| Investigating the dynamics of single λ-DNA molecules in various flow fields is the scope of this thesis. We first present the results of Brownian dynamics simulations to study the dynamics of a single DNA molecule in steady shear flow. We find that the normalized average molecular extension asymptotes to nearly 0.5 even for large Wi. To investigate the different frequency regimes observed in the experiments and simulations, we have derived analytic expressions for the power spectrum for the Hookean dumbbell, the Rouse and Zimm models. This analysis shows that the three different frequency regimes arise from the coupling of the Brownian fluctuations and the hydrodynamic forces. Next, we investigate the dynamics of dilute (10−5C*) and semi-dilute (<6C*) DNA solutions both in steady and in the start-up of shear flow by combining fluorescence microscopy, bulk rheological measurements and Brownian dynamics simulations. While the transient dynamics of individual molecules is highly variable, an overshoot in the ensemble-averaged molecular extension is observed above a critical Wi following an overshoot in shear viscosity for both dilute and semi-dilute DNA solutions. These two overshoots are further analyzed and explained on a physical basis from our simulation findings. We also find that, for both the steady and the start-up of shear flow, when time is scaled with the longest polymer relaxation time, no measurable change in the character of the individual chain dynamics is observed in DNA solutions up to six times the overlap concentration (C*). Finally, we examine the dynamics of DNA molecules in more general linear mixed flows where the ratio of vorticity to strain rate maybe slightly above and below unity via Brownian dynamics simulation. When the magnitude of the strain rate that of the vorticity, it is found that the dynamics are primarily driven by the “extra” straining. For flows where the vorticity exceeds the strain rate, the flows are “elliptic vortices” and periodic chain extension dynamics are found. Our simulation results, especially in light of the excellent agreement obtained with experiment, demonstrate the basic physical elements necessary for any rheological model to capture the dynamics of single polymer chains in flow. |
