Standing Air Bubble-Based Micro-Hydraulic Capacitors for Flow Stabilization in Syringe Pump-Driven Systems.

Unstable liquid flow in syringe pump-driven systems due to the low-speed vibration of the step motor is commonly observed as an unfavorable phenomenon, especially when the flow rate is relatively small. Upon the design of a convenient and cost-efficient microfluidic standing air bubble system, this paper studies the physical principles behind the flow stabilization phenomenon of the bubble-based hydraulic capacitors. A bubble-based hydraulic capacitor consists of three parts: tunable microfluidic standing air bubbles in specially designed crevices on the fluidic channel wall, a proximal pneumatic channel, and porous barriers between them. Micro-bubbles formed in the crevices during liquid flow and the volume of the bubble can be actively controlled by the pneumatic pressure changing in the proximal channel. When there is a flowrate fluctuation from the upstream, the flexible air-liquid interface would deform under the pressure variation, which is analogous to the capacitive charging/discharging process. The theoretical model based on Euler law and the microfluidic equivalent circuit was developed to understand the multiphysical phenomenon. Experimental data characterize the liquid flow stabilization performance of the flow stabilizer with multiple key parameters, such as the number and the size of microbubbles. The developed bubble-based hydraulic capacitor could minimize the flow pulses from syringe pumping by 75.3%. Furthermore, a portable system is demonstrated and compared with a commercial pressure-driven flow system. This study can enhance the understanding of the bubble-based hydraulic capacitors that would be beneficial in microfluidic systems where the precise and stable liquid flow is required.


Equivalent Circuit Model
In a microfluidic network, it can be found that a constant pressure drop will result in a constant flow rate. This result can be summarized in the Hagen-Poiseuille law [1]: The Hagen-Poiseuille law is completely analogous to Ohm's law. Thus, the proportionality factors Rhyd and Chyd can be introduced as the hydraulic resistance and capacitance, respectively. The hydraulic resistance of a long straight channel with a rectangle cross-section shape can be given as: where L is the length of the channel, μm; h is the height of the channel, μm, and w is the width of the channel, μm; η is the dynamic viscosity, mPa·s. Here η=1 mPa·s (water). As the pressure increases by ΔP in a liquid the channel with a passive deformable part embedded in, the volume available to the liquid increases by ΔW. This process is very similar to the charging of the capacitor where an increase in voltage by ΔU increases the charge of the capacitor by Δq=CΔU. Therefore, the hydraulic capacitance is given by [2] hyd d d Thus, to make this fluidic stabilizer easier to understand, an equivalent circuit model was demonstrated in Figure S1. This report respectively corresponded the increased flowrate in the upstream ΔQ, the increased flow rate in the downstream of the main channel ΔQ1 and the amount of flow rate to press the bubble ΔQ2 to the increased current ΔI, ΔI1, and ΔI2. The hydraulic resistance of the upstream channel was corresponded to the R, and the hydraulic resistance of the downstream of the main channel was corresponded to the R1, while, R2 stands for the subsequent flow channel and component connected to this flow stabilizers. We treat it as a load during the calculation. In Figure  S1, the transfer function is as follow: Here, Zhyd = 1/jωChyd, further rearrangement yields the following equations: According to equation (3), the Chyd of the bubble bubble hyd C can be derived as: where V0 is the initial volume of the bubble, and p0 is the initial pressure. Therefore, According to the equation (8), the low pass filter attenuates fluctuations with frequencies higher than the cutoff frequency. The cutoff frequency of the low-pass filter is mainly decided by V0. The larger the size of the bubble is, the lower the cutoff frequency would be.

Bubble Volume Calculation
First, we import the experiment video into the ImageJ. In software, we use ImageJ's built-in algorithm to identify each frame of the video. That is, the image of each frame is converted into a grayscale image in the software. And the target area (bubble) and the background are marked according to the grayscale difference between the target and the background.
Then, with the help of the ImageJ's built-in algorithm, we can obtain the area data of the target area. This data is the cross-sectional area of the bubble from top view.
The volume of a bubble can be obtained by multiplying its area from top view by its height in the Z direction. Due to the shape and structure of the microchannel, we can consider the height of the channel as the height of the bubble. Thus, the volume of the bubble can be obtained by multiplying its area from top view by the height of the channel.

Additional Simulation
The driven pressure pin = 20 +5sin(10 6 t) +3sin(10 4 t) +3sin(10 2 t) Pa. And the result is shown in Figure 4. The input and output flow rate can be seen in the Figure S2a. The spectrum analysis of the results in Figure S2a is shown in Figure S2b. Both Figure S2a,b prove that the bubble-based fluidic stabilizer can function as a fluidic stabilizers similar to an electric filter.

Low-Cost and Precise Microfluidic Injection Application
To validate the practical application of the system in this paper we designed a portable microfluidic system integrated with a bubble-based fluidic stabilizer for the smooth flowrate delivery in the downstream. the bubble-based fluidic stabilization is realized using cost-efficiency and easyaccessible tools.
The schematic of the portable microfluidic system is shown in Figure S3a. The portable stabilizer is composed of a small diaphragm pump, a pressure regulating valve, and a microfluidic stabilizer chip. Here the small vacuum pump is used for bubble generation, and the pressure regulating valve for bubble controlling.
So far, the most widely used sample loading methods are pressure pumping and syringe pump. Syringe pump with fluidic stabilization set up can output relatively smooth flow, similar to the pressure pump as shown in Figure S3b. For syringe pump, the average flow rate in the device does not change due to the actual change in the device flow resistance. The amount of liquid injected is known for experiments. Thus, the syringe pump is the top option when the precisely controlled flow is required, compared with the pressure pumping method.
It is obviously illustrated in Figure S3b that with this bubble-based flow stabilizer, the pulse generated by the syringe pump can be effectively damped in a cost-efficiency and controllable method. Meanwhile, the flow rate output of this easy-accessible stabilizer with syringe pumping, and pressure pumping, has consistency in stability. The cost of a syringe pump with an easy-assessible fluidic stabilization set up, is relatively low, compared to a pressure pump. Generally, the easyassessible fluidic stabilization's cost will not exceed 100 USD, while a precisely pressure driven pump can cost up to 1000 USD.