Adhesive Force on Particle Size

Relationships in Adhesive Interaction of Particles of Various Sizes. The 

In order to clarify the relationship between adhesive force and particle size, let us turn to Fig. IV.12. These plots show that, over a certain range of adhesive force (Zone A), for particles with diameter of 20 or 100 jum, the adhesive force varies directly with particle size. The straight lines characterizing the distribution of particles with respect to adhesive force intersect at the point K, with a value of the number ap-10% or yp = 90%. At the point K we observe independence of adhesive force of particle size. In Zone B we find inverse variation of the adhesive force with particle size. 

In air, for particles differing in size, the intersection of the integral curves often takes place below the 50% level of ap, i.e., at ap 50%. For narrower fractions, the intersection of the straight lines may occur at a point lying in the region where ap 50% (Fig. IV. 13). 

For one and the same system (particle and surface) we may find different relationships between particle size and adhesive force. In Zone A (see Fig. IV.12), when the adhesion number is greater than 90%(i.e., with yp 90% and ap 10%), we find a direct variation of adhesive force with particle size and in Zone B, with yp 90% and ap 10%, the variation is inverse. When yp = 90% oLp = 10%), we observe exactly the same adhesive force for particles with diameters from 20 to 100 jum. Hence it is impossible to speak in general terms of any relationship between adhesive force and particle size it is necessary to know what sort of adhesive force we are talking about. The adhesive interaction of weakly adherent particles may be characterized by means of the minimum force and that of difficult to remove particles by means of the maximum force Corresponding to each adhesion number is a certain 

Let us now consider in more detail those conditions under which the various relationships between adhesive force and particle size may be manifested. 

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A very slight dependence of adhesive force on particle size was found in [94] ... 

In the general case, in which the adhesive interaction is determined by two parameters, the force of adhesion and the adhesion number, the comparison of adhesive forces for different particles should be performed at a certain fixed value of adhesion number. The dependence of adhesive forces on particle size will be determined not only by the actual value of the adhesion number, but also by the position relative to the point characterizing the intersection of the integral lines indicating the distribution of adherent particles with respect to adhesive force. 

Dependence of Adhesive Force on Particle Size, with Allowance for Surface Roughness. Surface roughness changes not only the magnitude of adhesive interaction, but also the dependence of adhesive force on particle size. In evaluating this dependence, it is not the absolute values of the particle size that are important, but rather the ratio between particle diameter and the dimensions of the asperities of the rough surface. 

Dependence of Adhesive Force on Particle Size in Detachment by Inclination of Surface. Detachment of particles by tilting the surface (see Section 11) has been used to investigate the adhesion of quartz particles of various sizes in an aqueous medium [4] and also in certain organic solvents and alcohols [190, 197]. 

Adherent particles will be removed from a surface if the condition expressed by Eq. (X.l) is observed. The dependence of the adhesive force on particle size for the case under consideration can be represented by Eq. (VI.42). After substituting the quantities determined by Eqs. (XI.6), (XI.7) and (VI.42) into (X.l),... 

Dependence of the Adhesive Forces on Particle Size. A key question in theory and practice is the dependence of the adhesive forces on the sizes of the particles. This dependence appears in various ways. Let us consider, for example, under what conditions the adhesive force is directly proportional to the particle size. 

The different relationships between adhesive force and particle size can be justified on a theoretical basis if we consider the nature of the forces responsible for adhesion. Each of the components of adhesive force is dependent on particle size ... 

The position of the point of intersection of the integral curves will depend on the properties of the specific system (particle-surface-ambient medium). In some cases, the integral adhesion curves for a specific range of particles may not intersect. Such a case has been found for particles with diameters of 30-80 jum with values of ap from 12 to 85% (see Fig. 1.3). Under these conditions, for all values of ap, the dependence of the forces of adhesion (including the median force) on particle size will be one and the same. 

The average force of adhesion, the same as the median force, increases with decreasing particle diameter in accordance with Fig. IV. 14. An inverse dependence of average and median force on particle size is also observed for the hydro-phobic glass surface (curves 1 and 2 ) and the hydrophilic glass surface (curves l"and 2"). 

