Direct simulations of large populations of confined hydrodynamically interacting swimming particles at low Reynolds number are performed. Hydrodynamic coupling between the swimmers leads to large-scale coherent vortex motions in the flow and regimes of anomalous diffusion that are consistent with experimental observations. At low concentrations, swimmers propelled from behind (like spermatazoa) strongly migrate toward solid surfaces in agreement with simple theoretical considerations; at higher concentrations this localization is disrupted by the large-scale coherent motions.

We present a fully parametrized bead–spring chain model for stained λ-phage DNA. The model accounts for the finite extensibility of the molecule, excluded volume effects, and fluctuating hydrodynamic interactions (HI). Parameters are determined from equilibrium experimental data for 21 μm stained λ-phage DNA, and are shown to quantitatively predict the non-equilibrium behavior of the molecule. The model is then used to predict the equilibrium and nonequilibrium behavior of DNA molecules up to 126 μm. In particular, the HI model gives results that are in quantitative agreement with experimental diffusivity data over a wide range of molecular weights. When the bead friction coefficient is fit to the experimental relaxation time at a particular molecular weight, the stretch in shear and extensional flows is adequately predicted by either a free-draining or HI model at that molecular weight, although the fitted bead friction coefficients for the two models differ significantly. In shear flow, we find two regimes at high shear rate $\mathrm{(\gamma ̇)}$ that follow different scaling behavior. In the first, the viscosity and first normal stress coefficient scale roughly as ${\mathrm{\gamma ̇}}^{\text{−6/11}}$ and ${\mathrm{\gamma ̇}}^{\text{−14/11}},$ respectively. At higher shear rates, these become ${\mathrm{\gamma ̇}}^{\text{−2/3}}$ and ${\mathrm{\gamma ̇}}^{\text{−4/3}}.$ These regimes are found for both free-draining and HI models and can be understood based on scaling arguments for the diffusion of chain ends.

Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. Perhaps more surprisingly, the instabilities produce flows with many of the hallmarks of turbulence—even though the effective Reynolds numbers may be $O\left(1\right)$ or smaller. We provide perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences.

Molecular confinement offers new routes for arraying large DNA molecules, enabling single-molecule schemes aimed at the acquisition of sequence information. Such schemes can rapidly advance to become platforms capable of genome analysis if elements of a nascent system can be integrated at an early stage of development. Integrated strategies are needed for surmounting the stringent experimental requirements of nanoscale devices regarding fabrication, sample loading, biochemical labeling, and detection. We demonstrate that disposable devices featuring both micro- and nanoscale features can greatly elongate DNA molecules when buffer conditions are controlled to alter DNA stiffness. Furthermore, we present analytical calculations that describe this elongation. We also developed a complementary enzymatic labeling scheme that tags specific sequences on elongated molecules within described nanoslit devices that are imaged via fluorescence resonance energy transfer. Collectively, these developments enable scaleable molecular confinement approaches for genome analysis.

Populations of swimming micro-organisms produce fluid motions that lead to dramatically enhanced diffusion of tracer particles. Using simulations of suspensions of swimming particles in a periodic domain, we capture this effect and show that it depends qualitatively on the mode of swimming: swimmers “pushed” from behind by their flagella show greater enhancement than swimmers that are “pulled” from the front. The difference is manifested by an increase, that only occurs for pushers, of the diffusivity of passive tracers and the velocity correlation length with the size of the periodic domain. A physical argument supported by a mean field theory sheds light on the origin of these effects.

We simulate dilute solution dynamics of long flexible polymer molecules in pressure driven flow in channels with widths of roughly 0.1–10 times the polymer bulk radius of gyration. This is done using a self-consistent coarse-grained Langevin description of the polymer dynamics and a numerical simulation of the flow in the confined geometry that is generated by the motions of polymer segments. Results are presented for a model of DNA molecules of ∼10–100 μm contour length in micron-scale channels. During flow, the chains migrate toward the channel centerline, in agreement with well-known experimental observations. The thickness of the resulting hydrodynamic depletion layer increases with molecular weight at constant flow strength; higher molecular weight chains therefore move with a higher average axial velocity than lower molecular weight chains. In contrast, if the hydrodynamic effects of the confining geometry are neglected, depletion of concentration is observed in the center of the channel rather than at the walls, contradicting experimental observations. The mechanisms for migration are illustrated using a simple kinetic theory dumbbell model of a confined flexible polymer. The simple theory correctly predicts the trends observed in the detailed simulations. We also examine the steady-state stretch of DNA chains as a function of channel width and flow strength. The flow strength needed to stretch a highly confined chain away from its equilibrium length is shown to increase with decreasing channel width, independent of molecular weight; this is fairly well explained using a simple blob picture.