Capillary suspensions: Particle networks formed through the capillary force
Graphical abstract
Introduction
Ternary particle–liquid–liquid systems composed of particles dispersed in two immiscible liquids can form a variety of structures depending on the ratio of the three components and their material properties. The particles can stabilize emulsions forming Pickering emulsions [1], which cluster together forming spherical agglomerates that readily separate from a bulk fluid [2], [3], or prevent the spinodal decomposition of the two fluids forming a Bijel [4]. Recently, it was determined that when a small amount of the second immiscible liquid is added to the continuous phase of a suspension, the rheological properties of the mixture are dramatically altered from a fluid-like to a gel-like state or from a weak to a strong gel [5••]. This transition increases the yield stress and viscosity by several orders of magnitude as the volume fraction of the second fluid increases and is attributed to the capillary forces of the two fluids on the solid particles. Thus, these systems have been termed capillary suspensions. Capillary suspensions are a new class of materials that can be used to create tunable fluids, stabilize mixtures that would otherwise phase separate, and create new materials such as low-fat foods or porous ceramics [6], [7], [8••].
Capillary suspensions have been divided into two distinct states: the pendular state where the minority liquid preferentially wets the particles; and the capillary state where the secondary fluid wets the particles less well than the primary fluid. Both states are associated with a transition in the suspension from a fluid-like to gel-like state or from a weak gel to a strong gel. The texture and flow of these suspensions dramatically alter upon the addition of an immiscible secondary liquid at low volume fractions as shown in Fig. 1. In the pendular state, the particle network is formed through individual particles linked through capillary bridges and in the capillary state, clusters of particles surrounding secondary fluid droplets are linked together.
The creation of the network, formed by adding a preferentially wetting liquid to a suspension, has been investigated previously in higher volume fraction suspensions. Early work on sedimentation determined that the addition of a secondary fluid (usually water to an organic solvent) caused the particles to flocculate and significantly increased the sedimentation volume [9]. Later, the rheological properties of the suspensions were measured where it was observed that the admixture creates a strong gel and that the yield stress greatly increases [10]. This network structure was attributed to the formation of pendular bridges between the particles [11], though an increase in electrostatic charge on the particle surface might have contributed to some of the observed rheological changes [12]. An increase in the viscosity for lower volume fractions was also observed by McCulfor and coworkers [13]. Rheological changes due to the addition of water to an oil-based suspension of hydrophobically modified calcium carbonate (capillary state) were first observed by Cavalier and Larché [14], but they attributed the gelation to hydrogen bonding. This initial work on pendular state suspensions was extended and the first confirmation of the influence of the capillary force in capillary state suspensions was demonstrated by Koos and Willenbacher [5••] where both states were termed capillary suspensions.
These capillary suspensions are differentiated based on which fluid preferentially wets the particles. Using a fluorescent dye to mark the location of the secondary fluid, a diluted capillary suspension sample may be imaged, as shown in Fig. 2A. The addition of water to these oil-based suspensions of glass particles causes the particles to agglomerate tightly into clusters. In the pendular state (Fig. 2A.i), the capillary bridges are clearly visible binding particle dimers and trimers together. A shielding of the second fluid phase by particle clusters is observed in the capillary state (Fig. 2A.ii). In contrast, the glass particles without added water agglomerate slightly due to vdW attraction, but are generally well distributed throughout the sample.
Following the convention of wet granular materials, each sample was characterized using the saturation S,which is close to zero for the pendular state (Vw = Vl) and approaches one for the capillary state (Vw = Vb). The gel-like transition in capillary suspensions dramatically increases the yield stress and viscosity above the corresponding values of the single-fluid suspensions. The full dependence of yield stress on the saturation is shown in Fig. 2B for PVC (r = 16.4 μm) and hematite, both in various percentages of water and diisononyl phthalate (DINP). For PVC and similar systems, the greatest yield stress occurs in the capillary state at a fraction of S ≈ 0.7, but for systems similar to hematite (for instance, silica and hydrophilic glass), the yield stress was the greatest in the pendular region (S ≈ 0.2). While the formation of capillary suspensions is a general phenomenon, each material combination appears to have a preference for either the capillary state or the pendular state. While this may be a physical restriction depending on, for example, how well the secondary fluid can re-wet the particle surface, it may also depend on the droplet breakup as the suspension is created.
