# A 3D Printed Membrane-Based Gas Microflow Regulator for On-Chip Cell Culture
## 3 Results and Discussion  
### Flow Characteristics of the Regulator  
Flow charts of the regulator were devised for three PDMS membrane thicknesses (200, 300, \(400\pm 5\) um) and three types of gases (air, CO\({}_{2}\), N\({}_{2}\)), concerning increases and decreases in the operational pressure (Figures 5 and 6). The measurements were repeated three times for each set.  
Figure 4: Measurement setup for on-chip cell culture: (**a**) scheme; (**b**) real view.  
Figure 3: Measurement setup scheme for evaluation of flow values. PC: personal computer.  
The attached graphs represent the mean value from every configuration. In order to check the gas flow repeatability, the standard deviation within the particular measurement group is indicated. Its value ranges from 2.6% to 7.2% in the case of CO\({}_{2}\) flow, 2.8-5.4% for N\({}_{2}\), and 3.7-6% for air flow, according to the different membrane thicknesses.  
Figure 5: Gas flow characteristics of the regulator for different polydimethylosiloxane (PDMS) membrane thicknesses: (**a**) CO\({}_{2}\) flow; (**b**) N\({}_{2}\) flow; (**c**) air flow; (**d**) flow comparison for the selected gases with a 400 \(\upmu\)m thick PDMS membrane.  
Figure 6: Pneumatic hysteresis of the regulator with a 400 \(\upmu\)m thick PDMS membrane: (**a**) air flow; (**b**) N\({}_{2}\) flow; (**c**) CO\({}_{2}\) flow.  
The statistical analysis showed that the flow changes parabolically with applied pressure, also depending on the membrane thickness. Diversities in the flow rate were also noticed depending on the type of gas. The shape of the characteristics (approximately parabolic) is consistent with the data found in the literature [31; 32; 33]. Obtained curves are, amongst other things, associated with an increasing solubility of gases as the pressure value increases. This phenomenon causes the growth of gas concentration, which slightly plasticizes the polymer bulk and increases permeability [31]. It is especially noticeable for organic penetrants, like CO\({}_{2}\), and less for sorbing gases, such as N\({}_{2}\) and O\({}_{2}\). It justifies the characteristics presented in the Figure 4d, in which the flow value of CO\({}_{2}\) increases the fastest with applied pressure. Another factor that points to a higher permeability is the molecule size; the flow value of CO\({}_{2}\) in this case is the highest [33]. According to the formula (1) shown in the first section of the article, the flow ought to change linearly depending on the membrane thickness. In our case, the results depart from the linearity by circa 25%. The reason why such diversities were observed may be related to the preparation and polymerization of the membranes. The membranes were obtained by manual mixing of the prepolymer. In this way, the crosslinking network of each membrane could have had some irregularities, i.e., smaller or greater pores that influenced the flow characteristics. The measurements also revealed that the regulator exhibited pneumatic hysteresis (Figure 6). This phenomenon may be related to the gathering of gas particles in the polymer bulk and their gradual release. This could be reduced or even avoided by waiting a short time for stabilization after changing the parameters of the pressure.