Aggregation of Charged Particles under Electrophoresis or Gravity at Arbitrary Péclet Numbers

Collision efficiencies are considered for colloidal suspensions of solid spheres moving in a viscous fluid under the influence of electrophoresis or gravity, Brownian motion, and electrostatic and van der Waals forces. The results are compared to those for convection (electrophoresis or gravity) and diffusion (Brownian motion) acting independently. The collision efficiency increases by many orders of magnitude over that predicted by simply adding diffusive and convective efficiencies in a specific parameter regime. This regime occurs when there is a large energy barrier in the interparticle potential, causing a stable region of parameter space if there is no diffusion. Brownian motion alone will only cause small amounts of aggregation under these conditions. However, for electric fields or buoyancy effects which are only slightly too weak to allow particles to overcome the potential barrier, the addition of weak Brownian motion to a system with convection can cause significant numbers of particles to overcome the energy barrier and aggregate. Copyright 2000 Academic Press.     

Diffusiophoresis of colloidal spheres in nonelectrolyte gradients at small but finite Péclet numbers

The diffusiophoretic motion of a spherical particle in a uniform imposed gradient of a nonionic solute is analyzed for small but finite Péclet numbers. The range of the interaction between the solute molecules and the particle surface is assumed to be small relative to the radius of the particle, but the polarization effect of the mobile solute in the thin diffuse layer surrounding the particle caused by the strong adsorption of the solute is incorporated. A normal flux of the solute and a slip velocity of the fluid at the outer edge of the diffuse layer are used as the boundary conditions for the fluid domain outside the diffuse layer. Through the use of a method of matched asymptotic expansions along with these boundary conditions, a set of transport equations governing this problem is solved in the quasisteady situation and an approximate expression for the diffusiophoretic velocity of the particle good to O(Pe ²) is obtained analytically. The analysis shows that the first correction to the particle velocity is O(Pe ²). The normalized particle velocity is found to decrease monotonically with the Péclet number and to increase monotonically with the dimensionless relaxation coefficient. The stronger the polarization effect in the diffuse layer, the weaker the convective effect on the diffusiophoresis. Received: 25 May 2000 Accepted: 6 September 2000     

Approximate analytical solutions for arbitrary l-state of the Hulthén potential with an improved approximation of the centrifugal term

An approximate analytical solution of the radial Schr?dinger equation for the generalized Hulthén potential is obtained by applying an improved approximation of the centrifugal term. The bound state energy eigenvalues and the normalized eigenfunctions are given in terms of hypergeometric polynomials. The results for arbitrary quantum numbers n _r and l with different values of the screening parameter δ are compared with those obtained by the numerical method, asymptotic iteration, the Nikiforov-Uvarov method, the exact quantization rule, and variational methods. The results obtained by the method proposed in this work are in a good agreement with those obtained by other approximate methods.      

Mechanism of the unusual substituent exchange in the reactions of alkylene oxides with organic compounds bearing β-hydroxyalkyl groups at heteroatoms S,Se, N,and P

The review summarizes the data on the study of the unusual exchange reaction between alkylene oxides and organic compounds of groups 15 and 16 of the Periodic Table bearing β-hydroxyalkyl substituents at the S, Se, N, and P heteroatoms. Despite the apparent identity of one of the starting reagents and the reaction product (retention of the three-membered ring), the structures of the formed alkylene oxide and organic compound with β-hydroxyalkyl group at the heteroatom differ from the structures of the starting materials. Using β-hydroxyalkyl sulfides as a model, the plausible mechanisms of the exchange reactions were discussed taking into account the change in the reaction order in β-hydroxyalkyl sulfide with its concentration increase. Irrespectively of the mechanism, the first stage of the reaction is the formation of an intermediate H-complex due to the H-bond formation between the OH sulfide group and the alkylene oxide oxygen atom and subsequent (for the dilute solutions) monomolecular intracomplex transformation of this H-complex. The mechanism was confirmed by semi-empirical quantum chemical calculations. In the case of concentrated solutions of β-hydroxyalkyl sulfides, possibility of the formation of intermediate sulfonium salt was discussed. Each pathway proceeds via its unique intermediates and transition states but the final stage results in the same intermediate bipolar ion with an intramolecular H-bond thus leading to the same nature and compositions of the reaction products for all reaction pathways.