We study the rapid collapse of gels formed from strongly aggregating colloidal suspensions. This gravity-driven collapse is associated with the apparition of fractures in the bulk of the gels that provide an easy route to the gel-supernatant interface for the solvent and are the cause for the strong increase of the settling velocity. We propose a model that connects the apparition of a fracture in the gel to the settling velocity of the interface. This description takes into account the microscopic structure of the gel and is consistent with the experimental results.
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 ...
We present a study of the settling of a strongly-aggregating colloidal suspension. Using wellcontrolled samples, the different settling behaviours have been systematically investigated according to the values of the volume fraction Φ of the suspension and of the inclination angle of the cell. In a vertical cell, three velocity regimes are observed. To describe the first and final regimes, we propose a simple 1D model that takes into account the microscopic structure of the gel constituted by a packing of fractal aggregates. The second regime coincides with the opening of fractures within the gel and its description would require a more complex model. When the cell is inclined at an angle α to the vertical, new settling regimes can emerge and an enhancement of the settling velocity can be observed as in usual macroscopic suspensions. Using both our 1D model and arguments similar to the ones used for macroscopic suspensions (PNK model), we propose a description of the influence of inclination that is in good agreement with the experimental data. We also present the various experimental settling behaviours we have observed in a Φ vs. α diagram that covers the whole range of experimental conditions. PACS. 82.70.Dd Colloids -47.20.Bp Buoyancy-driven instability -61.43.Hv Fractals; macroscopic aggregates (including diffusion-limited aggregates)In the past years, increasing attention has been paid to aggregation phenomena in colloidal suspensions [1,2]. Beside their fundamental interest, colloids are involved in many practical applications (drilling muds, paints, concrete, food industry. . .) for which their ability to remain in a well-dispersed state, or, on the contrary, to flocculate is of great importance. Moreover, it is essential to predict their stability under the action of an external field and in particular when submitted to gravity.Colloidal aggregation is encountered in several different systems that can be more or less complex (e.g., containing anisotropic particles, added polymer. . .) in which aggregation results from different natures of attractive interparticle interactions. For instance, attraction can be depletion induced: a depletant such as a non-adsorbing polymer is added to the colloidal suspension that can form a gel [1]. The interparticle attraction is then generally weak (of the order of kT) and the formed structure is therefore time dependent ("transient" gel). This feature combined with the effect of the gravitational force leads to specific sedimentation/creaming behaviours that have been the object of several recent studies [3][4][5][6]. On the contrary, when the attractive forces are strong enough, the particles form irreversible bonds and thermal motion does not induce restructuration of the so-called "permanent" a e-mail: talini@fast.u-psud.fr gel [7]. These gels can however be very loose and compact under the action of their own weight [8][9][10].In this paper, we will focus on colloidal suspensions in which aggregation is induced by van der Waals attractive forces and which form such "...
Résumé -Agrégation et sédimentation dans les suspensions colloïdales -Dans une suspension colloïdale où les particules s'agrègent, il existe une gamme de fractions volumiques pour laquelle la suspension forme un gel si fragile qu'il se tasse sous son propre poids. Nous présentons une étude de la cinétique de sédimentation d'un gel colloïdal formé par une suspension de particules de carbonate de calcium dans l'eau. La fraction volumique des particules a été systématiquement variée et différents régimes de sédimentation ont été observés. Les résultats expérimentaux sont décrits en utilisant un modèle 1D qui prend en compte à la fois la structure microscopique du gel colloïdal, assimilé à un empilement compact d'agrégats fractals, et ses propriétés mécaniques. L'angle d'inclinaison de la cellule par rapport à la verticale a également été varié et nous montrons que l'inclinaison peut induire l'apparition de nouveaux régimes de sédimentation. Les résultats, qui correspondent à une large gamme de conditions expérimentales, sont résumés dans un diagramme représentant les variations de Φ et α. L'influence de l'inclinaison de la cellule a pu être décrite par un modèle 2D utilisant les résultats du modèle 1D introduit précédemment, ainsi que les arguments du modèle PNK (Ponder, Nakamura et Kuroda), classiquement utilisé pour décrire la sédimentation de suspensions de particules macroscopiques dans une géométrie inclinée. La description proposée est non seulement en très bon accord avec les résultats expérimentaux mais permet également de prédire le comportement de ce type de suspensions colloïdales, qui sont utilisées dans de nombreux processus industriels.Mots-clés : gel colloïdal, sédimentation, effet Boycott, agrégats fractals. Abstract -Settling in Aggregating Colloidal
Les suspensions agrégées se divisent généralement en un surna geant transparent et un sédiment gélifié volumineux. La suspension demeure homogène (gel stable sous l'effet de la gravité) seulement quand la fraction volumique des particules dépasse une valeur don née La présente étude porte sur le calcul de $**. Un modèle simplifié décrivant l'équilibre du gel a été mis au point et sa validité est vérifiée en comparant de ses prédictions avec des mesures sys tématiques du volume du sédiment effectuées sur des suspensions de carbonate de calcium. Si nous appliquons ce modèle à la prédic tion de nous démontrons que n'est pas une caractéristique du système physicochimique mais qu'il dépend de la hauteur de l'échantillon, de son rapport d'aspect et des frottements entre le gel et la paroi. Pour les grands (respectivement petits) rapports d'as pect, nous montrons que Φ** est une fonction en loi de puissance de la largeur (respectivement la hauteur) de l'échantillon compor tant un exposant 1 / ( k -1) qui est relié à la dépendance du seuil d'écoulement avec la fraction volumique de la suspension. SEDIMENTATION AND COMPACTION OF CALCIUM CARBONATE AGGREGATING SUSPENSIONS: SCALING ANALYSIS OF THE EQUILIBRIUMAggregating suspensions generally separate into a clear super natant and a voluminous gelled sediment. The suspension remains homogeneous (Le. a gel stable under gravity forms) only when the volume fraction of particles exceeds a given value Φ**. The pre sent study is devoted to the determination of Φ**. A simplified model describing the gel equilibrium has been developed and its validity is checked comparing its predictions to systematic mea surements of the sediment volume performed on calcium carbon ate suspensions. Applying this model to the prediction of Φ **, we show that Φ ** is not a characteristic of the physico-chemical sys tem but depends on the height of the sample, its aspect ratio and friction between the gel and the side wall. For large (respectively small) aspect ratios, we find that Φ ** is a power law function of the width (respectively the height) of the sample involving an exponent (1) Bat SEDIMENTACIÓN Y COMPACTACIÓN DE SUSPENSIONES DE AGREGADOS DE CALCIO : ANÂLISIS DE ESCALA DES EQUILIBRIOLas suspensions agregadas se dividen, por lo general, en una fracción transparante que sobrenada y un sedimento geleficado voluminoso. La suspension quedarse homogénea (gel estable sobre el efecto de la gravedad) unicamente cuando la fracción de volumen de particuias sobrepasa un valor determinado Φ**. El presente estudio presenta un al càlculo de Φ**. Se ha desarrollado un modelo simplificado que describe el estado de equilibrio del gel, cuya validez esta verificado mediante una comparación de sus predicciones con mediciones sistemàticas del volumen de sedimento debajo de suspensiones de carbonato de calcio. Si se aplica este modelo para la predicción de Φ **, se demuestra que Φ** no constituye una caracterlstica del sistema fisicoquimico pero que, en cambio depende de la altura de la muestra, de su relación de ...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.