## 2 Materials and Methods
### Working Principle of DC-FluTENG  
The fundamental theory of a liquid-solid TENG relates to the formation of the electrical double layer (EDL), consisting of an inner layer (or Stern layer) and a diffuse layer, at the liquid-solid contact interfaces. When water comes into contact with a solid surface, the ions existing in the water, such as H\({}_{3}\)O\({}^{+}\), OH\({}^{-}\), and other positive/negative ions, form an electrical double layer. According to the \"two-step\" model proposed by [PERSON] et al. [2], the origin of forming EDL was demonstrated as the result of CE in the first step, due to the electron transfer occurring when the molecules/atoms inside the water interact directly with the atoms on the solid surface. We can assume that charges in the Stern layer are close to the solid surface, which can only move along the surface. Meanwhile, the movement of charges in the diffuse layer is not restricted to the surface. These charges can separate from the EDL and move along with the water flow. At a static state, the ions can distribute themselves in EDL, in which the concentration of the counter-ions is high near the wall and decreases dramatically away from the wall. When the water flow is applied, the diffuse layer in EDL is dragged downstream and temporarily replaced by neutral liquid. As the charges on the solid surface are immobile, the movement of ions in EDL will cause an accumulation of charges downstream and the deficit of counter-ions upstream. In this instant, counter-ions will be drawn back; meanwhile, co-ions from the EDL and liquid bulk will be pushed away by the charges on the solid surface and the accumulated charges downstream in an attempt to recover the initial EDL structure [39; 40; 41; 42]. In other words, the diffuse layer is shrunk due to part of the diffuse layer being washed away by the flowing water. Thus, the flowing water carries part of the electric charge of the double layer and generates free electrostatic charges (excess negative), as presented in Figure 2b. The charge carried by water droplets dispensed from a capillary is studied by [PERSON] et al. [39], which demonstrated that the droplets exposed from a water-filled capillary could carry excess negative charges.  
The step-by-step illustrations of the working principle of DC-FluTENG are presented in Figure 2a. At the initial state, an EDL is formed due to CE occurring at the contact interface between water and the inner surface of the pipe (see Figure 2a(i)). At this time, no output signal is observed in the external circuit. As the droplet carries excess negative charges, when the droplet contacts the electrode, charges on the droplet can be transferred to the electrode, forming an unbalance potential between the electrode and the ground Simultaneously, positive charges from the ground are attracted to neutralize the potential, generating an immediately current of charges from the ground to the electrode via the  
Figure 2: (**a**) Step-by-step illustrations of the working mechanism of DC–FluTENG; the dotted line indicates the shear plane. (**b**) Schematic diagram of an electrical double layer under flow pressure.  
external circuit, as seen in Figure 2a(ii). During the contact process of the droplet and the electrode, almost all of the charges on the droplet are transferred to the electrode until the potential difference between water and electrode disappears, as shown in Figure 2a(iii,iv). As the charges across the metal surface are distributed equally, the electric potential of the metal electrode is equal to zero when the droplet completely separates from the electrode (see Figure 2a(v)). Consequently, a direct current is induced from the ground to the electrode via the external circuit. Due to the continuous flow of water droplets through the system, the electricity-generation process is repeated.