An Efficient Moment Method for Modelling Nanoporous Evaporation

TL;DR

This paper introduces a higher-order moment method based on linearised Grad 13 and Regularised 13 equations for modeling nanoporous evaporation, offering improved accuracy and efficiency over traditional macroscopic approaches at nanoscale.

Contribution

The paper develops and applies a higher-order moment method for nanoporous evaporation, demonstrating enhanced accuracy and computational efficiency compared to NSF and Monte Carlo methods.

Findings

Non-linear boundary conditions improve results with minimal extra cost

The method achieves a balance of accuracy and efficiency for nanoscale simulations

Results compare favorably with Monte Carlo solutions

Abstract

Thin-film-based nanoporous membrane technologies exploit evaporation to efficiently cool microscale and nanoscale electronic devices. At these scales, when domain sizes become comparable to the mean free path in the vapour, traditional macroscopic approaches such as the Navier-Stokes-Fourier (NSF) equations become less accurate, and the use of higher-order moment methods is called for. Two higher-order moment equations are considered; the linearised versions of the Grad 13 and Regularised 13 equations. These are applied to the problem of nanoporous evaporation, and results are compared to the NSF method and the method of direct simulation Monte Carlo (i.e. solutions to the Boltzmann equations). Linear and non-linear versions of the boundary conditions are examined, with the latter providing improved results, at little additional computational expense, compared to the linear form. The outcome is a simultaneously accurate and computationally efficient method, which can provide simulation-for-design capabilities at the nanoscale.