The pendular and capillary states are shown on a ternary diagram with other particle–liquid–liquid systems in Fig. 3. In capillary suspensions, the secondary fluid droplets are typically smaller than the particles and the total secondary fluid volume is a small fraction of the total volume. In Pickering emulsions, solid particles stabilize the emulsion droplets; hydrophilic particles tend to form stable oil-in-water (o/w) emulsions and hydrophobic particles tend to form water-in-oil (w/o) emulsions. To create stable Pickering emulsions, the particle size must be much smaller than the droplet size. The opposite behavior is demonstrated in spherical agglomerates where many particles are enveloped by a larger droplet of preferentially wetting liquid. Gelation in Pickering emulsions and from spherical agglomerates is caused primarily through the van der Waals interaction among the particles on the surface of adjacent droplets. The capillary force causes gelation in capillary suspensions. The available states for ternary systems depend on the specific material properties and on the processing history. Key among these material properties are the interfacial tension and contact angle, both of which contribute to the strength of the capillary force.
When a liquid meniscus forms between two surfaces, an attractive force between these surfaces results. In suspensions, this capillary force usually dominates over other forces, such as the van der Waals force [15]. The capillary force, which plays an important role in a wide range of natural phenomena and technical processes [16], [17], is composed of two parts: the Laplace pressure inside the liquid and the surface tension acting at the solid–liquid–gas contact line. The capillary force Fc between two solid particles connected by a pendular bridge depends on the radius r of the particles, their separation distance S, the surface tension of the liquid Γ, the wetting angle θ, as well as the volume Vl and shape of the liquid bridge. Analytical as well as computational solutions for Fc assume a certain bridge shape (e.g. toroidal, cylindrical, etc.) or solve the Laplace–Young equation. For a finite particle separation of equally sized spheres connected by a fluid bridge, the capillary force is given bywhich simplifies to the well-known expression Fc = 2πrΓcosθ for spheres that are in contact [18]. The equations for the capillary force may be modified to account for spheres of different sizes [19] or surface roughness [20].
The relationship between the capillary force connecting individual grains and the macroscopic stress for a sample depends on the coordination number, i.e. the number of contacts per particle in the agglomerate and the number of particles per unit area. For a uniform packing of equally sized spheres with liquid bridges between particles in direct contact, the relationship is given by,where f(ϕ) is a function of the particle volume fraction. For ϕ ≪ 1, as is often the case in capillary suspensions, f(ϕ) = ϕ2 would be a reasonable approximation.
The very strong capillary force may lead to distinct flow behavior in suspensions. Indeed, the gel strength or yield stress is orders of magnitude higher than with van der Waals attraction and can be tuned in a wide range through the amount of added secondary liquid. Typically, the capillary force Fc is two or three orders of magnitude stronger than the van der Waals force FvdW. The ratio is independent of particle size in first approximation.
Section snippets
Colloidal clusters
Evaporating emulsion droplets when small numbers of particles are attached to these droplets can create clusters of particles. Such colloidal clusters were described by Manoharan et al. [21•], where it was hypothesized that these clusters form structures that minimize the second moment of mass distribution. This reorganization of the droplets into clusters was modeled by Lauga and Brenner [22] and is shown in Fig. 4A.i. The particles follow the interface until they reach close-packing on the
Rheological properties
The addition of a secondary fluid can induce a transition from fluid-like to gel-like behavior or from a weak gel to a strong gel due to the formation of a strong network induced by the capillary force. This transition is shown in sample images (Fig. 1) and in the magnitude of the shear modulus |G*| as a function of the oscillatory frequency for a CaCO3 suspension in an organic solvent. The shear modulus transitions from a linear dependence on frequency – indicative of fluid-like systems –
Spontaneous formation
The spontaneous formation of a sample-spanning network can occur when particles coated with a small amount of fluid are immersed into an immiscible, bulk fluid or upon a change in temperature in partially miscible fluids, as sketched in Fig. 8, and are applicable to capillary state as well as pendular state suspensions. Using starch stored over water in a closed vessel, Hoffmann and coworkers [8••] found that the yield stress of the conditioned starch particles suspended in sunflower oil
Applications
Capillary suspensions can aid in our understanding of existing materials, can be used to tune material properties to meet process or application demands, or even to create new materials. The addition of a small amount of secondary fluid to a suspension creates a strong sample-spanning network that prevents sedimentation so that these suspensions can be stored for long periods of time without the need for continuous agitation or remixing before use even in the case of a strong density mismatch
Conclusions and outlook
Capillary suspensions are ternary particle–liquid–liquid systems where one of the liquid components is a minority phase — usually present as less than 10% of the total volume. The addition of the secondary fluid can transition a suspension from fluid-like or weakly gelled into a strong gel where the viscosity and yield stress increase by several orders of magnitude. These capillary suspensions are named as such due to the strong influence of the capillary force on the network structure and
Acknowledgements
The author would like to thank Norbert Willenbacher for fruitful discussions and careful reading of the manuscript. Financial support was provided from the European Research Council under the European Union's Seventh Framework Program (FP/2007-2013)/ERC Grant Agreement no. 335380.
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