Dynamic Mobility of Two Spherical Particles with Thick Double Layers

The dynamic electrophoretic mobility of a pair of nearby spherical particles is analyzed in the case when the thickness of the electrical double layer around each particle is comparable to the particle radius. By means of an integral reciprocal relation, a formal expression is obtained for the force and torque on N spheres subject to an oscillating electric field which may be spatially varying. Upon linearizing in the surface potential, this expression is shown to depend upon a set of purely hydrodynamic problems involving N neutral spheres, the calculation of the electric field around N neutral spheres, and the equilibrium charge distribution around N charged spheres. In the case of a single particle, the known analytic formula for the dynamic mobility is recovered. For a pair of identical particles, the dynamic mobility is calculated numerically, using known solutions to the required subproblems. An analytical expression for the mobility of a pair of widely separated spheres is also obtained by a method of reflections, and this is in excellent agreement with the numerical results outside the range of double layer overlap. Copyright 2000 Academic Press.     

Thermodynamic properties of a fluid of hard spheres with water-like dipole and quadrupole moments

The thermodynamic properties of a fluid of hard spheres with dipole and tetrahedral quadrupole moments are investigated using thermodynamic perturbation theory. The drpole-quadrupole coupling is found to be very important at values of the multipole moments that are close to those of water.     

Measurement of dynamical forces between deformable drops using the atomic force microscope. I. Theory

Recent experimental developments have enabled the measurement of dynamical forces between two moving liquid drops in solution using an atomic force microscope (AFM). The drop sizes, interfacial tension, and approach velocities used in the experiments are in a regime where surface forces, hydrodynamics, and drop deformation are all significant. A detailed theoretical model of the experimental setup which accounts for surface forces, hydrodynamic interactions, droplet deformation, and AFM cantilever deflection has been developed. In agreement with experimental observations, the calculated force curves show pseudo-constant compliance regions due to drop flattening, as well as attractive pull-off forces due mainly to hydrodynamic lubrication forces.     

Transient responses of a wetting film to mechanical and electrical perturbations

This article reports real-time observations and detailed modeling of the transient response of thin aqueous films bounded by a deformable surface to external mechanical and electrical perturbations. Such films, tens to hundreds of nanometers thick, are confined between a molecularly smooth mica plate and a deformable mercury/electrolyte interface on a protuberant drop at a sealed capillary tube. When the mercury is negatively charged, the water forms a wetting film on mica, stabilized by electrical double layer forces. Mechanical perturbations are produced by driving the mica plate toward or by retracting the mica plate from the mercury surface. Electrical perturbations are applied to change the electrical double layer interaction between the mica and the mercury by imposing a step change of the bias voltage between the mercury and the bulk electrolyte. A theoretical model has been developed that can account for these observations quantitatively. Comparison between experiments and theory indicates that a no-slip hydrodynamic boundary condition holds at the molecularly smooth mica/electrolyte surface and at the deformable mercury/electrolyte interface. An analysis of the transient response based on the model elucidates the complex interplay between disjoining pressure, hydrodynamic forces, and surface deformations. This study also provides insight into the mechanism and process of droplet coalescence and reveals a novel, counterintuitive mechanism that can lead to film instability and collapse when an attempt is made to thicken the film by pulling the bounding mercury and mica phases apart.     

Dynamic Mobility of Particles with Thick Double Layers in a Nondilute Suspension

The dynamic mobility of a nondilute suspension of spherical particles is investigated in the case where the thickness of the electrical double layer around each particle is comparable to the particle radius. A formula is obtained for the O(φ) correction in a random suspension of particles with volume fraction φ, involving an integral over the dynamic mobility of a pair of spheres. This formula is then evaluated using both analytical approximations and numerical results previously obtained for the pair mobilities and valid for low surface potentials. The effect of double-layer thickness on the O(φ) coefficient is most pronounced at low frequencies, and lessens once the hydrodynamic penetration depth is smaller than the particle radius. Various approximations are considered that use the O(φ) result to predict the dynamic mobility in concentrated suspensions, and at high frequencies these approximations are shown to give results qualitatively different from those of recent cell models. Copyright 2000 Academic Press.     

