Wavenumber dependent viscosity of a system of particles coupled dissipatively to a lattice Boltzmann fluid

We investigate a particle based molecular dynamics (MD) system coupled to a lattice Boltzmann (LB) fluid. The coupling mechanism employed is dissipative, meaning that the velocity of an MD particle is damped relative to the velocity of the LB fluid, which is interpolated at the particle’s position. While this model has a well-established history in simulating systems with hydrodynamic interactions, there has been limited knowledge regarding its collective viscous behavior. In this study, we focus on exploring this behavior in the linear regime. Remarkably, we discover that the particles exhibit two distinct Stokes radii, each describing a different aspect: one for translational diffusion and another for the viscous response. These two Stokes radii typically differ significantly due to the model’s coupling scheme. Additionally, the Stokes coupling parameter introduces two critical hydrodynamic screening lengths, one for each sub-fluid, which become pivotal length scales within the system. Consequently, the viscosity becomes dependent on wave number, and for larger wave numbers, it also matters how external stresses couple to each of the sub-fluids. In the limit of long wavelengths, the viscosities of the solvent and the isolated particle system simply add up. These findings are established within the framework of a two-fluid model and are corroborated through simulations.