DLVO theory of colloid stability
The framework of DLVO theory (Derjaguin, Landau, 1940 and Verwey, Overbeek, 1948) essential in understanding colloid stability has been expressed via the potential energy of interaction, as a sum of two components: (i) electrostatic repulsion arising from the overlap of diffuse double layers and (ii) van der Waals dispersion forces arising from dipoles interactions in fluctuating electromagnetic field. Schematically, the combined action of these two forces in a 1:1 electrolyte solution between two similarly charged surfaces is illustrated in Figure 1.4.
Accordingly, it follows that the VDW attraction decays quite rapidly, since it is an inverse power law function, i.e. W –1/Rn, while the double-layer interaction potential decreases slower: it decays exponentially with separation R, and typically has a range of the order of the Debye length -1. As a result, the VDW attraction exceeds the double-layer repulsion at a very small separation distance, whereas the double-layer repulsion is dominant at larger R. Variations in the ionic strength (as it is a measure of the concentration of charge species in a given electrolyte solution and it is inversely proportional to Debye length -1), as well as pH control the range of the electrostatic repulsion, while the van der Waals attraction is dependent on particle size, medium bulk properties (dielectric permittivity and refractive indices) and particle-to-particle separation distance R. One can notice that the curves exhibit two characteristic minima and one maximum. The energy minimum at contact is known as a deep primary minimum, which is located at very close separation distances (several 100 kBT units). In more concentrated electrolyte solution appearance of secondary minimum occurs, separated by the energy barrier from the primary minimum. Electrostatic repulsion gives rise to this energy barrier, usually between 1 and 5 nm, in cases where highly charged surfaces are concerned (in dilute conditions). When approaching this barrier, the particle should have sufficient kinetic energy due to thermal motion to overcome the primary minimum resulting in aggregation. When the surface charges approaches zero or at high ionic strength, particles experience only the VDW attraction and attract each other at all positions (approaching lower dashed curve in Figure 1.4). There is a critical concentration of electrolyte, Ccrit, at which the barrier fully disappears and particles proceed towards slow aggregation, known as coagulation or flocculation .
Colloidal interactions in practice: diversity of particular characteristics
When suspended in aqueous medium, particles usually acquire charges. Interactions are mainly established via electrostatic repulsion that counteracts particles aggregation, precipitation processes induced by natural attractive Van der Waals forces. From this point, the role of electrostatic interactions in combination with the given physico-chemical characteristics of colloidal systems is of considerable importance that might result, for instance, in formation of ordered lattice (latex spheres in water), Wigner glass transition (laponite) and causes the dispersibility of boehmite in water, similarly to clay minerals. It suggests therefore that focusing on the nature of interparticle interactions allows explaining the broad range of phase behavior, also taking into account the physico-chemical aspects (particle size and shape, surface charges, rheological behavior,…). Thus, the next section introduces a brief characterization of anisometric systems with particular focus on boehmite dispersions.
Synthesis of ultradispersed boehmite particles
Colloidal boehmite dispersions are often synthesized by precipitation in aqueous solution from alumina salts. The shape of boehmite nanoparticles can be well controlled during its synthesis by varying pH conditions. Thus, after heating procedure at pH 4-5 fiber and rod structures are produced with length around 100 nm. The fibers consist of aggregated platelets (3 6 nm), exhibiting (100) lateral faces and (010) basal planes. The particles synthesized at pH = 6.5 look like pseudohexagonal platelets ( 15 5 nm) with (100) and (101) lateral faces, whereas synthesis at pH = 11.5 leads to diamond-shape particles 10–25 nm wide with (101) lateral faces, as illustrated in Figure 1.6. Boehmite particles acquire a net positive charge in aqueous suspending media until the isoelectric point is reached. The pHiep ranges between 4.5 to 9.8 depending on the nature and amount of impurities present.
