Brownian diffusion of hard spheres at finite concentrations

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Abstract

We investigated the effect of concentration on the Brownian diffusion of uncharged rigid spheres. Monosize silica spheres were prepared according to the method of Stöber (1968). The particles were sterically stabilized by chemisorption of stearic alcohol at their surface by the method developed by van Helden (1981).Particle radius was 14.5 nm from electron micrographs of the coated particles. Osmotic pressure measurements of the sterically stabilized particles dispersed in cyclohexane showed that the particles behaved as hard spheres. The measurements agreed well with predictions from the Carnahan-Starling equation over the concentration range 0.0458 < ϕ < 0.37 where ϕ is the volume fraction of the particles in the suspension. Viscosity measurements of silica dispersions were made over the concentration range 0 < ϕ < 0.25. The relative viscosity over the range 0 < ϕ < 0.2 was fitted by ηr = 1 + 2.4ϕ + 7.1ϕ2. The coefficients 2.4 and 7.1 in this equation are in good agreement with the theoretical values of 2.5 and 6.2 obtained by Einstein(1906) and Batchelor(1977), respectively. The Brownian diffusion coefficient of the particles dispersed in cyclohexane was measured over the concentration range 0.0055 < ϕ < 0.248 using Taylor's hydrodynamic stability method. A laser fiber-optic system was used to measure the transient concentration profile along the capillary as indicated by a fluorescent dye. This technique offers the advantage of being direct and nonintrusive. The experimental diffusivity data were found to be well described by the generalized Stokes-Einstein equation(Batchelor, 1976) over the entire concentration range studied.

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