Control of the length of microfibers.

Uniform polymeric microfibers of prescribed lengths were synthesized in microfluidic devices using two different approaches--valve actuation and pulses of ultraviolet (UV) light. The more versatile valve approach was employed to demonstrate control of the length of the microfiber as a function of the frequency of valve actuation.

Dynamics of fibers in a wide microchannel.

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.

Hydrodynamic interactions suppress deformation of suspension drops in Poiseuille flow.

Evolution of a suspension drop entrained by Poiseuille flow is studied numerically at a low Reynolds number. A suspension drop 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 suspension drop 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, suspension drops destabilize by fragmentation, and at low volume fractions, by dispersing into single particles.

Hydrodynamic radii and diffusion coefficients of particle aggregates derived from the bead model.

The multiple expansion method was applied for calculating friction tensors and hydrodynamic radii R(H) of rigid molecules of various shape, composed of n(s) equal sized, touching spheres. The maximum value of n(s) 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 n(s)<100. For larger n(s), studied exclusively in our work, interpolating analytical expressions were formulated for the hydrodynamic radii R(H). 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 q(f) was calculated, which is a parameter of vital significance. It was determined that q(f) attained values close to 0.95 for n(s) approximately 450. This suggests that the previous analytical results derived by Tchen [19], in the slender body limit, who predicted that q(f)-->12/11=1.09, are not applicable for n(s)<450. Using the R(H) 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.

Streaming current and streaming potential for particle covered surfaces: virial expansion and simulations.

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.

Friction of rodlike particles adsorbed to a planar surface in shear flow.

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.