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

Abstract

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.

Scaling Laws for Optimal Turbulent Flow in Tree-Like Networks with Smooth and Rough Tubes and Power-Law Fluids

“…However, when subsequent daughter channel dimensions shrink to the nanoscale, additional complexities emerge. Particularly, the characteristics of Newtonian fluids start to rely on the geometric attributes of the network [23][24][25][26].…”

Scaling Laws for Optimal Power-Law Fluid Flow within Converging-Diverging Dendritic Networks of Tubes and Rectangular Channels

“…In a recent study Garg [29], investigate the yield stress fluid flow in tree-like networks where proposing the conjecture with its proof, they find that one of the optimal solution obey Murray law under constraint volume. Additionally, Lee et al [30] introduced a theory on capillary microchannel flows within tree-like branches, while investigations at the nanoscale, conducted by Garg [21,31], Garg and Bishnoi [32] and Mishra and Garg [33], explored the impact of network geometry on Newtonian fluid behavior, adding further complexity to the analysis.…”

Investigation of mechanical properties of laminated polymer nanocomposites modified by Graphene Oxide

“…Epoxy/CNT nanocomposites offer exciting possibilities due to their unique properties. These composites hold promise for applications in automotive and aerospace materials, packaging (films and containers), high strength flexible deformable channels (which under nanoscale dimensions shows unique flow characteristics [11][12][13][14]), EMI shielding, adhesives, and coatings [15]. Also, replacing costly fiber with cheaper ones will reduce costs and provide different mechanical behavior combinations [16][17][18].…”