From this discussion it is clear that these relationships between adhesive interaction and the dimensions of the particles and atomic-molecular and mechanical roughness, which we have examined in general form, are supported by both calculated and experimental results. These relationships supplement the information that was set forth previously (see Section 20) on the variation of adhesive force with particle size. 

Thus we see that the adhesion of irregular particles can be characterized by means of the average force of adhesion, which is determined from the distribution of the irregular adherent particles with respect to adhesive force, on the basis of equivalent size (diameter). The relationship between the average adhesive force and particle size is more complex for the irregular particles than for the equivalent-size spherical particles. For a certain size range of the irregular particles, there will be a maximum in adhesion. 

The relationship between adhesive force and particle size cannot be fully determined by the tilted-plate technique. As the detaching force is increased by approximately 3 orders of magnitude (7.6 10 dyn for 5-15 fjm particles and 1.0 10" for 100-300 fjtm particles), the adhesion number drops off by a factor of only 12. As the size of the particles lying on the surface increases, the pressure of these particles on the surface also increases, distorting the true relationship between adhesive force and particle size. A directly proportional relationship has been found between the minimum force of adhesion Fj in and the size of quartz particles with a range of diameters from 3 to 40 jitm. For these particles, the adhesive force increases from 0.1 to 4.4 iudyn. For these particles and also for particles with diameters up to 100 jum, the relative force of adhesion, which is equal to Finin/ (where P is the particle weight), or the force of adhesion expressed in g-units, is constant and equal, with a value of 3.4 for quartz particles and 1.7 for rosin particles [15]. 

The dependence of adhesive force on the size of cylindrical glass particles in an aqueous medium is more complex in nature than the relationship for spherical particles, for which we typically find a direct variation of adhesive force with particle size [20]. 

For an aqueous medium, the experimental data on the relationship between adhesive force and particle size are in agreement with theoretical values, thus providing practical support for Deryagin s thermodynamic theory of adhesion (see Section 3). 

We can see now that the detachment of adherent particles by an air stream can be characterized by the velocity of detachment. This velocity depends on the adhesive force, the particle size, and the properties of the contiguous bodies. The distribution of the detached particles with respect to adhesion number, in relation to the velocity of detachment, follows a log-normal law. If we know the parameters of this distribution, we can find the median and average velocities of detachment for the adherent particles the average velocity gives an unambiguous quantitative characterization of the effect of the air stream on the dusty surface across which it is blowing. 

In simple terms, a cohesive powder can be defined as a material where the adhesive forces between particles exceed the particle weight by at least an order of magnitude. In such systems, particles no longer flow independently rather, they move in chunks whose characteristic size depends on the intensity of the cohesive stresses. 

When lp>L, the probability of removal is = 1 when Ip distribution parameters with respect to adhesive force are known for adherent particles having sizes from min to c/max we can determine the average force of adhesion and its dependence on particle size, i.e., F y Then, assigning a specific detaching force... 

Theoretically, we should expect, as indicated by Eqs. (IV.39) and (IV.40), that the magnitude of the capillary forces will depend on the particle size, the surface tension of the liquid making up the bridge formed by vapor condensation (see Fig. IV.6), and the wettability of the contiguous bodies. Since capillary forces are proportional to particle size, the forces of adhesion should be identical for particles of a given size in any case in which the capillary component of the adhesive forces is dominant. The difference in adhesive force for particles of a... 

Dependence of Adhesive Force on Size of Irregularly Shaped Particles. Experiments have been performed [194] to characterize the relationship between the adhesion of irregularly shaped particles and the size of these particles. The equivalent diameter (see Section 14) was taken as a single parameter characterizing the size of irregularly shaped particles. 

A liquid medium reduces the force of adhesion and reverses the dependence on particle size. For example, in comparison with the data just listed, we found that the adhesive force in a liquid medium was 1.1- 10 dyn for 30-jum particles and 1.8-10 dyn for 1 lO-pm particles i.e., the adhesive force varied directly with particle size, as noted previously (see Section 30). 

