Double-layer repulsion forces

The contribution of double-layer forces to the osmotic pressure of HIPEs was also investigated [98], These forces arise from the repulsion between adjacent droplets in o/w HIPEs stabilised by ionic surfactants. It was observed that double-layer repulsive forces significantly affected jt for systems of small droplet radius, high volume fraction and low ionic strength of the aqueous continuous phase. The discrepancies between osmotic pressure values observed by Bibette [97] and those calculated by Princen [26] were tentatively attributed to this effect. 

Particle electrophoresis studies have proved to be useful in the investigation of model systems (e.g. silver halide sols and polystyrene latex dispersions) and practical situations (e.g. clay suspensions, water purification, paper-making and detergency) where colloid stability is involved. In estimating the double-layer repulsive forces between particles, it is usually assumed that /rd is the operative potential and that tf/d and (calculated from electrophoretic mobilities) are identical. 

In the case of Brownian diffusion and interception, particle capture is enhanced by London attractive forces and reduced by electrostatic double layer repulsive forces. 

Compared to small molecules the description of convective diffusion of particles of finite size in a fluid near a solid boundary has to account for both the interaction forces between particles and collector (such as van der Waals and double-layer forces) and for the hydrodynamic interactions between particles and fluid. The effect of the London-van der Waals forces and doublelayer attractive forces is important if the range over which they act is comparable to the thickness over which the convective diffusion affects the transport of the particles. If, however, because of the competition between the double-layer repulsive forces and London attractive forces, a potential barrier is generated, then the effect of the interaction forces is important even when they act over distances much shorter than the thickness of the diffusion boundary layer. For... 

A modified theory of the double layer is proposed in which the Boltzmann distribution is replaced with a distribution which accounts for the volume exclusion of the hydrated ionB. The double-layer repulsion force between two parallel plates thus calculated can be much greater than that predicted by the traditional theory, when the distance between the plates is sufficiently 6mall. This may at least partly explain the excess repulsive force that has been measured experimentally between two mica plate9, when the distance between the plates is sufficiently small. 

Addition of soluble macromolecules (polymers) in the colloidal dispersion can stabilize the colloidal particles due to the adsorption of the polymers to the particle surfaces. The soluble polymers are often called protective agents or colloids. If the protective agents are ionic and have the same charge as the particles, the electrical double-layer repulsive forces will be increased and thus the stability of the colloidal particles will be enhanced. In addition, the adsorbed polymers may help weaken the van der Waals attraction forces among particles. However, the double-layer repulsion and the van der Waals attraction cannot account for the entire stabilization of the particle dispersions. 

For similar micellas concentrations, the effect of electrolyte will be more severe for the anionic surfactant as it will suppress the electrostatic double-layer repulsive forces acting between the micelles. For nonionic surfactant, the repulsive force between micelles is a steric force rather than an electrostatic force, such that electrolyte has less of an effect. 

These capture mechanisms are dependent on the critical re-entrainment velocity, which is the velocity at which droplets first break up from the rock surface and constrictions and are re-entrained into the flow stream. This critical velocity is a function of surface properties of the system and the droplet-size to pore-size ratio. Small double-layer repulsive forces and small droplet-size to pore-size ratios lead to large critical velocities. Soo and Radke (29) found the effect of velocity on emulsion flow in porous media to be dependent on the capillary number ([xv/0a, where x is fluid viscosity, v is velocity, is porosity, and a is surface tension). At low capillary numbers... 

The potential energy function, u(h), where h is the distance of separation, consists of London-van der Waals attractive forces, u and double-layer repulsion forces, u as given below ... 

Kitchener and coworkers (12, 16) have shown that when colloidal size particles with the same charge sign as that of the planar surface diffuse to and sorb on the latter, the rate of uptake may be considerably less than that predicted by simple Fickian diffusion across the unstirred liquid film, principally because of the double layer repulsive forces, as treated in the Derjagin-Landau-Verwey-Overbeek theory of colloid stability. It was found in some systems, particularly at high ionic strength, that the sorption rate decreased with time, eventually becoming negligible. 

The electric double layer repulsion force, FR, for the same system is (53)... 

Now the double layer repulsion force per unit surface area (the double layer pressure) riDL( ) found to be ... 

In the preceding section our analysis for Brownian diffusion assumed the particles were diffusing points, whereas for interception the center of a particle of finite size was assumed to follow the undisturbed streamline near a large collector. In both cases, no other forces were considered to act on the particles, and when they struck the collector it was assumed that they adhered. In reality, however, even in the absence of inertia there may be other external forces acting on the particles, including London forces of attraction, gravitational hydro-dynamic interactions between the particle and collector, and double layer repulsive forces. 

The effects due to electrical double-layer repulsion forces, electroviscous effects and the physical presence of adsorbed film are neglected. 

The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory is commonly used to describe interactions of charged surfaces across liquids [8, 9]. The DLVO theory models the interparticle interactions by superposing van der Waals attractions and electrostatic double layer repulsion forces. The direct force measurements have confirmed this theory down to surface separations of few nanometers [10]. 

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