Institute of Fundamental Technological Research

Dynamics of single flexible non-Brownian fibers, tumbling in a Poiseuille flow between two parallel solid plane walls, is studied with the use of the HYDROMULTIPOLE numerical code, based on the multipole expansion of the Stokes equations, corrected for lubrication. Fibers, which are closer to a wall, more flexible (less stiff) or longer, deform more significantly and, for a wide range of the system parameters, they faster migrate towards the middle plane of the channel. For the considered systems, fiber velocity along the flow is only slightly smaller than (and can be well approximated by) the Poseuille flow velocity at the same position. In this way, the history of a fiber migration across the channel is sufficient to determine with a high accuracy its displacement along the flow.

Stokes equations, flexible fiber, Poiseuille flow, solid walls

Recent developments in the electrokinetic determination of particle, protein and polyelectrolyte monolayers at solid/electrolyte interfaces, are reviewed. Illustrative theoretical results characterizing particle transport to interfaces are presented, especially analytical formulae for the limiting flux under various deposition regimes and expressions for diffusion coefficients of various particle shapes. Then, blocking effects appearing for higher surface coverage of particles are characterized in terms of the random sequential adsorption model. These theoretical predictions are used for interpretation of experimental results obtained for colloid particles and proteins under convection and diffusion transport conditions. The kinetics of particle deposition and the structure of monolayers are analyzed quantitatively in terms of the generalized random sequential adsorption (RSA) model, considering the coupling of the bulk and surface transport steps. Experimental results are also discussed, showing the dependence of the jamming coverage of monolayers on the ionic strength of particle suspensions. In the next section, theoretical and experimental results pertaining to electrokinetics of particle covered surfaces are presented. Theoretical models are discussed, enabling a quantitative evaluation of the streaming current and the streaming potential as a function of particle coverage and their surface properties (zeta potential). Experimental data related to electrokinetic characteristics of particle monolayers, mostly streaming potential measurements, are presented and interpreted in terms of the above theoretical approaches. These results, obtained for model systems of monodisperse colloid particles are used as reference data for discussion of experiments performed for polyelectrolyte and protein covered surfaces. The utility of the electrokinetic measurements for a precise, in situ determination of particle and protein monolayers at various interfaces is pointed out.

Colloid deposition, Nanoparticle deposition, Particle covered surfaces, Polyelectrolyte deposition, Protein deposition, Streaming potential of covered surfaces

In this paper we aim to create an experimental and numerical model of nano and micro filaments suspended in a confined Poiseuille flow. The experimental data obtained for short nanofibres will help to elucidate fundamental questions concerning mobility and deformation of biological macromolecules due to hydrodynamic stresses from the surrounding fluid motion. Nanofibres used in the experiments are obtained by electrospinning polymer solutions. Their typical dimensions are 100–1000 μm (length) and 0.1–1 μm (diameter). The nanofibre dynamics is followed experimentally under a fluorescence microscope. A precise multipole expansion method of solving the Stokes equations, and its numerical implementation are used to construct a bead-spring model of a filament moving in a Poiseuille flow between two infinite parallel walls. Simulations show typical behaviour of elongated macromolecules. Depending on the parameters, folding and unfolding sequences of a flexible filament are observed, or a rotational and translation motion of a shape-preserving filament. An important result of our experiments is that nanofibres do not significantly change their shape while interacting with a micro-flow. It appeared that their rotational motion is better reproduced by the shape-preserving Stokesian bead model with all pairs of beads connected by springs, omitting explicit bending forces.

Nanofibres suspension, Microchannels, Filament dynamics, Stokesian dynamics, Multipole expansion

Evolution of a suspensiondrop entrained by Poiseuille flow is studied numerically at a low Reynolds number. A suspensiondrop is modeled by a cloud of many nontouching particles, initially randomly distributed inside a spherical volume of a viscous fluid which is identical to the host fluid outside the drop. Evolution of particle positions and velocities is evaluated by the accurate multipole method corrected for lubrication, implemented in the HYDROMULTIPOLE numerical code. Deformation of the drop is shown to be smaller for a larger volume fraction. At high concentrations, hydrodynamic interactions between close particles significantly decrease elongation of the suspensiondrop along the flow in comparison to the corresponding elongation of the pure-fluid drop. Owing to hydrodynamic interactions, the particles inside a dense-suspension drop tend to stay for a long time together in the central part of the drop; later on, small clusters occasionally separate out from the drop, and are stabilized by quasiperiodic orbits of the constituent nontouching particles. Both effects significantly reduce the drop spreading along the flow. At large volume fractions, suspensiondrops destabilize by fragmentation, and at low volume fractions, by dispersing into single particles.

