Brownian dynamics simulations of planar mixed flows of polymer solutions at finite concentrations

Periodic boundary conditions for planar mixed flows are implemented in the context of a multi-chain Brownian dynamics simulation algorithm. The effect of shear rate $\dot{\gamma}$, and extension rate $\dot{\epsilon}$, on the size of polymer chains, \left, and on the polymer contribution to viscosity, $\eta$, is examined for solutions of FENE dumbbells at finite concentrations, with excluded volume interactions between the beads taken into account. The influence of the mixedness parameter, $\chi$, and flow strength, $\dot{\Gamma}$, on \left and $\eta$, is also examined, where $\chi \rightarrow 0$ corresponds to pure shear flow, and $\chi \rightarrow 1$ corresponds to pure extensional flow. It is shown that there exists a critical value, $\chi_\text{c}$, such that the flow is shear dominated for $\chi < \chi_\text{c}$, and extension dominated for $\chi > \chi_\text{c}$.Comment: 18 pages, 12 figures, to appear in Chemical Engineering Scienc

Simulating the flow of semidilute polymer solutions

There are a number of contexts involving polymer solutions, such as in the spinning of nano-fibres or in inkjet printing, where in order to achieve the most optimal outcome, the concentration of polymers must not be too dilute or too concentrated, but somewhere in between. While a lot is known about dilute and concentrated solutions and melts, not much is known about the vast regime of concentrations that lie in between, the so-called semidilute concentration regime. The reason much is known about dilute and concentrated solutions is because in either case, their behaviour can be understood by understanding the behaviour of single molecules. In the dilute case, this is obvious since there are few molecules interacting with each other. In the concentrated case, by treating all the molecules that surround a particular molecule as obstacles that constrain its motion, the entire problem is reduced to understanding the motion of a polymer in a tube. These approximations, however, are not valid in semidilute solutions and the problem of having to account for all the many-body interactions that arise in this regime must be addressed. The onset of the semidilute regime occurs at surprisingly low concentrations because even though the monomer concentration is very low, their being strung together into polymers that are extended objects in space gives rise to the early emergence of interactions. The broad aim of this thesis is to develop a predictive understanding of the flow behaviour of semidilute polymer solutions. In order to achieve this, firstly, an optimised mesoscopic multi-particle Brownian dynamics (BD) simulation algorithm is developed that is capable of accurately capturing both excluded volume and hydrodynamic interactions, and which can predict rheological properties of semidilute polymer solutions in shear, extensional and mixed flows. Secondly, the multi-particle BD algorithm is used to solve a number of different physical problems involving flowing semidilute polymer solutions. For instance, we have studied the dynamics of DNA molecules in semidilute solutions undergoing extensional flows, and carried out a detail comparison with the corresponding experimental results. We have found an excellent agreement between the two results. In another study, we have examined the non-monotonic influence of concentration on the extent of coil-stretch hysteresis. Our simulation results, which shown an increase followed by a decrease in coil-stretch hysteresis window size with increasing concentration, are supported by recent scaling arguments and experiments carried out by Prabhakar, Sridhar and Nguyen at Monash University. Moreover, de Gennes in his original theory predicted that in planar mixed flows, the coil-stretch hysteresis window would progressively decrease with increasing shear rate. We have investigated the competitive influences of polymer concentration and flow mixedness on the extent of coil-stretch hysteresis in polymer solutions undergoing planar mixed flows, and map out the dependence of window size on concentration and shear rate