[Paper Review] 2D microscopic and macroscopic simulation of water and porous material interaction

E. G. Nikonov, Miron Pavluš+1 more|arXiv (Cornell University)|Sep 18, 2017

Gas Dynamics and Kinetic Theory5 references3 citations

TL;DR

This paper presents a hybrid simulation approach combining 2D molecular dynamics (microscopic) and macroscopic diffusion models to study water vapor interaction with slit-like pores. It demonstrates that the two models yield consistent results for diffusion coefficients and density, validating a hybrid method for more accurate simulation of water-pore dynamics under varying thermodynamic conditions.

ABSTRACT

In various areas of science, technology, environment protection, construction, it is very important to study processes of porous materials interaction with different substances in different aggregation states. From the point of view of ecology and environmental protection it is particularly actual to investigate processes of porous materials interaction with water in liquid and gaseous phases. Since one mole of water contains $6,022140857\cdot 10^{23}$ molecules of $\mathtt{H_2O}$, macroscopic approaches considering the water vapor as continuum media in the framework of classical aerodynamics are mainly used to describe properties, for example properties of water vapor in the pore. In this paper we construct and use for simulation the macroscopic two-dimensional diffusion model describing the behavior of water vapor inside the isolated pore. Together with the macroscopic model it is proposed microscopic model of the behavior of water vapor inside the isolated pores. This microscopic model is built within the molecular dynamics approach. In the microscopic model a description of each water molecule motion is based on Newton classical mechanics considering interactions with other molecules and pore walls. Time evolution of water vapor - pore system is explored. Depending on the external to the pore conditions the system evolves to various states of equilibrium, characterized by different values of the macroscopic characteristics such as temperature, density, pressure. Comparisons of results of molecular dynamic simulations with the results of calculations based on the macroscopic diffusion model and experimental data allow to conclude that the combination of macroscopic and microscopic approach could produce more adequate and more accurate description of processes of water vapor interaction with porous materials.

Motivation & Objective

• To investigate the interaction of water vapor with isolated 2D slit-like pores under varying thermodynamic conditions.
• To compare the accuracy and consistency of microscopic molecular dynamics simulations with macroscopic diffusion modeling.
• To evaluate the feasibility of a hybrid micro-macro approach for simulating water-pore interactions in porous media.
• To validate simulation results against experimental data and theoretical diffusion models.
• To determine the conditions under which microscopic and macroscopic models converge in predicting key transport properties.

Proposed method

• Employed classical molecular dynamics (MD) with Lennard-Jones potential (σ = 3.17 Å, ε = 6.74×10⁻³ eV) to simulate individual H₂O molecule motion in a 2D pore.
• Used a macroscopic 2D diffusion model based on the Bitsadze-Kalinichenko framework to describe water vapor transport in the pore.
• Calculated time-dependent diffusion coefficients for both drying and wetting processes using MD simulations.
• Computed constant diffusion coefficients from the macroscopic model using the formula D = (kT / (6πηr)) × (1 / (1 + 2r / (3λ))) with temperature and pressure inputs.
• Simulated systems with varying outer space scaling factors (k = 1, 2, 3) to assess boundary condition effects.
• Tracked and compared time evolution of water vapor concentration (via spatial mean) and molecular density between MD and macro models.

Experimental results

Research questions

• RQ1 How do microscopic molecular dynamics and macroscopic diffusion models compare in predicting water vapor diffusion in 2D slit-like pores?
• RQ2 To what extent do the diffusion coefficients from MD simulations align with those derived from the macroscopic diffusion model?
• RQ3 How do changes in external pressure and temperature affect the equilibrium state and transport properties in the pore system?
• RQ4 What is the impact of outer space scaling (k = 1, 2, 3) on the diffusion dynamics and system equilibration?
• RQ5 Under what conditions do the micro- and macro-models converge in their predictions of water vapor density and concentration?

Key findings

• The macroscopic diffusion model produced constant diffusion coefficients of 1121.58 m²/s at 25 °C and k=2, which closely matched the time-averaged MD results.
• For T₀ = 25 °C and k=2, the MD simulation yielded a final system density of approximately 1.2×10²⁵ molecules/m³, consistent with macroscopic predictions.
• The space mean water vapor concentration (w_sm) from MD simulations showed convergence with the macroscopic model’s solution over time, particularly at t₀ = 66532 psec.
• At T₀ = 25 °C and k=2, the macroscopic model predicted a constant diffusion coefficient of 326.88 m²/s, which aligned with the MD-estimated value during equilibrium phases.
• The hybrid approach demonstrated improved accuracy when the number of molecules in MD simulations was sufficient, supporting the findings of Norman & Stegailov (2012).
• Diffusion coefficients varied significantly with temperature: D dropped from 1542.39 m²/s (k=1, T=15 °C) to 168.95 m²/s (k=3, T=35 °C), reflecting strong thermal dependence.