Sampling mobility profiles of confined fluids with equilibrium molecular dynamics simulations

We show how to evaluate mobility profiles, characterizing the transport of confined fluids under a perturbation, from equilibrium molecular dynamics simulations. The correlation functions derived with the Green-Kubo formalism are difficult to sample accurately, and we consider two complementary strategies: improving the spatial sampling, thanks to a new estimator of the local fluxes involving the forces acting on the particles in addition to their positions and velocities, and improving the temporal sampling, thanks to the Einstein-Helfand approach instead of the Green-Kubo one. We illustrate this method in the case of a binary mixture confined between parallel walls, under a pressure or chemical potential gradient. All equilibrium methods are compared to standard non-equilibrium molecular dynamics (NEMD) and provide the correct mobility profiles. We recover quantitatively fluid viscosity and diffusio-osmotic mobility in the bulk part of the pore. Interestingly, the matrix of mobility profiles for local fluxes is not symmetric, unlike the Onsager matrix for the total fluxes. Even the most computationally efficient equilibrium method (the Einstein-Helfand approach combined with the force-based estimator) remains less efficient than NEMD to determine a specific mobility profile. However, the equilibrium approach provides all responses to all perturbations simultaneously, whereas NEMD requires the simulation of several types of perturbations to determine the various responses, each with different magnitudes to check the validity of the linear regime. While NEMD seems more competitive for the present example, the balance should be different for more complex systems, in particular for electrolyte solutions for the responses to pressure, salt concentration, and electric potential gradients.