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

Abstract

The transport of fluids in nanometer and Angstrom-sized pores has gotten much attention because of its potential uses in nanotechnology, energy storage, and healthcare sectors. Understanding the distinct material properties of fluids in such close confinement is critical for enhancing their performance in various applications. These properties dictate the fluid's behavior and play a crucial role in determining flow dynamics, transport processes, and, ultimately, the performance of nanoscale devices. Remarkably, many researchers observed that the size of the geometry, such as the diameter of the confining nanotube, exerts a profound and intriguing influence on the material properties of nanoconfined fluids, including on the critical parameters such as density, viscosity, and slip length. Many researchers tried to model these material properties: viscosity $\eta$, density $\rho$, and slip $\lambda$ using various models with many dependencies on the tube diameter. It is somewhat confusing and tough to decide which model is appropriate and needs to be incorporated in the numerical simulation. In this paper, we tried to propose a simple single equation for each nano confined material property such as for density $\displaystyle \rho(D)/\rho_o = a+ b/(D-c)^n$, viscosity $\displaystyle \eta(D)/\eta_o = a+ b/(D-c)^n$, and the slip length $\lambda(D) = \lambda_1~D~e^{-n~D}+ \lambda_o$ (where $a,~b,~c,~n,~\lambda_1,~\lambda_o$ are the free fitting parameters). We model a wealth of previous experimental and MD simulation data from the literature using our proposed model for each material property of nanoconfined fluids at the nanometer and Angstrom scales. Our single proposed equation effectively captures and models all the data, even though many different models have been employed in the existing literature to describe the same material property. Our proposed model exhibits exceptional agreement with multiple independent datasets from the experimental observations and molecular dynamics simulations. Additionally, the model possesses the advantageous properties of continuity and a continuous derivative, so the proposed model is well-suited for integration into numerical simulations. Further, the proposed models also obey the far boundary conditions, i.e., when tube diameter $D \implies \infty$, the material properties tend to the bulk properties of the fluid. Due to the models' simplicity, smooth, and generic nature, this heuristic model holds promise to apply in simulations to design and optimize nanoscale devices.

Modelling of enhanced water flow in deformable carbon nanotubes using a linear pressure-diameter relationship

“…at temperature 298 K as shown by Garg and Bishnoi [32] on the solid-green line, they get η o = 1 mPa-s, a = 0.9, b = −3.21 X 10 −10 m, c = 1 X 10 −10 m, and n = 1. We model for tube diameter D ≥ 25 Å in this study, for that, the slip length is approximately constant.…”

“…We use the same density, viscosity, and slip length models as used by Garg [1] from Garg and Bishnoi [32] where for the density ρ(D)…”

“…We model for tube diameter D ≥ 25 Å in this study, for that, the slip length is approximately constant. Although multiple studies reported this constant to be between 50nm to 300nm Garg and Bishnoi [32]. When the tube wall undergoes minor displacements, we make the assumption that the density and viscosity, denoted as ρ(D) and η(D), respectively, to be approximately, ρ(D o ) and η(D o ).…”

“…Using the same literature data as taken by Garg [1], we compare the prediction by our flow rate model using the linear pressure-diameter relationship with pressure p = 1 bar, viscosity and density as the fitted confined water properties as described in previous section 2.3, for diameter D o ≥ 25 Å , (i.e., Region II, where the slip length does not depend on the diameter and can be assumed constant [16,32]) as shown in figure 2.…”

“…We show the enhancement factor using the rigid tube model (dashed red and dotted green with λ = 500 Å , and λ = 3000 Å , respectively), and the deformable tube model (solid black line) as a function of the diameter of the nano/Angstrom-sized tubes and compared with many previous experimental results and Molecular Dynamic simulation's predictions (shown with various symbols) on the log-log scale. Here, for diameter D o ≥ 25 Å , i.e., Region II, the slip length does not depend on the diameter and can be assumed constant [16,32].…”