Stable Configurations of Charged Sedimenting Particles.

The qualitative behavior of charged particles in a vacuum is given by Earnshaw's theorem, which states that there is no steady configuration of charged particles in a vacuum that is asymptotically stable to perturbations. In a viscous fluid, examples of stationary configurations of sedimenting uncharged particles are known, but they are unstable or neutrally stable-they are not attractors. In this Letter, it is shown by example that two charged particles settling in a fluid may have a configuration that is asymptotically stable to perturbations for a wide range of charges, radii, and densities. The existence of such "bound states" is essential from a fundamental point of view and it can be significant for dilute charged particulate systems in various biological, medical, and industrial contexts.

Motion of a spherical particle near a planar fluid-fluid interface: the effect of surface incompressibility.

Hydrodynamic coupling of a spherical particle to an undeformable planar fluid-fluid interface under creeping-flow conditions is discussed. The interface can be either surfactant-free or covered with an incompressible surfactant monolayer. In the incompressible surfactant limit, a uniform surfactant concentration is maintained by Marangoni stresses associated with infinitesimal surfactant redistribution. Our detailed numerical calculations show that the effect of surface incompressibility on lateral particle motion is accurately accounted for by the first reflection of the flow from the interface. For small particle-interface distances, the remaining contributions are significant, but they are weakly affected by the surface incompressibility. We show that for small particle-wall gaps, the transverse and lateral particle resistance coefficients can be rescaled onto corresponding universal master curves. The scaling functions depend on a scaling variable that combines the particle-wall gap with the viscosity ratio between fluids on both sides of the interface. A logarithmic dependence of the contact value of the lateral resistance function on the viscosity ratio is derived. Accurate numerical calculations are performed using our Cartesian-representation method.

Hydrodynamic coupling of spherical particles to a planar fluid-fluid interface: theoretical analysis.

We have developed a new technique (based on our Cartesian-representation method) to describe hydrodynamic interactions of a spherical particle with an undeformable planar fluid-fluid interface under creeping-flow conditions. The interface can be either surfactant-free or covered with an incompressible surfactant monolayer. We consider the effect of surface incompressibility and surface viscosity on particle motion. The new algorithm allows to calculate particle mobility coefficients for hydrodynamically coupled particles, moving either on the same or on the opposite sides of the interface.

Streaming potential studies of colloid, polyelectrolyte and protein deposition.

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.

Rotation due to hydrodynamic interactions between two spheres in contact.

We analyze the rotational and translational motion of two close spheres in a fluid at low Reynolds number to investigate if their surfaces come into mechanical contact. The rotational motion of a sphere settling close to another fixed ball is calculated from a model in which contact interactions between the spheres are added to the gravitational and hydrodynamic forces. The model predicts a transition from pure rolling to rolling with slip, determined by the Coulomb's law, when the ratio of the mechanical friction to the load increases up to the static friction coefficient. The dependence of the angular and translational velocities on the kinetic friction coefficient and on the separation between the particle surfaces is analyzed. The angular and translational velocities of a millimeter size bead in a viscous oil, close to a fixed bead of a similar size, are measured from video images. Interferometric data on translational motion are also collected according to the method introduced in our earlier studies. A systematic fitting procedure of the model to the experiment is developed and applied to the rotational and translational measurements. The model parameters are determined.