Stochastic entangled chain dynamics of dense polymer solutions.

We propose an adjustable-parameter-free, entangled chain dynamics model of dense polymer solutions. The model includes the self-consistent dynamics of molecular chains and solvent by describing the former via coarse-grained polymer dynamics that incorporate hydrodynamic interaction effects, and the latter via the forced Stokes equation. Real chain elasticity is modeled via the inclusion of a Pincus regime in the polymer's force-extension curve. Excluded volume effects are taken into account via the combined action of coarse-grained intermolecular potentials and explicit geometric tracking of chain entanglements. We demonstrate that entanglements are responsible for a new (compared to phantom chain dynamics), slow relaxation mode whose characteristic time scale agrees very well with experiment. Similarly good agreement between theory and experiment is also obtained for the equilibrium chain size. We develop methods for the solution of the model in periodic flow domains and apply them to the computation of entangled polymer solutions in equilibrium. We show that the number of entanglements Π agrees well with the number of entanglements expected on the basis of tube theory, satisfactorily reproducing the latter's scaling of Π with the polymer volume fraction φ. Our model predicts diminishing chain size with concentration, thus vindicating Flory's suggestion of excluded volume effects screening in dense solutions. The predicted scaling of chain size with φ is consistent with the heuristic, Flory theory based value.

Entangled chain dynamics of polymer knots in extensional flow.

We formulate a coarse-grained molecular-dynamics model of polymer chains in solution that includes hydrodynamic interactions, thermal fluctuations, nonlinear elasticity, and topology-preserving solvent mediated excluded volume interactions. The latter involve a combination of potential forces with explicit geometric detection and tracking of chain entanglements. By solving this model with numerical and computational methods, we study the physics of polymer knots in a strong extensional flow (Deborah number De=1.6 ). We show that knots slow down the stretching of individual polymers by obstructing via entanglements the "natural," unraveling, and flow-induced chain motions. Moreover, the steady-state polymer length and polymer-induced stress values are smaller in knotted chains than in topologically trivial chains. We indicate the molecular processes via which the rate of knot tightening affects the rheology of the solution.

Interaction of solid particles with a tangle of vortex filaments in a viscous fluid.

Homogeneous isotropic turbulence consists of coherent filamentary vortex structures superimposed to a more incoherent background. The question which we address is the effect of these structures on the dynamics of small, neutrally buoyant solid particles. Rather than generating the turbulence by direct numerical simulation (DNS) of the Navier-Stokes equations, we use a model of turbulence based entirely on viscous vortex filaments which interact via inertial forces and reconnect with each other. Using this model, we show that solid particles can become trapped around vortex filaments, something difficult to achieve with DNS. Unlike most studies, we have not neglected inviscid inertial effects. By comparing the Stokes, local, and convective components of the particle's acceleration, we also show that the convective part clearly identifies the trapping.

Coherent structure formation in turbulent thermal superfluids.

By means of numerical calculations, we show that in turbulent thermal superfluids the normal fluid induces coherent bundles of quantized line vortices in the superfluid. These filamentary structures are formed in between the normal fluid vortices, acquiring eventually comparable circulation. They are self-stretched and evolve according to self-regulating dynamics. Their spectrum mimics the normal fluid spectrum with the mutual friction force exciting the large scales and damping the small scales. Strongly interacting triads of them merge sporadically into stronger, braided vortex filaments, inducing strong fluctuations in the system's energetics. A theoretical account of the system's statistical mechanics is proposed.

Measurement of the normal-fluid velocity in superfluids.

Numerical calculations of (finite temperature) superfluid vortex ring propagation against a particulate sheet show that the solid particle trajectories collapse to a very good approximation to the normal-fluid path lines. We propose an experiment in which, by measuring the solid particles' velocities, direct information about the instantaneous normal-fluid velocity values could be obtained.

Quantized turbulence physics.

We elaborate the physics of systems of unconstrained, reconnecting vortex filaments with dynamic finite cores of uniform ("quantized") circulation interacting via Biot-Savart and viscous forces. The phenomenology of this purely structured turbulent system includes an inertial range with Kolmogorov's k(-5/3) scaling for the energy spectrum, as well as Kolmogorov's linear in r scaling for the third order longitudinal structure function.

Reconnection of colliding vortex rings.

We investigate numerically the Navier-Stokes dynamics of reconnecting vortex rings at small Reynolds number for a variety of configurations. We find that reconnections are dissipative due to the smoothing of vorticity gradients at reconnection kinks and to the formation of secondary structures of stretched antiparallel vorticity which transfer kinetic energy to small scales where it is subsequently dissipated efficiently. In addition, the relaxation of the reconnection kinks excites Kelvin waves which due to strong damping are of low wave number and affect directly only large scale properties of the flow.