Mesoscopic modelling of flowing complex matter, memory and Galilean invariant Brownian Dynamics

Complex soft matter usually consists of large molecules with extremely many degrees of freedom. In this talk we are especially interested in molecules which interact with many neighboring particles, typically in the order of a few hundreds. Typical examples are star polymers whose arms mix with those of neighboring stars, or even entangle with them in the rheological sense when they are sufficiently long. Other example are systems of tri-block-copolymers of which the middle block is solvophillic and the two outer blocks are solvophobic. Such polymers will arrange their solvophobic parts into micelles, with the solvophillic inner blocks dangling around them. At high concentrations the solvophilic middle blocks may form bridges from one micelle to another, thereby forming transient networks.When set into shearing motion, particles will displace with respect to each other, and their internal structure will be disrupted. The typical time scale for rupture and re-establishing of this structure will give rise to long time processes strongly interacting with the externally imposed motion. These long time processes may of course be studied by models including all the relevant small scale information of the molecules. When coarse graining the molecules this possibility gets lost and the long time processes must be introduced as memory into the dynamics of the coarse objects. In this presentation I will present a way to do this, which is still computationally efficient. After presenting the general concept and some examples, I will address shortcomings of the present implementation of the model and suggest possible ways to solve the problems.In the last part of the presentation I will present a way to generalize Brownian Dynamics to a Galilei invariant simulation scheme. As is well known this can be done by adding to the displacements of the particles affine contributions due to the average flow in the neighborhoods of the particles. The challenge is to devise a model to calculate these average flows as they develop in response to the perturbations at the boundaries of the system. I will demonstrate how this can be done and pay attention to differences between this method and the traditional Brownian Dynamics codes. In particular in strongly sheared systems the traditional Brownian Dynamics method doesn’t seem very realistic