Mark L. Henle

Distribution of counterions near discretely charged planes and rods

Realistic charged macromolecules are characterized by discrete (rather than homogeneous) charge distributions. We investigate the effects of surface charge discretization on the counterion distribution at the level of mean-field theory using a two-state model. Both planar and cylindrical geometries are considered; for the latter case, we compare our results to numerical solutions of the full Poisson-Boltzmann equation. We find that the discretization of the surface charge can cause enhanced localization of the counterions near the surface; for charged cylinders, counterion condensation can exceed Oosawa-Manning condensation.

Equilibrium bundle size of rodlike polyelectrolytes with counterion-induced attractive interactions

Multivalent counterions can induce an effective attraction between like-charged rodlike polyelectrolytes, leading to the formation of polyelectrolyte bundles. In this paper, we calculate the equilibrium bundle size using a simple model in which the attraction between polyelectrolytes (assumed to be pairwise additive) is treated phenomenologically. If the counterions are pointlike, they almost completely neutralize the charge of the bundle, and the equilibrium bundle size diverges. When the counterions are large, however, steric and short-range electrostatic interactions prevent charge neutralization of the bundle, thus forcing the equilibrium bundle size to be finite. We also show that if the attractive interactions between the rods become frustrated as the bundle grows, finite-size bundles can be obtained with pointlike counterions.

The effect of curvature and topology on membrane hydrodynamics

We study the mobilities of point-like and extended objects (rods) on a spherical membrane to show how these quantities are modified in a striking manner by the curvature and topology of the membrane. We also present theoretical calculations and experimental measurements of the membrane fluid velocity field around a moving rod bound to the crowded interface of a water-in-oil droplet. By using different droplet sizes, membrane viscosities, and rod lengths, we show that the viscosity mismatch between the interior and exterior fluids leads to a suppression of the fluid flow on small droplets that cannot be captured by the flat-membrane predictions.

Effective viscosity of a dilute suspension of membrane-bound inclusions

When particulate suspensions are sheared, perturbations in the shear flows around the rigid particles increase the local energy dissipation so that the viscosity of the suspension is effectively higher than that of the solvent. For bulk (three-dimensional) fluids, understanding this viscosity enhancement is a classic problem in hydrodynamics that originated over a century ago with Einstein’s study of a dilute suspension of spherical particles [A. Einstein, Ann. Phys. 19, 289 (1906)]. In this paper, we investigate the analogous problem of the effective viscosity of a suspension of disks embedded in a two-dimensional membrane or interface. Unlike the hydrodynamics of bulk fluids, low-Reynolds number membrane hydrodynamics is characterized by an inherent length scale generated by the coupling of the membrane to the bulk fluids that surround it. As a result, we find that the size of the particles in the suspension relative to this hydrodynamic length scale has a dramatic effect on the effective viscosity of t...

Diffusion and binding of finite-size particles in confined geometries

Describing the diffusion of particles through crowded, confined environments with which they can interact is of considerable biological and technological interest. Under conditions where the confinement dimensions become comparable to the particle dimensions, steric interactions between particles, as well as particle-wall interactions, will play a crucial role in determining transport properties. To elucidate the effects of these interactions on particle transport, we consider the diffusion and binding of finite-size particles within a channel whose diameter is comparable to the size of the particles. Using a simple lattice model of this process, we calculate the steady-state current and density profiles of both bound and free particles in the channel. We show that the system can exhibit qualitatively different behavior depending on the ratio of the channel width to the particle size. We also perform simulations of this system and find excellent agreement with our analytic results.

Erratum: Capillary wave dynamics on supported viscoelastic films: Single and double layers [Phys. Rev. E. 75 , 021604 (2007)]

We study the capillary wave dynamics of a single viscoelastic supported film and of a double layer of immiscible viscoelastic supported films. Using both simple scaling arguments and a continuum hydrodynamic theory, we investigate the effects of viscoelasticity and interfacial slip on the relaxation dynamics of these capillary waves. Our results account for the recent observation of a wavelength-independent decay rate for capillary waves in a supported polystyrene/brominated polystyrene double layer [X. Hu, Phys. Rev. E 74, 010602(R) (2006)].