Interaction force between particles

The main objective of the present section, however, is to begin with a very standard technique such as optical microscopy and to use it to illustrate why colloids are difficult to see and what modern developments have emerged in recent years to allow us to see and do things that were considered impossible until a decade ago. We also use this opportunity to review briefly some new techniques that are currently available to measure interaction forces between particles directly. We appeal to some of these techniques in other chapters when we discuss colloidal forces. 

A simple long-range interaction force between particles of the fcth component at site x and the Mi component at site x is introduced and the total fluid/fluid interaction force on the Mi component at site x is given by ... 

The rate of deposition of Brownian particles is predicted by taking into account the effects of diffusion and convection of single particles and interaction forces between particles and collector [2.1] -[2.6]. It is demonstrated that the interaction forces can be incorporated into a boundary condition that has the form of a first order chemical reaction which takes place on the collector [2.1], and an expression is derived for the rate constant The rate of deposition is obtained by solving the convective diffusion equation subject to that boundary condition. The procedure developed for deposition is extended to the case when both deposition and desorption occur. In the latter case, the interaction potential contains the Bom repulsion, in addition to the London and double-layer interactions [2.2]-[2.7]. Paper [2.7] differs from [2.2] because it considers the deposition at both primary and secondary minima. Papers [2.8], [2.9] and [2.10] treat the deposition of cancer cells or platelets on surfaces. 

The objective of the present research is to predict the rate of deposition of Brownian particles by considering the effects of diffusion, convection, and interaction forces between particle and collector. It will be shown that, when the repulsion due to the double-layer is sufficiently large, the interaction forces can be incorporated into a boundary condition for the convective-diffusion equation. This boundary condition takes the form of a virtual first-order chemical reaction which occurs on the surface of the collector. 

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... 

The flux of particles is the sum of a dif-fusional contribution and of a contribution due to the interaction forces between collector and particles [the interaction forces between particles are neglected here but are discussed elsewhere (6)]. Hence... 

The second chapter examines the deposition of Brownian particles on surfaces when the interaction forces between particles and collector play a role. When the range of interactions between the two (which can be called the interaction force boundary layer) is small compared to the thickness of the diffusion boundary layer of the particles, the interactions can be replaced by a boundary condition. This has the form of a first order chemical reaction, and an expression is derived for the reaction rate constant. Although cells are larger than the usual Brownian particles, the deposition of cancer cells or platelets on surfaces is treated similarly but on the basis of a Fokker-Plank equation. 

DLVO theory [2,3] can be used to calculate the interaction forces between the slurry particle and the wafer surface to be polished. The interaction forces between particles and between particles and surfaces could provide important information on the stability of slurry and the degree of particle contamination on surfaces after CMP. 

Aggregating Particles. Repulsive colloidal interaction forces between particles hardly affect sedimentation, but the effect of attractive forces can be very strong. Aggregates naturally sediment faster than single particles. Fractal aggregates containing N particles tend to move faster than... 

Thus we see that the evaluation of adhesion on the basis of the detachment force at identical adhesion numbers (i.e., on the basis of F, in, F ax or so) can lead to errors. In exactly the same manner, the evaluation of adhesion on the basis of adhesion numbers at equal detachment forces can serve only as a relative characterization of the interaction forces between particles and surface. 

This section, which is by no means exhaustive, will deal with the following topics (i) Surfactants used in cosmetic formulations, (il) Interaction forces between particles or droplets in a dispersion and their combination, (iil) Description of stability in terms of the interaction forces, (iv) Self-assembly structures and their role in stabilization, skin feel, moisturization and delivery of actives, (v) Use of polymeric surfactants for stabilization of nanoemulsions, multiple emulsions, liposomes and vesicles. 

Chemical compositions Influences the interaction force between particles. 

By means of the ionic strength I, the Debye length 1/k of the electrostatic interaction forces between particles can be influenced ... 

Nestor, J., Esquena, J., Solans, C. et al. (2007) Interaction forces between particles stabilized by a hydrophobically modified innlin surfactant. J. Colloid Interface Sci., 311 (2), 430-437. 

Tadros, T. 2003. Interaction forces between particles contahting grafted or adsorbed polymer layers. 

Depending on the surface and colloid chemistry of the system, the nature and magnitude of various interaction forces between particles will change and influence colloid stabUity and the rate of aggregation. The influence of these surface forces is taken into account by the collision efficiency factor in the population balance. The collision efficiency factor for aggregates is computed as reciprocal of the modified Fuchs StabUity ratio W for two primary particles k and I [26-29] ... 

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