Heuristic Modeling of Material Properties in Nano/Angstrom-Scale Channels: Integrating Experimental Observations and MD Simulations

Nanofluidics, the study of fluids confined within nanoscale channels, holds immense potential for various applications. However, these fluids exhibit unique properties (density, viscosity, and slip length) that deviate from their bulk counterparts and critically impact flow dynamics. Understanding and characterizing these properties is essential for designing efficient nanofluidic systems. Traditionally, numerous models, often complex and disparate, have been used to describe these properties. The current abundance of models makes selecting the most suitable one for numerical simulations a challenging task. In this paper, we propose a simpler, unified framework: a single power-law model for each property such as for density $\displaystyle \rho(H)/\rho_o = 1+ m_1~H^{-n_1}$, viscosity $\displaystyle \eta(H)/\eta_o = 1+ m_2~H^{-n_2}$, and the slip length $\lambda(H) = \lambda_o + m_3~H^{-n_3}$ (where $m_1, m_2, m_3, n_1, n_2, n_3, \lambda_o$ are the free fitting parameters). This model effectively captures data from experiments and simulations, even where existing literature employed diverse models. A key advantage of our model lies in its mathematical properties. Continuity and a continuous derivative ensure seamless implementation into numerical simulations and theoretical predictions, leading to more understable, stable and accurate results. Additionally, the model adheres to physical principles, predicting convergence to bulk properties as channel size increases. Further this proposed unified power-law model for density, viscosity, and slip length compared to existing exponential models, offers flexibility where it captures non-linear relationships and diverse data curvatures. Interpretability with clear physical meaning for parameters. Adaptability to combine with other functions for complex phenomena. Simplicity for easy parameter estimation, model interpretation, and computations. Robustness and less sensitive to outliers and noise in data and with fewer parameters to easy relate to underlying physics and scaling-laws. Hence proposed model's simplicity, smoothness, physical validity and generality make it a significant heuristic model for efficient design and optimization of nanoscale devices using theory and simulations across a wide range of applications.