Stokes equations, Poiseuille flow, suspension drop, hydrodynamic interactions

The multiple expansion method was applied for calculating friction tensors and hydrodynamic radii RH of rigid molecules of various shape, composed of ns equal sized, touching spheres. The maximum value of ns studied was 450, which covers most situations met in practice. Calculations were performed for linear chains, half-circles, circles (cyclic molecules) and S-shaped aggregates. It was shown that our results agreed with previous theoretical data obtained for linear chains and cyclic aggregates, for ns < 100. For larger ns, studied exclusively in our work, interpolating analytical expressions were formulated for the hydrodynamic radii RH. These expressions, involving logarithmic function of the aspect ratio parameter (length to width ratio of the macromolecules), are the main finding of our work. Using these expressions, the ratio of the hydrodynamic radius of cyclic-to-linear aggregate qf was calculated, which is a parameter of vital significance. It was determined that qf attained values close to 0.95 for ns ∼450. This suggests that the previous analytical results derived by Tchen [19], in the slender body limit, who predicted that qf → 12/11 = 1.09, are not applicable for ns < 450. Using the RH values, the average translation diffusion coefficients and the sedimentation coefficients for these aggregate shapes were calculated. It was shown that our theoretical results are in good agreement with experimental data obtained for polyelectrolytes and for DNA fragments of various molecular mass. It was concluded that our results can be effectively used to determine the shape of macromolecules, in particular to discriminate between linear and cyclic DNA configurations.

Aggregates of particles of various shapes, Bead model of particle aggregates, Diffusion coefficients of particle aggregates, DNA bead model of, DNA fragment hydrodynamic radii, Hydrodynamic radius of aggregates, Linear chain aggregates, Sedimentation coefficients of aggregates and macromolecules

Streaming potential changes induced by deposition of particles at solid/liquid interfaces are considered theoretically. The solution is obtained in terms of a virial expansion of the streaming potential up to the third order of the surface coverage of particles, assumed to be distributed according to the hard sphere equilibrium distribution function. Theoretical methods, including the idea of cluster expansion, are adopted from statistical physics. In the cluster expansion, two-body and three-body hydrodynamic interactions are evaluated with a high precision using the multipole method. The multipole expansion algorithm is also used to perform numerical simulations of the streaming potential, valid for the entire surface coverage range met in practice. Results of our calculations are in good agreement with the experimental data for spherical latex particles adsorbed on a mica surface.

Streaming current, streaming potential, particle-covered wall, Stokes equations, hydrodynamic interactions, multiple expansion, viral exapnsion

A planar hard surface covered with elongated stiff rodlike particles in shear flow is considered in the low-Reynolds-number regime assuming low particle surface coverage. The particles are modeled as straight chains of spherical beads. Multipole expansion of the Stokes equations (the accurate HYDROMULTIPOLE algorithm) is applied to evaluate the hydrodynamic force exerted by the fluid on the rodlike particles, depending on their shape, i.e., on the number of beads and their orientation with respect to the wall and to the ambient shear flow.

Stokes flow, hydrodynamic interactions, rigid rod, solid wall, hydrodynamic friction

A rigid polymer model consisting of two identical spherical particles, irreversibly adsorbed on a planar channel wall is considered. The linear dimensions of the polymer are assumed to be small enough to validate an expansion of the flow inside the channel to linear terms only. The polymer is therefore effectively immersed in a shearing flow. Total hydrodynamic force acting on the polymer is calculated. The dependence of that force on the polymers orientation is derived taking into account symmetries of the system. Large differences in the force are found for different polymer orientations. Applications of these results are sketched.

Stokes equations, hydrodynamic interactions, hydrodynamic friction, rigid rod, plane wall