# Development and Validation of a Capacitor-Current Circuit Model for Evaporation-Induced Electricity
## 1 Introduction  
In recent years, global warming has become an increasingly pressing matter to the world due to fossil fuel consumption. The need for sustainable energy solutions and a reduction of carbon emissions has never been greater [1]. Among the various green energy technologies, a newcomer called evaporation-induced electricity has gained considerable interest [2, 3]. This technology generates electric power from natural water evaporation, making it particularly suitable for remote, off-grid devices, especially Internet-of-Things (IoT) applications [4, 5].  
Despite significant progress in evaporation-induced electricity over the past decade, the underlying mechanism of electricity generation remains unclear. Various models have been proposed, ranging from traditional streaming potential [2] and ion concentration gradient [6, 7], to more recent approaches like microbial electricity [8], ionovoltaic [9],pseudostreamning [10; 11], and evaporative potential [12]. While each model provides a reasonable explanation, certain aspects remain unexplained [13].  
In addition to efforts to understand the physical mechanisms of evaporation-induced electricity, progress has also been made in developing circuit models to explain the electrical characteristics of the working device. Notably, [PERSON] et al. developed comprehensive mathematical formulations to describe the transient-ion transport and charge storage/discharge features [14; 15; 16]. However, despite their accuracy and thoroughness, the mathematical complexity of these models limits their applicability in understanding, designing, and optimizing real-world devices. To enhance the practicality and understanding of evaporation-induced electricity, a more accessible and adaptable model is needed.  
Previously, our group reviewed the mainstream mechanisms and highlighted the advantages and limitations of each [13]. We also proposed a hybrid model that combines a capacitor and streaming current source to explain evaporation-induced electricity. In this work, we introduce this model as an innovative, simplified, and robust alternative to existing models for explaining the electrical characteristics of evaporation-induced electricity. The proposed model will be validated using experimental data obtained from wood-based nanogenerators with modified aligned microchannels, chosen for their hydrophilicity and energy generation capabilities.  
We will first discuss the limitations of the [PERSON]'s model and explain the need for a simplified alternative [14]. Then, we will introduce the simplified model, followed by an analysis of the wood-based nanogenerator's device performance and data fitting to validate the model. We will also discuss the practical implications for device design, with a focus on porous structures and microchannel configurations. The primary goal is to develop a framework that balances simplicity with predicative accuracy, thereby accelerating the advancement of evaporation-induced electricity technology. This paper is organized as follows. Section 1 introduces the background and motivation of the study. Section 2 presents the theoretical development of the capacitor-current circuit model, including key equations and assumptions. Section 3 describes the experimental methods and materials used to validate the model. Section 4 discusses the results, including model fitting and parameter sensitivity analysis. Finally, Section 5 summarizes the key findings and highlights future research directions.