(142t) Dynamics of Single Semiflexible Biopolymers: Equilibrium Properties and Dynamics in External Flows

Recent advances in experimental capabilities using microfluidics has led to a renewed interest in the dynamics of biopolymers in external flow fields. We present a detailed and efficient simulation method for solutions of semiflexible polymers using slender-body theory in Stokes flow. We consider inextensible polymers of length of the order of the persistence length, and develop an algorithm that incorporates Euler-Bernoulli elasticity as well as Brownian forces. The model is shown to work excellently in reproducing established equilibrium properties of single free polymers. Furthermore, we report agreement with previously observed scaling laws with respect to filament rigidity. We then focus on flow fields commonly observed in microfluidic devices – particularly linear shear flows and flows near hyperbolic stagnation points. In shear flows, Brownian forces are seen to dislodge polymers from an otherwise stable axis leading to a characteristic tumbling motion – a phenomenon that has been previously observed experimentally. The frequency of tumbling is seen to vary with flow strength according to previous scaling predictions. In the hyperbolic flow geometry, if the filament is aligned with the extensional axis, fluctuations due to Brownian forces are suppressed due to tension in the filament. A theory is presented to predict this suppression, and numerical results agree with the proposed theory. When aligned with the compressional axis, a competition between elasticity and the line tension induced in the filament due to flow causes it to buckle in a way analogous to Euler buckling of beams, taking on higher mode shapes with increasing flow strength. Using a linear stability analysis, we are able to predict the critical flow strength associated with each of these mode shapes in the non-Brownian case and supplement it with numerical simulations. In the presence of Brownian forces, the thresholds for the so called stretch-coil transition are rounded by thermal fluctuations – however, numerical simulations show that these instability thresholds are broadly consistent with non-Brownian predictions.