Incorporation of Structure in Molecular Simulations of Complex Fluid Flow

One of the key steps in solving complex fluid flow problems is the calculation of the tensorial stress term t. Polymer rheologists have traditionally used closed form constitutive equations (CCE), which do not contain the configuration distribution function of the polymer molecules. Unfortunately, CCEs exist for only the simplest of kinetic theory models for polymers, such as Hookean dumbbells. More advanced and realistic microscopic descriptions do not generally lead to a CCE. Thus, purely equation-based approaches to simulating Non-Newtonian flow phenomena reach a natural limit at these very simple microscopic descriptions. In order to graduate to more sophisticated models, a new method of determining the polymeric stress contribution must be introduced.

This project is focused on several methods of determining the stress term for non-linear polymers such as dendrimers, and branched polymers. The first of these methods is field-based Brownian Dynamics simulations, called Brownian Configuration Fields (BCF). The key difference between this and traditional Brownian Dynamics is that in BCF, the multiplicity of individual molecules is replaced by an ensemble of configurational fields which represent the internal configuration of the polymer molecules. Configuration fields carry with them the advantage of being defined at every point within the flow domain. As a result of this, the statistical error at any given point is determined by the number of fields simulated, and is independent of the mesh size. In a particle based simulation, the number of polymer molecules in an element determines the statistical accuracy, so refining the mesh necessitates increasing the number of molecules. This difficulty is avoided in BCF.

While BCF is a good method with which to approach dilute solutions, the algorithm does not include provisions for interactions between polymer molecules, as is required in a melt. For this case, we are exploring the use of dissipative particle dynamics (DPD) simulations to study the behavior of structured polymer melts under flow. DPD models fluid elements as mesoscopic particles which interact with each other via conservative, dissipative, and random thermal forces in a manner similar to MD, although at a much larger scale. The method can be extended to model polymers by connecting DPD particles with springs.

Figure: 10 x 10 x 20 DPD simulation of a branched polymer in solvent.