# A Review of Passive Constant Flow Regulators for Microfluidic Applications
## 3 Mechanical Passive Constant Flow Regulators
### Spring Valve with a Spiral Groove on a Moving Piston  
The design of the passive microfluidic devices described in the previous sections required two-dimensional (2D) or 3D FEM simulations of fluid flows fully coupled with structures undergoing large deformation, nonlinear material response, and contact conditions [58; 59; 60; 61; 62; 63]. The non-well-defined Young's Modulus of some elastomeric materials (e.g., PDMS), coupled with the difficult adaptative meshing of high aspect ratio structures, are a challenge in computational engineering. The complexity is also due to the nonlinear change of the hydraulic resistance of the fluid path as its cross-section is varied. [PERSON] et al. [16] and [PERSON] et al. [30] already considered a long channel with a fixed cross-section but the calculation of the spiral shape, to achieve a linear increase of the channel length as the pressure increases, is difficult due to notably the highly nonlinear deformation of the membrane after contact with the substrate [64]. A simpler design consists of a moving cylinder with a spiral groove and a linear compression spring inside a hollow cylinder with openings (see Figure 12). Due to the spring pretension, a minimum threshold pressure shall be applied at the inlet to move the piston that is initially partly engaged into the narrow part of the cylinder. As the pressure force on the piston increases, the piston is engaged further into the narrow part of the cylinder and the fluid is forced to flow through a longer channel length. If the linear spring is maintained within its nominal compression range, the counterforce generated by the spring increases linearly with the applied pressure. The induced movement of the piston leads to a linear increase of the channel length as the pressure increases, and since the channel cross-section and spiral pitch are constant, the flow is regulated at a predetermined fixed value. At high pressure, the piston movement is stopped, and the hydraulic resistance of the device can be either fixed (as illustrated in Figure 12), infinite (flow stopped) if the piston completely obstructs the fluid path, or very low (free flow) if openings are machined along the outlet port of the cylinder to by-pass the channel [7]. The pressure threshold that delimits the flow regulating stage of this valve can be modified by adjusting, for instance, the pretension or the length of the spring. Such a device structure, which is very well suited for a high throughput application (up to 4 L/min or more), was also considered for hydrocephalus treatment [7]. A prototype in titanium was designed to drain CSF from the brain ventricles toward the peritoneal cavity. The piston has a diameter of 4 mm and the lathe tool with a tip curvature of 0.1 mm and an angle of 55\({}^{\circ}\) was used to form a 200 \(\upmu\)m deep spiral groove with a pitch of 1.249 mm. The 10 mm custom-made spring used for the test exhibited a stiffness larger than expected (10 N/m instead of 8.3 N/m). The tests performed in a horizontal position using water at 20 \({}^{\circ}\)C showed, after extrapolation at 37 \({}^{\circ}\)C, a regulated flow rate of 0.35 mL/min \(\pm\) 5% in the pressure range \([10;35]\) mbar. The spring stiffness offset induced a slight positive slope in the \(Q(\delta p)\) curve in good agreement with the theoretical expectations. In a vertical position, the gravitational force acts either in the same or opposite direction as the pressure forces onto the piston. To limit the effect of this induced pressure offset on the flow rate, a specific hollow piston that exhibits an overall density equal to water density has been machined. This gravity force on this piston in polyether ether ketone (PEEK) is balanced by Archimedes' force and the fluidic tests showed that the flow rate became insensitive to the device orientation. The different parts of this passive constant flow regulating spring valve are compatible with standard machining techniques and can be characterized and sorted before the final assembly to improve the production yield.