# Computational Mathematics and Scientific Computing Seminar

## Modeling Hydrodynamic Fluctuations in Non-equilibrium Gas Mixtures during Effusion

**Speaker:**
Ishan Srivastava, Lawrence Berkeley National Laboratory

**Location:**
Online

**Date:**
Nov. 19, 2021, 10 a.m.

**Synopsis:**

Various separation technologies involve the transport of gas mixtures across species-selective membranes. At mesoscopic scales, where the mean free path of the gas is larger than the characteristic membrane pore size, the effusive gas transport across the membrane can significantly modify hydrodynamic fluctuations that are thermally intrinsic in the system. This talk will describe our numerical framework to investigate the structure of hydrodynamic fluctuations in gas mixtures that are driven by concentration gradients across an effusion membrane. To describe thermal fluctuations in a continuum sense at mesoscale, a fluctuating hydrodynamics framework is utilized that extends the deterministic compressible Navier-Stokes equations by incorporating stochastic fluxes in a manner consistent with statistical mechanics. Additionally, recent developments in the fluctuation theorems for gas effusion are incorporated into this framework to model the stochastic effusive process at the membrane. A numerical method is developed for solving the resulting stochastic partial differential equations on a finite-volume grid with staggered momenta, where the stochastic, diffusive and advective fluxes are discretized in a manner that satisfies the fluctuation-dissipation balance. The effusive membrane is modeled by implementing a Langevin equation for the fluxes crossing the interface with a given effusion probability. Numerical results that validate the methodology will presented and the impact of effusive membrane on hydrodynamic fluctuations will be discussed.