# Progress of Capillary Flow-Related Hydrovoltaic Technology: Mechanisms and Device Applications
## 2 Current Understandings of Capillary Flow-Related Electricity Generation Mechanisms
### Streaming Potential  
Since the discovery of evaporation-induced electricity from porous carbon film, streaming potential theory has been utilized to explain the phenomenon and predict device performance [13]. This is understandable considering the similarities between the working device and the ideal scenario of streaming potential. Hence, we first briefly review the theory of streaming potential. As a classical electrokinetic phenomenon, an ideal scenario of streaming potential involves a liquid flowing through a narrow channel, where an electrical signal is detected at both ends of the channel [34]. The origin of this electrical signal is the movement of hydrated ions in the electrical double layer (EDL). The EDL forms through the interaction between the liquid flow and solid surface. When a liquid, especially water, comes into contact with the solid surface, the surface is hydrolyzed and becomes charged. A layer of counter-ions is adsorbed to the surface to form the so-called Stern layer, which is basically stationary. Mobile counter-ions in the liquid are then attracted toward the Stern layer, forming a diffuse layer. The mobile ions in this diffuse layer are dragged by the liquid flow, accumulating at one end of the channel and creating an electrical potential, thus generating a streaming potential (Figure 1a). The streaming potential, \(V_{\text{S}}\), in this scenario can be quantified as:  
\[V_{\text{S}}=\frac{\varepsilon_{0}\varepsilon_{\text{r}}\Delta P\zeta}{\sigma\mu} \tag{1}\]  
where \(\Delta P\) is the external pressure difference exerted on the channel's two ends, \(\varepsilon_{0}\varepsilon_{\text{r}}\), \(\sigma\), and \(\mu\) are the dielectric constant, conductivity, and viscosity of the liquid, respectively, and \(\zeta\) is the surface zeta potential. The streaming current, \(I_{\text{S}}\), is expressed as:  
\[I_{\text{S}}=\frac{A\sigma V_{\text{S}}}{L}=\frac{A\varepsilon_{0}\varepsilon _{\text{r}}\Delta P\zeta}{\mu L} \tag{2}\]  
where \(L\) is the channel length, and \(A\) is the channel cross-sectional area. Figure 1: Streaming potential mechanism. (**a**) Electrokinetic movement and double layer formation. (**b**) Evaporation-induced electricity from a device made of porous carbon film. (**c**) Continuous open-circuit voltage output. Reproduced from ref. [23] with permission from Springer Nature, copyright 2018. In addition to a narrow channel, streaming potential can also be generated in a porous medium. As a parallel comparison, the porous carbon film effectively serves as the porous medium. Water flows through the film via capillary action and ultimately evaporates into the air, generating electricity (Figure 1b,c). Consequently, it is reasonable to hypothesize that evaporation-induced electricity is rooted in the mechanism of streaming potential. Indeed, several subsequent studies have designed devices based on the streaming potential mechanism and successfully harnessed evaporation-induced electricity [35; 36; 37; 38; 39]. In these studies, the streaming potential mechanism successfully explained the electricity generation phenomena and improved key device performance according to Equations (1) and (2) by enhancing the zeta potential of the porous material, increasing the film's porosity, and suppressing liquid conductivity. Specifically, [PERSON] et al. demonstrated the use of MOF-integrated porous carbon to significantly improve ion mobility and voltage output [35]. This approach highlights how the material's surface chemistry can be optimized for better performance. [PERSON] et al. provided a new perspective by employing nanostructured silicon, which led to substantial gains in electricity generation due to improved control over water flow through the material's nanochannels [36]. This suggests that nanostructures could be a promising path for enhancing the streaming potential effect. Despite these successes, certain phenomena remain challenging to explain using the streaming potential mechanism.