A Simple Approach to Characterize Gas-Aqueous Liquid Two-phase Flow Configuration Based on Discrete Solid-Liquid Contact Electrification

In this study, we first suggest a simple approach to characterize configuration of gas-aqueous liquid two–phase flow based on discrete solid-liquid contact electrification, which is a newly defined concept as a sequential process of solid-liquid contact and successive detachment of the contact liquid from the solid surface. This approach exhibits several advantages such as simple operation, precise measurement, and cost-effectiveness. By using electric potential that is spontaneously generated by discrete solid–liquid contact electrification, the configurations of the gas-aqueous liquid two-phase flow such as size of a gas slug and flow rate are precisely characterized. According to the experimental and numerical analyses on parameters that affect electric potential, gas slugs have been verified to behave similarly to point electric charges when the measuring point of the electric potential is far enough from the gas slug. In addition, the configuration of the gas-aqueous liquid two-phase microfluidic system with multiple gas slugs is also characterized by using the presented approach. For a proof-of-concept demonstration of using the proposed approach in a self-triggered sensor, a gas slug detector with a counter system is developed to show its practicality and applicability.


Numerical analysis of the system
For numerical analysis, the system of the gas slug inside the microfluidic channel with the additional external electrode for electric potential measurement is simplified as the numerical domain shown in Figure S1a. Since the gas slug inside the microfluidic channel could be treated as a net negative electric charge, the gas slug corresponds with the surface charge in the domain.
To determine the amount of the surface charge density, the amount of the charge of the DI water droplet dispensed from the PDMS-coated capillary is measured by using the Faraday cup method. After simple calculation, the surface charge density is determined as -1.175×10 -7 C/m 2 .
To represent the aqueous liquid around the gas slug, four imaginary lines are drawn. Since the aqueous liquid is all electrically grounded, the electrical ground boundary condition is applied.
The sizes of the imaginary ground including length of the aqueous liquid are decided large enough to not affect to the electric potential generated by the gas slug as shown in Figure S1b and S1c. To check its possibility of use, the electric potential behavior caused by the moving gas slug is simulated by changing the relative distance between the gas slug and the electric potential measuring point, r, from -5 to 5 mm. As shown in Figure S2, the behavior is similar with the U-shaped electric potential behavior in the experimental result.

Thickness of the substrate to assume the gas slug as a point electric charge source
The dependency of t on VOC is numerically investigated by varying substrate thickness. As shown in Figure S3a, the electric potential shows linearly proportional relationship with the inverse of the substrate thickness when the thickness is sufficiently thick (over 500 µm, in this experiment). However, as the substrate becomes thinner, the slope becomes flatten, which indirectly means that the gas slug behaves like a plane electric charge source rather than a point electric charge source. It could be simply explained with the equipotential lines around the gas slug as shown in Figure S3b. Although the equipotential lines which locate sufficiently far from the gas slug show similar characteristics of the electric potential generated from the point electric charge source as plotted in Figure S3c, the lines nearby the gas slug follow the characteristic of the electric potential generated from the plane electric charge source in Figure   S3d. This behavior mainly be attributed to the existence of the grounded aqueous liquids around the gas slug. The further study is needed to clarify the role of the grounded aqueous liquids around the gas slug.

Width of the microfluidic channel to assume the gas slug as a point electric charge source
The dependency of w on VOC is experimentally investigated to explore the validity of the present approach to the bulk-system by varying w from 250 to 4000 µm with fixed t (= 500 µm). As shown in Figure S4a, VOC is linearly proportional to w with range from 250 to 1500 µm. However, as the channel becomes broader, the increase behavior of VOC becomes retarded compared to the proportional relationship. To deeply investigate such behavior, VOC per contact area (|Voc|/A) is calculated to ignore the effect of the gas slug contact area (A). The amount of |Voc|/A is maintained as constant at w range from 250 to 1500 µm as shown in Figure S4b.
Although the experimental data in that range shows the validity of the point electric charge assumption, the remaining data at the higher w range implies that there exists in critical width which is a maximum width where the point electric charge source assumption is valid. In our experiment, the critical width seems to exist within the w range of 1500 ~ 2000 µm and thus, it indirectly shows that the point electric charge source assumption is invalid with higher w than the critical width. Consequently, for applying the present approach to the bulk-system, there is a need to perform further study about critical width of the microfluidic channel.