An empirical experimental observations and MD simulation data-based model for the material properties of confined fluids in nano/Angstrom size tubes

Garg, Ashish; Bishnoi, Swati

doi:10.1088/2632-959x/ad2b83

Cited by 10 publications

(7 citation statements)

References 50 publications

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“…Consequently, characterizing these critical properties: density ρ, viscosity η, and slip length λ require a consolidated modelling effort as a function of dimensions of the nanogeometries. While Garg and Bishnoi [14] proposed a generic and user-friendly model for predicting fluid properties within nanotubes, a comparable unified modeling approach remains elusive for understanding how these properties change in nanochannels. Our review of the literature revealed an interesting discrepancy.…”

Section: Introductionmentioning

confidence: 99%

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

Mishra,

Garg

2024

Preprint

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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.

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Section: Introductionmentioning

confidence: 99%

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

Mishra,

Garg

2024

Preprint

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Garg,

Mishra,

Sarkar

et al. 2024

Preprint

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In this study, we develop a comprehensive analytical framework to derive the optimal scaling laws for turbulent flows within tree-like self-similar branching networks, integrating a non-Newtonian power-law fluid model with index $n$. Our analysis encompasses turbulent flows occurring in both smooth and rough tubes under constraints of network's tube-volume and tube surface area. We introduce the non-dimensional conductance parameter $E$ to quantify flow conditions, investigating its variations with diameter ratio $\beta$, length ratio $\gamma$, branch splitting $N$, and branching generation levels $m$. Our findings reveal a decrease in $E$ with increasing $\gamma$, $N$, and $m$, highlighting the influence of these parameters on flow conductance. Under volume constraint, we identify optimal flow conditions for both smooth and rough tube networks, characterized by distinct scaling laws as $ D_{k+1}/D_{k} = \beta^* = N^{-(10n+1)/(24n+3)} $, and $D_{k+1}/D_{k} = N^{-3/7} $ (or flow rate proportional to $D_k^{(24n+3)/(10n+1)}$ and $D_k^{7/3}$ ), respectively, where $D_k$ is tube-diameter and $\dot{m}_k$ is the mass flow-rate in a branch at the $k_{th}$ level . Notably, the scaling in the rough tube network remains independent of the power-law index $n$, unlike the smooth tube network where it depends on $n$. Similarly, under surface-area constraint, we observe distinct optimal flow conditions for smooth and rough tube networks as with different scaling laws as $D_{k+1}/D_{k} = \beta^* = N^{-(10n+1)/(21n+2)} $, and $D_{k+1}/D_{k} = N^{-1/2} $ (or flow rate proportional to $D_k^{(21n+2)/(10n+1)}$ and $D_k^{2}$ ), respectively, again smooth tube network showing dependency on the power-law index $n$. Moreover, we uncover a trend where the scaling exponent slope decreases with increasing $n$ in volume constraint networks, while the opposite holds true for surface-area constraint networks. In conclusion, our research significantly extends the applicability of Murray's Law, offering valuable insights into the design and optimization of branching networks under various constraints and fluid properties. By incorporating non-Newtonian fluid behavior and considering tube-wall characteristics, our findings contribute to enhancing the efficiency and performance of diverse engineering systems involving fluid flow.

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“…However, as subsequent daughter channel dimensions shrink to the nanoscale, additional complexities arise. Notably, the very properties of Newtonian fluids begin to depend on the network's geometric features [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Optimal Flow and Scaling Laws for Power-Law Fluids in Elliptical Cross-Section Self-Similar Tree-Like Networks

Garg,

Mishra,

Pattanayek

2024

Preprint

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Tree-like self-similar branching networks with power-law fluid flow in elliptical cross-sectional tubes are ubiquitous in nature and engineered systems. This study optimizes flow conductance within these networks under tube-volume and tube's surface-area constraints for fully developed laminar power-law fluid flow in elliptical cross-sectional tubes. We identify key network parameters influencing flow conductance and find that the efficient flow occurs when a specific ratio of the semi-major or semi-minor axis lengths is achieved. This ratio depends on the number of daughter branches splitting at each junction (bifurcation number $N$) and the fluid's power-law index $n$. This study extends the Hess-Murray's law to non-Newtonian fluids (thinning and thickening fluids) with arbitrary branch numbers for elliptical cross-sectional tubes. We find that the maximum flow conductance occurs when a non-dimensional semi-major or semi-minor axis length ratio $\beta^*$ satisfies $\beta^* = N^{-1/3}$, and $\beta^* = N^{-(n+1)/(3n+2)}$ under constrained-volume and constrained tube's surface-area, respectively. When semi-major and semi-minor axis are equal, our findings are validated through experiments, and theory under limiting case of circular tube. These insights provide important design principles for developing efficient and optimal transport and flow systems inspired by nature's and engineered intricate networks.

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An empirical experimental observations and MD simulation data-based model for the material properties of confined fluids in nano/Angstrom size tubes

Cited by 10 publications

References 50 publications

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

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

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

Optimal Flow and Scaling Laws for Power-Law Fluids in Elliptical Cross-Section Self-Similar Tree-Like Networks

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