Thus we see that the presence of a paint or varnish coating on a metal surface may change the actual magnitude of forces of particle adhesion, but the general relationships characterizing the adhesion remain the same as on the unpainted surface. Among these relationships, we should mention the log-normal distribution of particles with respect to adhesive force, the dependence of adhesion on particle size, and the lower adhesive forces in water in comparison with air. 

From all of the data presented here, it is evident that the relationship between the average force of adhesion and the particle size is much the same for oily surfaces as for clean painted surfaces, the only difference being that the absolute values of the average force of adhesion of oily surfaces are 2 or 3 orders of magnitude greater than on oil-free painted surfaces. 

Theoretically we should expect [see Eqs. (III.36) and (III.38)] that the value of the capillary forces would depend on the particle size, the surface tension of the liquid formed as a meniscus by vapor condensation (see Fig. III.11), and also the capacity of the contiguous bodies to become wetted. Since the capillary forces are proportional to the particle dimensions, in cases in which the capillary component of the adhesive forces is dominant, the adhesion should be the same for all particles of the same size, while the difference between the adhesive forces of particles belonging to a particular fraction with a spread of particle sizes should not exceed the ratio of the dimensions of the extreme members of this fraction. For example, the adhesive forces calculated from Eq. (ni.36) should be 4.52 dyn for particles 100 /x in diameter and 5.43 dyn for those 120 p. in diameter. Experimental results disagree with the calculated values. Actually the adhesive forces for particles 100-120 M in diameter (for = 97-25%) fluctuate between 0.4 and 4.7 dyn, i.e., they vary by a factor of 12 over the fraction in question. Thus the scatter of the experimental data is much greater than would be expected, and hence the capillary effect fails to eUminate the indeterminacy of adhesive properties. 

Fuks [164] came to analogous conclusions regarding the dependence of the minimum adhesive force Fuiin on particle size (on the basis of earlier work [12, 15, 59] he found that the minimum particle size for which a direct proportionality between Fa j in dynes) and d p persisted was 5. ... 

There are several techniques available for the measurement of the adhesion force of particles on substrates. These techniques involve both the study of individual particles (as in the microbalance technique) and of multiple particles by statistical counting (as in the centrifuge method). In each type of study the conditions of both the particles and the substrates must be known with high precision. The exact chemistry, physical size and shape, surface condition, temperature, and properties of the surrounding gas are vital parameters that must be quantified in order to obtain reproducibility. 

Even the void fraction together with particle size distribution does not provide all of the necessary information on the kind of flow. The mutual forces between distinct particles depend not only on the distance between the particles but also on the surface properties of the particles. The strength of the attractive forces between particles depends on conditions. For instance, the moisture content of the solid is essential for determining the attractiv c forces between particles, especially for hydroscopic materials such as wood. Airflow between particles usually tends to separate particles, whereas the surface forces, adhesion forces, tend to bring them together. 

A certain amount of shearing forces have to be applied in order to overcome the surface forces that maintain the adhesion between agglomerated pigment crystals. In practice, the shearing forces that are necessary to reduce the particles in a given pigment sample to smaller or even optimal particle size, i.e., the dispersibility of a pigment powder, depends on a number of factors ... 

Commonly, roughness can be tailored by using additives. These are mainly based on combinations of inert, inorganic particles of different sizes and the weight ratio of large to small particle sizes. These particles should be well dispersed in the base film to prevent abrasion, which is influenced by the particle shape and the kind of embedding in the polymer matrix. The affinity of these particles to the solid polymer seems to be based on adhesion of the melt to the solids and to cohesive forces in the solid state. This phenomenon, however, has not yet been explored in sufficient detail. 

Once manufactured, small particles present another challenge. At small particle size diameters, gravity ceases to be the major force exerted on the particles and interparticle forces become more prominent. The resultant increase in the cohesive and adhesive nature of the particles produces problems such as poor flowability, fillability, and dispersibility. These problems are typically minimized by blending with larger. 

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