A dynamic density functional theory for particles in a flowing solvent

We present a dynamic density functional theory dDFT which takes into account the advection of the particles by a flowing solvent. For potential flows, we can use the same closure as in the absence of solvent flow. The structure of the resulting advected dDFT suggests that it could be used for nonpotential flows as well. We apply this dDFT to Brownian particles e.g., polymer coils in a solvent flowing around a spherical obstacle e.g., a colloid and compare the results with direct simulations of the underlying Brownian dynamics. Although numerical limitations do not allow for an accurate quantitative check of the advected dDFT both show the same qualitative features. In contrast to previous works which neglected the deformation of the flow by the obstacle, we find that the bow wave in the density distribution of particles in front of the obstacle as well as the wake behind it are reduced dramatically. As a consequence, the friction force exerted by the polymer particles on the colloid can be reduced drastically.Deutsche Forschungsgemeinschaft. SPP 1164 “Micro- and Nanofluidics” RA 1061/2-

Diffusion of a sphere in a dilute solution of polymer coils

We calculate the short time and the long time diffusion coefficient of a spherical tracer particle in a polymer solution in the low density limit by solving the Smoluchowski equation for a two-particle system and applying a generalized Einstein relation (fluctuation dissipation theorem). The tracer particle as well as the polymer coils are idealized as hard spheres with a no-slip boundary condition for the solvent but the hydrodynamic radius of the polymer coils is allowed to be smaller than the direct-interaction radius. We take hydrodynamic interactions up to 11th order in the particle distance into account. For the limit of small polymers, the expected generalized Stokes-Einstein relation is found. The long time diffusion coefficient also roughly obeys the generalized Stokes-Einstein relation for larger polymers whereas the short time coefficient does not. We find good qualitative and quantitative agreement to experiments.Comment: 9 Pages, 6 Figures, J. Chem. Phys. (in print

Stability of thin liquid films and sessile droplets under confinement

The stability of nonvolatile thin liquid films and of sessile droplets is strongly affected by finite size effects. We analyze their stability within the framework of density functional theory using the sharp kink approximation, i.e., on the basis of an effective interface Hamiltonian. We show that finite size effects suppress spinodal dewetting of films because it is driven by a long-wavelength instability. Therefore nonvolatile films are stable if the substrate area is too small. Similarly, nonvolatile droplets connected to a wetting film become unstable if the substrate area is too large. This instability of a nonvolatile sessile droplet turns out to be equivalent to the instability of a volatile drop which can attain chemical equilibrium with its vapor.Comment: 14 pages, 13 figure

Selectivity in binary fluid mixtures: static and dynamical properties

Selectivity of particles in a region of space can be achieved by applying external potentials to influence the particles in that region. We investigate static and dynamical properties of size selectivity in binary fluid mixtures of two particles sizes. We find that by applying an external potential that is attractive to both kinds of particles, due to crowding effects, this can lead to one species of particles being expelled from that region, whilst the other species is attracted into the region where the potential is applied. This selectivity of one species of particle over the other in a localized region of space depends on the density and composition of the fluid mixture. Applying an external potential that repels both kinds of particles leads to selectivity of the opposite species of particles to the selectivity with attractive potentials. We use equilibrium and dynamical density functional theory to describe and understand the static and dynamical properties of this striking phenomenon. Selectivity by some ion-channels is believed to be due to this effect.Comment: 11 pages, 9 figure

Shear flow pumping in open microfluidic systems

We propose to drive open microfluidic systems by shear in a covering fluid layer, e.g., oil covering water-filled chemical channels. The advantages as compared to other means of pumping are simpler forcing and prevention of evaporation of volatile components. We calculate the expected throughput for straight channels and show that devices can be built with off-the-shelf technology. Molecular dynamics simulations suggest that this concept is scalable down to the nanoscale.Comment: 4 pages, 4 figure, submitted to Phys. Rev. Let

A thin film model for corotational Jeffreys fluids under strong slip

We derive a thin film model for viscoelastic liquids under strong slip which obey the stress tensor dynamics of corotational Jeffreys fluids

A thin-film equation for viscoelastic liquids of Jeffreys type

We derive a novel thin film equation for linear viscoelastic media describable by generalized Maxwell or Jeffreys models. As a first application of this equation we discuss the shape of a liquid rim near a dewetting front. Although the dynamics of the liquid is equivalent to that of a phenomenological model recently proposed by Herminghaus et al. [19], the liquid rim profile in our model always shows oscillatory behaviour, contrary to that obtained in the former. Our finding supports recent conclusions, based on calculations for Newtonian liquids, that the monotonely decaying rim profiles are a consequence of large slip effects in thin polymer films