Dynamics of interactions involving deformable drops: hydrodynamic dimpling under attractive and repulsive electrical double layer interactions

A model developed previously to analyze force measurements between two deformable droplets in the atomic force microscope [Langmuir 2005, 21, 2912-2922] is used to model the drainage of an aqueous film between a mica plate and a deformable mercury drop for both repulsive and attractive electrical double-layer interactions between the mica and the mercury. The predictions of the model are compared with previously published data [Faraday Discuss. 2003, 123, 193-206] on the evolution of the aqueous film whose thickness has been measured with subnanometer precision. Excellent agreement is found between theoretical results and experimental data. This supports the assumptions made in the model which include no-slip boundary conditions at both interfaces. Furthermore, the successful fit attests to the utility of the model as a tool to explore details of the drainage mechanisms of nanometer-thick films in which fluid flow, surface deformations, and colloidal forces are all involved. One interesting result is that the model can predict the time at which the aqueous film collapses when attractive mica-mercury forces are present without the need to invoke capillary waves or other local instabilities of the mercury/electrolyte interface.     

Fluids of polarizable hard spheres with dipoles and tetrahedral quadrupoles Integral equation results with application to liquid water

The mean spherical, linearized hypernetted chain and quadratic hypernetted chain approximations are solved for a fluid of hard spheres with embedded point dipoles and tetrahedral quadrupoles and this system is shown to be quite similar to the dipole-linear quadrupole case previously studied. However, tetrahedral quadrupoles have a larger influence upon the structural and thermodynamic properties and are slightly more effective in decreasing the dielectric constant from the purely dipolar value. Also we describe a simple self-consistent mean field theory which allows molecular polarizability to be taken into account. This approximation together with the integral equation methods is applied to a polarizable dipole-tetrahedral quadrupole fluid with water-like parameters. The dielectric constant of this system is found to be in good agreement with the experimental results for liquid water for temperatures ranging from 25°C to 300°C. The influence of molecular polarizability is shown to be very large. At 25°C the mean dipole moment is ～2·56 D compared with ～1·85 D in the gas phase and the dielectric constant increases from ～25 for non-polarizable particles to ～80 for the polarizable model.     

Electrophoretic Motion of a Spherical Particle with a Thick Double Layer in Bounded Flows

The electrophoretic mobility of a spherical colloidal particle with low zeta potential near a solid charged boundary is calculated numerically for arbitrary values of the double layer thickness by a generalization of Teubner's method to the case of bounded flow. Three examples are considered: a sphere near a nonconducting planar wall with electric field parallel to the wall, near a perfectly conducting planar wall with electric field perpendicular to the wall, and on the axis of a cylindrical pore with electric field parallel to the axis. The results are compared with recent analytical calculations using the method of reflections. For the case of a charged sphere near a neutral surface, the reflection results are quite good, provided there is no double layer overlap, in which case there can be extra effects for constant potential particles that are entirely missed by the analytical expressions. For a neutral sphere near a charged surface, the reflection results are less successful. The main reason is that the particle feels the profile of the electroosmotic flow, an effect ignored by construction in the method of reflections. The general case is a combination of these, so that the reflections are more reliable when the electrophoretic motion dominates the electroosmotic flow. The effect on particle mobility of particle-wall interactions follows the trend expected on geometric grounds in that sphere-plane interactions are stronger than sphere-sphere interactions and the effect on a sphere in a cylindrical pore is stronger still. In the latter case, particle mobility can fall by more than 50% for thick double layers and a sphere half the diameter of the pore. The agreement between numerical results and analytical results follows the same trend, being worst for the sphere in a pore. Nevertheless, the reflections can be reliable for some geometries if there is no double layer overlap. This is demonstrated for a specific example where reflection results have previously been compared with experiments on protein mobility through a membrane (J. Ennis et al., 1996, J. Membrane Sci. 119, 47). Copyright 1999 Academic Press.