London attractive force

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... 

The combined effect of attraction and repulsion forces has been treated by many investigators in terms borrowed from theories of colloidal stability (Weiss, 1972). These theories treat the adhesion of colloidal particles by taking into account three types of forces (a) electrostatic repulsion force (Hogg, Healy Fuerstenau, 1966) (b) London-Van der Waals molecular attraction force (Hamaker, 1937) (c) gravity force. The electrostatic repulsion force is due to the negative charges that exist on the cell membrane and on the deposition surface because of the development of electrostatic double layers when they are in contact with a solution. The London attraction force is due to the time distribution of the movement of electrons in each molecule and, therefore, it exists between each pair of molecules and consequently between each pair of particles. For example, this force is responsible, among other phenomena, for the condensation of vapors to liquids. 

The strength of London dispersion forces increases with the molecular masses of the molecules. The larger the molecular mass, the stronger the London attractive force. London forces exist in all substances. 

The London attractive force between a sphere and a plane is given by... 

The parameter governing the relative importance of the London attractive force to the hydrodynamic interaction force may be obtained simply by taking the ratio of Eq. (8.4.8) to Eq. (8.4.11) to give... 

Here, is a dimensionless number termed the adhesion group. Clearly the larger the value of the adhesion group the more dominant is the London attractive force for a fixed gap width and particle location. On the other hand, for smaller values of hydrodynamic interactions dominate. 

The Van-der Waals-London attractive forces have molecular origin, although on the basic level, they are still caused by electric interactions. By their nature, these forces are caused by the polarization of a molecule under the action of charge distribution fluctuations in the neighboring molecule and vice versa. They are also known as London dispersive forces. 

As stated earlier we shall assume that the attractive potential between the particles o a colloid system is mainly due to Van Der Waals-London attractive forces. When the particles come into contact forces of a different origin will also have to be considered, for instance attractive forces caused by residual chemical valency fields. For the present, however, we arc interested in comparatively long-range forces, for which the type mentioned above is the only type coming up for consideration. 

These equations are found in the following way. We first consider an atom opposite to an infinitely large plate of thickness The distance from the atom to the surface plane of the plate will be R. The Van Der Waals-London attractive force is then found by adding together the components of all attractive forces exercised by the atoms of the plate substance, in a direction perpendicular to the surface plane. 

VanDer Waals— London attraction forces 8. The interaction of colloidal particles.. . . ... 

Hydrocarbons such as benzene are slightly more polar than hexane because of their pi (jt) bonds, which allow for greater van der Waals or London attractive forces. 

This energy-based method of calculation of viscosity rj is due to Einstein [87], who considered hydrod)mamic dissipation in a very dilute suspension of non-interacting spheres. Tanaka and White [86] base their calculations on the Frankel and Acrivos [88] cell model of a concentrated suspension, but use a non-Newtonian (power law) matrix. The interaction energy is considered to consist of both van der Waals-London attractive forces and Coulombic interaction, i.e. 

Stabilization of colloidal dispersions can be divided into the two basic mechanisms electrostatic and steric (Fig. 4) [57]. With the van der Waals-London attractive forces acting continuously between colloidal particles, it is necessary, in order to maintain stabiUly, to introduce a repulsive force (electrostatic and steric) to outweigh the attractive force. The electrostatic stabilization provides the repulsive forces between similarly charged electrical double layers to the interactive particles [58, 59] (Fig. 4). Thus, the electrical double layer imparts the electrostatic stabilization. The steric stabilization becomes important when there are hydrophilic macromolecules or chains adsorbed or bounded to the particle surface [60]. When the layers of two interacting particles overlap the concentrahon of these macromolecules (chains) increases as weh as free energy. The molecules of good solvent enter the overlap layer and then separate the particles. This phenomenon is accompanied with the increased osmohe pressure. 

In aqueous-suspended particles, or colloidal systems, there are two other forces between the particle and the collector. The unretarded London attraction force between a particle of radius Vp and a collector is given by (Spielman and Fitzpatrick, 1972)... 

For hydrosols in gremular filtration, the external force consists of gravitational force, particle-collector surface interaction forces, such as the unretarded London attraction force (defined in (3.1.16)) and electrokinetic force (3.1.17) in the double layer, and electrostatic forces, if any, such as coulombic attraction/repulsion forces (3.1.15) (usually important in aerosol-removal processes unless the collector particles are deliberately charged). In... 

London attraction force (3.1.16) force on species k in mass flux ji, force relation (3.1.202) net external force for gravity see (3.1.5)... 

The closely packed, -anti conformation of the alkyl chains results in many London attractive forces. 

London attractive forces Intermolecular forces from the attraction of temporary dipoles in adjacent molecules. 

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