Transport mechanisms across porous media
The basic principle of any liquid-solid separation process is linked to the transport of substances (particles, molecules) in a semipermeable membrane with appropriate pore size. After separation, two phases are obtained: a concentrated solid-like phase retained on the surface of membrane and a fluid stream (filtrate) driven by the applied force. In any situation involving fluid flow over the surface of solids, frictional losses lead to a pressure drop, which serves as a driving force. Darcy discovered that the driving force P per membrane thickness and flux J are related via a proportionality factor K (Darcy, 1856), i.e. J = K P . (1.11).
that defines how fast the component is transported through the membrane. In other words, parameter K represents a measure of the resistance (named therefore as permeability constant) from the membrane as a transport medium, when a driving force is applied.
It must be pointed out that Equation (1.11) does not provide any information about the nature of the membrane or its relation with transport mechanism. However, as mass transport occurs through the porous media rather than the dense matrix, its structural characteristics (pore size, pore size distribution, pore dimensions, tortuosity) might be also important to describe transport mechanism more adequately. One of such transport models accounting for membrane pore geometry is given in the Hagen-Poiseuille equation via J = r2 P . (1.12).
Equation (1.12) ascribes the simplest pores geometry, which consists of cylindrical and parallel pores with radius r perpendicular to the membrane surface. The length of each of the pores is taken to be roughly equal to the membrane thickness. Comparing with the phenomenological form of Equation (1.11), permeability according to the Hagen-Poiseuille will be given as K = r 2 , (1.13). where is the surface porosity, which is the fractional pore area and is the pore tortuosity (for cylindrical perpendicular pores the tortuosity approaches unity). The Hagen-Poiseuille Equation (1.13) gives a good description of transport through membranes, although very few of them have such a pore configuration in practice. In contrast, membranes exhibiting a system of closed packed spheres are best described by the Kozeny-Carman relationship, i.e. J = 3 P , (1.14) k KC S2 (1 − )2.
Pressure driven membrane processes
Pressure driven membrane processes are therefore categorized by the particle size of the solute and its chemical properties determining the type of required membrane with regard to its pore size and pore distribution. Accordingly, there are four types of such processes: microfiltration, ultrafiltration, nanofiltration and reverse osmosis. Their application range is schematically illustrated in Figure 1.18. From microfiltration towards reverse osmosis, the size of the particles/molecules to be separated diminishes, which consequently leads to reduction of pores size in the membrane. This, in turn, implies that the resistance of the membranes to mass transfer increases and hence the driving force, i.e. the applied pressure has to be increased in order to obtain the same flux. Accordingly, membranes for ultrafiltration, nanofiltration and reverse osmosis membranes usually possess an asymmetric structure with a relatively dense layer (thickness 0.1–1.0 m) on its top that determines the hydraulic resistance towards transport.
The main problem encountered in a pressure driven membrane process involves certain changes in the system perfomance over processing time, causing a typical decrease of the flux. It results from several factors, such as concentration polarisation, adsorption, gel layer formation and pores fouling. Flux decline is particularly impacted by fouling, giving values for process fluxes being typically less than 5% of pure water flux. This also implies that for industrial applications, the given above Hagen-Poiseuille and Kozeny-Carman equations are irrrelevant, as they do not account for these phenomena and other models should then be considered.
Pores fouling can be partially reduced by switching the mode of filtration configuration. Basically, two major processing modes can be distuinguished, i.e. dead-end and cross-flow filtration. Schematic illustration of these modes is given in Figure 1.19. In the dead-end filtration, the feed solution flows perpendicularly to the membrane surface, as opposed to the cross-flow regime, so that the retained particles form a deposit layer on its surface, which increases over the processing time resulting in a decrease of the permeation rate. In cross-flow mode, the feed solution flows along the membrane surface, so that filter cake formation is reduced or kept at a low level.
Effect of particles shape and aspect ratio
In Section I.2, it was shown that particles with asymmetric shape might undergo orientational ordering, resulting in optical (birefringence) or rheological (i.e. shear-thinning) features. Hence, it is evident that particles orientation with varied shape and aspect ratio might be likewise important in filtration of anisotropic particles.
