Particle-wall Distance Research Articles

Electroviscous sphere–wall interactions

A theoretical analysis is presented to determine the forces of interaction between an electrically charged spherical particle and a charged plane wall when the particle translates parallel to the wall and rotates around its axis in a symmetric electrolyte solution at rest. The electroviscous effects, arising from the coupling between the electrical and hydrodynamic equations, are determined as a solution of three partial differential equations, derived from Cox's general theory [R.G. Cox, J. Fluid Mech. 338 (1997) 1], for electroviscous ion concentration, electroviscous potential and electroviscous flow field. It is a priori assumed that the double layer thickness surrounding each charged surfaces is much smaller than the particle size. Using the matched asymptotic expansion technique, the electroviscous forces experienced by the sphere are explicitly determined analytically for small particle–wall distances, but low and intermediate Peclet numbers.

Electroviscous cylinder–wall interactions

A theoretical analysis is presented to determine the forces of interaction between an electrically charged cylindrical particle and a charged plane boundary wall when the particle translates parallel to the wall and rotates around its axis in a symmetric electrolyte solution at rest. The electroviscous effects, arising from the coupling between the electrical and hydrodynamic equations, are determined as a solution of three partial differential equations, derived from R.G. Cox's general theory [J. Fluid Mech. 338 (1997) 1], for electroviscous ion concentration, electroviscous potential, and electroviscous flow field. It is assumed a priori that the double layer thickness surrounding each charged surface is much smaller than the length scale of the problem. Using the matched asymptotic expansion technique, the electroviscous forces experienced by the cylinder are explicitly determined analytically for small particle–wall distances for low and intermediate Peclet numbers. It is found that the tangential force usually increases the drag above the purely hydrodynamic drag, although for certain conditions the drag can be reduced. Similarly the normal force is usually repulsive, i.e., it is an electrokinetic lift force, but under certain conditions the normal force can be attractive.

Polymer depletion interaction of small mesoscopic particles: Effects beyond leading order and anisotropic particles

We discuss the depletion interaction between a wall and a mesoscopic particle of ellipsoidal shape induced by long, flexible, nonadsorbing polymer chains. Both a force and a torque are exerted on the particle. We concentrate on the case in which the particle size is much smaller than typical polymer lengths, such as the radius of gyration Rg, where a rigid polymer approximation of the Asakura–Oosawa-type cannot be applied. Explicit analytical results are obtained for ideal polymers. For particle–wall distances z large compared to Rg an orientation of the ellipsoid perpendicular to the wall is favored. For z small compared to Rg (but z still large compared to the particle size), parallel orientation is favored. The perturbation of the polymer system due to the small particle is represented by a series of point-operators in the corresponding field theory, with next-to-next-to-leading anisotropic derivative-operators characterizing the particle orientation. For the interaction between a spherical particle and a wall the simple analytical results predicted by the proposed small particle expansion beyond leading order display an interesting structure which is confirmed by direct numerical computation.

CHARACTERIZATION OF HYDRODYNAMIC LIFT FORCES BY FIELD-FLOW FRACTIONATION. INERTIAL AND NEAR-WALL LIFT FORCES

Abstract Sedimentation/steric FFF has been used to measure hydrodynamic lift forces exerted on 2-30 μm latex microspheresdnven by flow through a 95 cm long ribbonlike FFF channel of ∼ 127 um thickness. Following a previous study, lift forces are examined as a function of shear rate, distance from the wall, and sphere size. Here, in contrast to the earlier study, measured lift forces are extended downward into a range corresponding to theoretical values of the inertial lift force. After corrections are made for secondary relaxation, it is found, as before, that a near-wall lift force proportional to l/δ (where δ is the particle-wall distance) dominates lift effects at small δ's. As δ increases and this force decays, the measured lift force assumes a value in good agreement with the inertial lift force predicted by the theory of Cox and Brenner as extended by subsequent workers. Over a broad range of conditions explored in almost 300 measurements, the results are consistent with a total lift force that equa...