Brownian Adhesion

The idea that molecules are involved in the adhesion process tells us that Brownian movement must be important. All molecules are in random motion. In fluids, the molecules wander around at great speeds in all directions, whereas in solids, the motion is tethered but the localized vibrations are still important. This means that an adhesive contact must not be viewed as a statical concept but as a dynamic one. Unfortunately, most books on adhesion fail to mention Brownian movement.  

A useful exercise is to compare the situation in which a liquid drop sits on a polymer surface with that of a smooth rubber sphere adhering to a glass plate, as in Fig. 7.6. 

Brownian adhesion occurs at very small dimensions, from O.l-lOOOnm, where thermal diffusion is dominant. Because of the small sizes. Brownian adhesion is difficult to observe experimentally, but it can be seen with small dispersed particles such as colloids and blood cells, for example (see Chapters 10 and 12). One result from this theory is that fine particles will stick together to form doublets whose number depends on the interparticle adhesion. Consider a number of fine particles immersed in dispersing fluid and undergoing Brownian motion in a box as in Fig. 7.7(a). With zero adhesion, no doublets should form. However, adhesion eauses doublets to develop, as in Fig. 7.7. 

The number of doublets divided by the total number of particles is related to the adhesion in a definite way, according to statistical mechanics. In a dilute system, the ratio of doublets to singlets can be calculated if simplifying 

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Figure 7.7. (a) Brownian adhesion producing doublets in a colloidal dispersion (b) Increase in the number of doublets as concentration and adhesion increases. 

There is little doubt that the theory of adhesion will improve rapidly as computer calculations become more rapid and sophisticated. These improvements will take place in three areas as shown schematically in Fig. 17.13 first is the enhanced understanding of molecular adhesion forces at the atomic level second is the modeling of the statistical behavior of Brownian adhesive systems finally, the analysis of adhesion in continuum mechanics terms will increase as specific adhesion computer packages become available. 

Adhesive force, non-Brownian particles, 549 Admicelle formation, 277 Adsorption flow rate, 514 mechanism, 646-647 on reservoir rocks, 224 patterns, on kaolinite, 231 process, kinetics, 487 reactions, nonporous surfaces, 646 surface area of sand, 251 surfactant on porous media, 510 Adsorption-desorption equilibria, dynamic, 279-239 Adsorption plateau, calcium concentration, 229... 

Both reversible and irreversible attachments are possible. Microbial cells can be held in close proximity to a surface by the long-range forces, but still be capable of Brownian motion. Under the fiow conditions, mild shear forces, brought about by fiow and disturbances in the viscous sublayer, may also be present. These effects may restrict or prevent attachment. It is anticipated that this could be the situation if no conditioning molecules were residing on the surface and would explain the reason for the observed delay in biofilm formation under fiowing conditions. Any adhesion of cells under these conditions could be said to be reversible. 

Microbial colonization of a solid—liquid interface may occur in the following sequence [69]. First, there is the transport to the cell surface. The next step is the initial adhesion, which is mainly a physicochemical process. Adhesion can be reversible or irreversible. Irreversibly adhering bacteria exhibit no Brownian motion and cannot be removed unless by a strong shear force. Adhesion is followed by firm attachment, which is reached by forming strong finks between the cells and the solid surface. The final sequence is the surface colonization. 

The rate of aggregation will depend essentially on probability of collision between particles, probability of attachment during such colhsions, and probability of their detachment from the aggregates snbsequently. While the probability of collision will depend on the Brownian motion determined essentially by the temperature of the system and on fluid flow motions determined by the viscosity of the fluid medium and external stirring, probabilities of adhesion and detachment are dependent on the type of physicochemical interactions between the particles and, to some extent, on velocity gradients in the medium. 

Transport—movement of the particles into adhesive contacts via perikinetic (Brownian) or orthokinetic motion resulting in aggregate growth (flocculation). 

Heterocoagulation is the mutual adhesion of particles of a dissimilar nature upon collision, as a result of their individual Brownian motion. Brownian motion is a stochastic, or random, movement of colloidal particles suspended in a fluid (or gas) as a result of the internal thermal energy of the system, and thus of collisions with the solvent (or gas) molecules, as pointed out independently by Einstein and Smoluchowski. Derjaguin pointed out that the term heteroadagulation should be used for adhesion of small particles that move through Brownian motion onto much larger objects, whose Brownian motion can be neglected, such as fibers [1]. For example, Jachowicz and Berthiaume [2] reported the deposition of cationic, anionic, and neutral silicon oil droplets in the form of oil-in-water emulsions on native or cationically modified human hair fibers, driven by electrostatic forces. 

Van der Waals model explained how a gas would condense into a liquid or solid as a result of the attractive forces, once the temperature was reduced to slow the Brownian motion. This cooling of a material to form an adhering solid is one of the most powerful adhesive processes, that of thermoplastic adhesion. The idea of a van der Waals adhesive force accounting for the effects of adhesive processes has been a potent one, allowing the well-known empirical adhesive technologies to be explained to some extent. 

Molecular adhesion forces are of such short range that various mechanisms can have large effects. Examples of such mechanisms are surface roughness. Brownian motion, cracking, viscous deformation, etc. These mechanisms lead to a rich variety of adhesion phenomena which may cause macroscopic adhesion to vary, even though the molecular adhesion remains the same. 

Just as Perrin concluded that a fluid s apparent repose is merely an illusion because the fluid molecules are in a state of eternal and spontaneous motion, so must we believe that all molecules adhere strongly, even though macroscopic objects appear nonsticky. The apparent lack of adhesion we see in engineering situations is really an illusion because adhesion is universal at the molecular level, according to the first law of adhesion above. However, there is a serious conundrum here because it seems impossible that particles can be in constant Brownian movement, where it is necessary for particles to collide and bounce off each other, yet also sticking together, which would cause agglomeration and... 

Brownian movement. Thus, the equilibrium of the droplet can be viewed as the rapid wetting and dewetting of the polymer surface by each individual molecule of water. If a force is applied to the drop, by tilting the plate, then the water can detach from the surface quite easily, while making new contact on the other side as the droplet rolls down the surface. Molecular adhesion at equilibrium is clearly only small in this instance, because the water does not strongly adhere to the polymo". 

It would be a superb experiment if two molecules could be gripped, brought together, and then pulled apart to measure their molecular adhesion. Unfortunately no-one has yet found a way to do this (see Chapter 13). And the very act of gripping the molecules would change their character by preventing Brownian motion, and also distorting their electronic attractive fields of influence. 

Once we have overcome this problem of definition, it is then possible to specify in detail what the forces are and how they act with Brownian motion to give adhesion. That is the purpose of the next chapter. 

The purpose of this chapter is to describe some of these adhesion mechanisms, especially starting with the Brownian and cracking mechanisms, then leading on to a whole range of subsidiary mechanisms which make adhesion... 

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