In this module we present a Brownian dynamics simulation in which the user may interact by adjusting important model parameters and flow conditions. In this way, the user will be able to experience a simulation of what takes place at the molecular level as macromolecules (or polymer chains) flow in solution. Rheology is the study of the flow and deformation of material. We focus specifically on the rheology of dilute polymer solutions, although the methods and concepts used here will apply to a wide range of other materials such as concentrated polymer melts, biological fluids such as blood, electromagnetic fluids and ferrofluids, inks and particle suspensions, just to name a few. These fluids all have complex microstructure which gives rise to complex material properties. This module will help you investigate this relation between the microscopic structure and the macroscopic properties.
Unlike low-molecular weight fluid (e.g., water, air, acetone, etc.) these more complex fluids require more detailed models to describe their behavior and properties. For example, water can be well described by the classical Navier-Stokes equations when a single material constant, the viscosity, is known. In comparison, a polymer solution requires a viscosity function that depends on the shear rate and two normal stress function of shear rate just to describe steady shear flow. For other types of flow, such as elongational flow, other unique material properties are required. It is estimated that nearly half of all fluids used in engineering applications are non-Newtonian and require this more detailed modeling for successful processing. Unfortunately, in many applications the process is designed by empirical experience or old-fashion trial and error. Our goal for this module is that the user will develop an understanding of the relation between the microstructure behavior and the macroscopic material function used in designing engineering applications.
The simulation focuses on a single polymer chain represented by beads (i.e., hydrodynamic resistance sites) and springs (i.e., intra-molecular potentials that model the action of the chain coiling and uncoiling). The chain is placed in an infinite bath of fluid. Initially the chain is at equilibrium and remains coiled up although the configuration fluctuates due to the Brownian forces interacting with it. The fluid can be set into motion by specifying the flow rate and the flow type, for example, a simple shear flow at either a low or high flow rate. The chain will respond to the flow by stretching and tumbling depending on the flow type and flow rate. The type of spring can also be adjusted from a simple Hookean spring for which the force is proportional to the bead separation, to a nonlinear force law in which the force increases more strongly with bead separation; and therefore, maintains the beads in closer proximity. Material properties are calculated from the average configuration of the ensemble of chains. The user will be able to explore different flow types in a two-dimensional flow. These include elongation, shearing and rigid-body rotation and all two-dimensional flow in between by setting a flow-type parameter we call a. If you want to learn more about modeling and simulation polymers, you can consult the following texts:
R. B. Bird, R.C. Armstrong, and O. Hassager, “Dynamics of Polymeric Liquids: Volume 1 Fluid Mechanics,” (1987) John Wiley & Sons
R. B. Bird, C. F. Curtiss, R.C. Armstrong, and O. Hassager, “Dynamics of Polymeric Liquids: Volume 2 Kinetic Theory,” (1987) John Wiley & Sons
H. C. Öttinger, Stochastic Process in Polymeric Fluids: Tools and Examples for Developing Simulation Algorithms,” (1996) Springer Verlag