyond a saturation pressure, to a constant flow rate (adapted from Reference [39]). A single mask process was used to fabricate the device in PDMS, with SU-8 negative photoresist structure as a mold master. The microchannel height of the different prototypes is 100 \(\upmu\)m and the main channel width is 400 \(\upmu\)m. The \(100\times 100\)\(\upmu\)m thin square membranes are 10 \(\upmu\)m thick. Four different prototypes having a width between the parallel membranes of 20, 30, 40, and 50 \(\upmu\)m respectively, were tested with water. The 20 \(\upmu\)m prototype fabricated by 10 : 1 PDMS (base/curing agent mixing ratio) and the 40 \(\upmu\)m prototype fabricated by 20 : 1 PDMS showed a constant flow rate of 0.3654 mL/min \(\pm\) 3.8% in the pressure range \([200;500]\) mbar and 0.8718 mL/min \(\pm\) 3.5% in the pressure range \([150;500]\) mbar, respectively. The other prototypes, including the 40 \(\upmu\)m prototype fabricated by 10:1 PDMS, did not show a constant flow rate. The prototypes made of 20 : 1 PDMS, which exhibits a lower Young's modulus than 10 : 1 PDMS, showed, as expected, a lower threshold pressure and a higher regulated flow rate than their counterparts made of 10:1 PDMS [42]. [PERSON] et al. further investigated this concept of passive flow regulators with elastomeric membranes and provided an analysis of the structural parameters that directly influence the flow rate [43; 44; 45; 46]. Several passive flow regulators were built using standard soft lithography techniques [43; 44], assembly of laser-structured thermoplastic films and PDMS membranes through roll-lamination method [45], or a combination of 3D printing and laser structuration/cutting [46]. PDMS, as a popular material for valve prototyping [47; 48; 49], was systematically used to form the thin membranes (10 \(\upmu\)m thick). Other layers are either made of PDMS [43; 44], polyvinyl chloride (PVC) and polyethylene terephthalate (PET) [45], or photopolymer and silicon film [46]. The five-layer-stacked PDMS flow regulator comprises a bottom layer with a first control channel, a first membrane layer, a middle layer to form the main channel, a second membrane layer, and finally an upper layer with the second control channel and inlet and outlet ports [43; 44]. The seven-layer-bond structure of the device made of PVC, PET, and PDMS comprises a base and a cover in PVC, and a fluidic layer in PVC between the upper and lower control layers in PET.