Scaling analysis of sediment equilibrium in aggregated colloidal suspensions

Abstract

The equilibrium of aggregated colloidal suspensions under gravity is studied both theoretically and experimentally. Using a simplified model to describe the compaction of the gelled suspension, we show that the volume fraction of the particles needed to form a stable gel is not intrinsic to the physicochemical system but depends on the height of the sample, its aspect ratio, and the friction between the suspension and the cell wall. A scaling analysis is developed to predict the various regimes encountered and to calculate the variations of the equilibrium sediment height as a function of the volume fraction of the particles and the height, and width of the sample. Good agreement is found with systematic measurements performed on aqueous colloidal calcium carbonate suspensions. ͓S1063-651X͑97͒11106-0͔PACS number͑s͒: 82.70. Ϫy, 64.60.Fr, 62.20.Fe Aggregation phenomena have been studied extensively in the past both experimentally and theoretically ͓1,2͔. When the growth rate is controlled solely by the Brownian diffusion of aggregates, the growth kinetics, and the cluster fractal geometry are well understood. The diffusion-limited cluster aggregation model gives a good description of the experimental and numerical simulation results ͓2-5͔. In the presence of a large difference between the density of the particle and that of the solvent, gravity acts as an external field and modifies the growth process ͓6-9͔. In a recent work, we have shown that the coupling between settling and aggregation leads to distinct behaviors depending on the volume fraction of particles in the suspension ⌽ ͓8͔. In the dilute regime ⌽Ͻ⌽*, deposition of individual clusters is observed. At the beginning of the phenomenon, the aggregate growth is controlled solely by Brownian diffusion. As their size becomes large enough, they settle separately and deposit onto the cell bottom, forming a sediment that compacts until equilibrium. In the semidilute regime ⌽*Ͻ⌽Ͻ⌽**, a collective behavior is observed. A close packing of aggregates filling the whole cell ͑i.e., a gel͒ forms very rapidly and collapses under its own weight. A sharp interface separates a clear supernatant from the suspension; this interface moves down until it reaches its equilibrium height. Finally, when ⌽Ͼ⌽**, the suspension forms a gel that does not collapse under gravity. A scaling analysis based on the comparison between the gel time and the time corresponding to the crossover from diffusive to settling movements allows one to predict ⌽* ͓8͔.The main objective of this paper is to determine the volume fraction ⌽**. We develop a simple model describing gel compaction and equilibrium under gravity. The predictions are compared to measurements of the relative volume occupied by the sediment: ⍀ϭH s /H, where H s represents the sediment height at equilibrium. A broad range of experimental conditions has been investigated by varying the volume fraction of the suspension, the height H, and the diameter D of the sample. We find that different regimes can be distinguished following the ...

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