Hydrodynamically Coupled Brownian Dynamics: A coarse-grain particle-based Brownian dynamics technique with hydrodynamic interactions for modeling self-developing flow of polymer solutions.

We present a novel coarse-grain particle-based simulation technique for modeling self-developing flow of dilute and semi-dilute polymer solutions. The central idea in this paper is the two-way coupling between a mesoscopic polymer model and a phenomenological fluid model. As our polymer model, we choose Responsive Particle Dynamics (RaPiD), a Brownian dynamics method, which formulates the so-called "conservative" and "transient" pair-potentials through which the polymers interact besides experiencing random forces in accordance with the fluctuation dissipation theorem. In addition to these interactions, our polymer blobs are also influenced by the background solvent velocity field, which we calculate by solving the Navier-Stokes equation discretized on a moving grid of fluid blobs using the Smoothed Particle Hydrodynamics (SPH) technique. While the polymers experience this frictional force opposing their motion relative to the background flow field, our fluid blobs also in turn are influenced by the motion of the polymers through an interaction term. This makes our technique a two-way coupling algorithm. We have constructed this interaction term in such a way that momentum is conserved locally, thereby preserving long range hydrodynamics. Furthermore, we have derived pairwise fluctuation terms for the velocities of the fluid blobs using the Fokker-Planck equation, which have been alternatively derived using the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) approach in Smoothed Dissipative Particle Dynamics (SDPD) literature. These velocity fluctuations for the fluid may be incorporated into the velocity updates for our fluid blobs to obtain a thermodynamically consistent distribution of velocities. In cases where these fluctuations are insignificant, however, these additional terms may well be dropped out as they are in a standard SPH simulation. We have applied our technique to study the rheology of two different concentrations of our model linear polymer solutions. The results show that the polymers and the fluid are coupled very well with each other, showing no lag between their velocities. Furthermore, our results show non-Newtonian shear thinning and the characteristic flattening of the Poiseuille flow profile typically observed for polymer solutions.

Coarse-grained simulations for flow of complex soft matter fluids in the bulk and in the presence of solid interfaces.

We present a coarse-grained particle-based simulation technique for modeling flow of complex soft matter fluids such as polymer solutions in the presence of solid interfaces. In our coarse-grained description of the system, we track the motion of polymer molecules using their centers-of-mass as our coarse-grain co-ordinates and also keep track of another set of variables that describe the background flow field. The coarse-grain motion is thus influenced not only by the interactions based on appropriate potentials used to model the particular polymer system of interest and the random kicks associated with thermal fluctuations, but also by the motion of the background fluid. In order to couple the motion of the coarse-grain co-ordinates with the background fluid motion, we use a Galilean invariant, first order Brownian dynamics algorithm developed by Padding and Briels [J. Chem. Phys. 141, 244108 (2014)], which on the one hand draws inspiration from smoothed particle hydrodynamics in a way that the motion of the background fluid is efficiently calculated based on a discretization of the Navier-Stokes equation at the positions of the coarse-grain coordinates where it is actually needed, but also differs from it because of the inclusion of thermal fluctuations by having momentum-conserving pairwise stochastic updates. In this paper, we make a few modifications to this algorithm and introduce a new parameter, viz., a friction coefficient associated with the background fluid, and analyze the relationship of the model parameters with the dynamic properties of the system. We also test this algorithm for flow in the presence of solid interfaces to show that appropriate boundary conditions can be imposed at solid-fluid interfaces by using artificial particles embedded in the solid walls which offer friction to the real fluid particles in the vicinity of the wall. We have tested our method using a model system of a star polymer solution at the overlap concentration.