Indeed, reorientation of plate-like particles in filter cakes was observed in several studies. For instance, Tanaka et al.  found orientational ordering of rod-shaped bacteria cells with the flow direction when switching from dead-end to cross-flow mode (Figure 1.26). Further estimations of specific cake resistance showed that such arrangement leads to a more compact deposit layer than those formed in dead-end filtration, which reduces filtration rate.
In work of Perdigon-Aller et al.  using neutron diffraction technique, weakly aggregated and deflocculated kaolinite particles were found also aligned parallel to the filter membrane in cross-flow filtration. Both systems displayed significantly different permeability. Thus, it might be suggested that particles orientation is not the only parameter controlling permeability, but its correlation with colloidal interactions must also be taken into account.
Table of contents :
CHAPTER I: LITERATURE REVIEW
I.1 Introduction: colloidal phenomena
I.2 Interactions in colloidal systems
I.2.1 Potential distribution around a charged surface: the Poisson-Boltzmann equation
I.2.2 Van der Waals interaction between two particles
I.2.3 DLVO theory of colloid stability
I.3 Colloidal interactions in practice: diversity of particular characteristics
I.3.1 Structure of boehmite
I.3.2 Synthesis of ultradispersed boehmite particles
I.3.3 Acidic peptization of boehmite
I.3.4 Speciation of aluminium in boehmite dispersions
I.3.5 Rheological features
I.3.5.1 Viscosity, shear-thinning and thixotropic behavior
I.3.5.2 Phase diagrams
I.3.5.3 Viscoelasticity and yield stress
I.4 Dead-end filtration of colloidal dispersions
I.4.1 Transport mechanisms across porous media
I.4.2 Pressure driven membrane processes
I.4.3 Membrane fouling
I.5 Experimental characterization of fouling mechanisms in colloidal systems
I.5.1 Effect of surface charge, pH and ionic environment
I.5.2 Effect of particles shape and aspect ratio
I.5.3 Effect of particle size distribution
I.5.4 Filtration studies in situ
CHAPTER II: MATERIALS AND METHODS
II.1 Product information
II.2 Samples preparation
II.3 Sols characterization
II.3.1 Particle size and shape
II.3.2 Volume fraction, pH and -potential
II.3.3 Ionic composition of the aqueous phase
II.3.4 Rheometric studies
II.3.5 Small angle X-ray scattering (SAXS)
II.4 Dead-end filtration studies on boehmite dispersions
II.4.1 Filtration unit for ex situ tests and data acquisition
II.4.2 Determination of the deposits permeability and compressibility
II.5 X-Ray tomography
II.5.1 Principle of X-Ray computed tomography
II.5.2 X-Ray tomography in membrane separation studies
II.5.3 Filtration cell for X-Ray radiography imaging
II.5.4 Synchrotron X-ray tomography
CHAPTER III: FRONTAL FILTRATION STUDIES ON BOEHMITE DISPERSIONS
III.1 Size and shape of boehmite particles
III.2 Ionic composition of the aqueous phase
III.3 Filtration studies ex situ: deposits permeability
III.4 The boehmite – solution interface
III.5 Structural organization of filtration deposits
III.6 Monitoring concentration profiles by X-Ray radiography imaging
CHAPTER IV: PROPERTIES OF OSMOTICALLY DENSIFIED BOEHMITE DISPERSIONS: MICROSTRUCTURE AND PARTICLES ORGANIZATION
IV.1 Osmotic pressure curves and phase diagram
IV.2 Structure and particle organization
IV.3 Rheological characterization
IV.3.1 Yielding behavior of boehmite gels
IV.3.2 Elasticity of boehmite gels
IV.3.3 Rheological determination of the interaction potential energy
CHAPTER V: PARTICLE MOTION IN A YIELD STRESS ENVIRONMENT
V.1 Bimodal mixture: in situ dead-end filtration by using synchrotron radiation
GENERAL CONCLUSIONS AND PERSPECTIVES