Coefficient of cohesion

A force balance over a differential element (Fig. 4.5) simply using pressure P instead of the compressive stress, with shear stress at the wall xw = aw tan fiw + cw, where [lw is the angle of internal friction and cw is the coefficient of cohesion at the wall... 

The above-mentioned boundaries between free-flowing and non-free-flowing are only approximate indicators. They are used because of their simplicity and ease of measurement. However, neither rearrangement compressibility nor the angle of repose are true measures of the flowability of particulate materials. Free-flowing materials are also referred to as non-cohesive materials and non-free-flowing materials as cohesive materials. The shear stress at incipient internal shear deformation in non-cohesive materials can be uniquely related to the normal stress. Consequently, the coefficient of cohesion (see Eq. 6.6) is zero for non-cohesive particulate materials. 

The actual tensile strength is usually less than the apparent tensile strength. The value of the shear stress at zero normal stress is often referred to as the coefficient of cohesion tanPj. This coefHcient is a measure of the magnitude of the cohesive forces in the particulate material that must he overcome for internal shearing to occur. 

Geophysicists prefer to talk about cohesive bed forms when exploring the movement of clays in rivers. For certain soils, cohesive forces develop between the solid particles. Graf (1971) indicated that Equation 6-43 should be modified to Include Xq> a coefficient of cohesion of the material. 

The Hamaker constant A can, in principle, be determined from the C6 coefficient characterizing the strength of the van der Waals interaction between two molecules in vacuum. In practice, however, the value for A is also influenced by the dielectric properties of the interstitial medium, as well as the roughness of the surface of the spheres. Reliable estimates from theory are therefore difficult to make, and unfortunately it also proves difficult to directly determine A from experiment. So, establishing a value for A remains the main difficulty in the numerical studies of the effect of cohesive forces, where the value for glass particles is assumed to be somewhere in the range of 10 21 joule. 

Fig. 22. The effect of the cohesive force on the excess compressibility. The coefficient of normal restitution is e = 1.0, and granular temperature is T = 1.0. The Hamaker constant is A = 3.0 x 10-12 (circles) and 3.0 x 1CT10 (crosses).

For a fixed coefficient of friction p. and a fixed dimensionless shear rate K, the measurement of the power consumption per unit volume of the moist powder mass is proportional to the cohesive stress Uc- Thus, if the granulating liquid is added to the powder mass at a constant rate, the power consumption profile describes in a first approximation the cohesive stress (Tc as a function of the relative saturation S of the void space between the particles (Fig. 5). 

Define the following terms and their relation to surface energies (a) work of adhesion, (b) work of cohesion, and (c) spreading coefficient. 

Differences in the frictional properties of most plastics can be explained in terms of the ratio of shear strenghth to hardness. Shooter and Tabor observed that the coefficients of friction for polytetrafluoroethylene are 2—3 times lower than anticipated by this calculation. It is believed that this discrepancy is caused by the inherently low cohesive forces between adjacent polymer chains and is responsible for the absence of stick-slip. The large fluorine atoms effectively screen the large carbon-fluorine dipole, reducing molecular cohesion so that the shear force at the interface is low. The shear strength of the bulk material is higher because of interlocking molecular chains. 

Thomas, E.R., Eckert, C.A. Prediction of limiting activity coefficients by a modified separation of cohesive energy density model and UNIFAC. End. Eng. Chem. Process Des. Dev., 1984,23 194-209. 

Secondary ingredients in epoxy adhesives include reactive diluents to adjust viscosity mineral fillers to lower cost, adjust viscosity, or modify the coefficient of thermal expansion and fibrous fillers to improve thixotropy and cohesive strength. Epoxy resins are often modified with other resins to enhance certain properties that are necessary for the application. Often these modifications take the form of additions of elastomeric resins to improve toughness or peel strength. 

There are several possible solutions to the expansion mismatch problem. One is to use a resilient adhesive that deforms with the substrate during temperature change. The penalty in this case is possible creep of the adhesives, and highly deformable adhesives usually have low cohesive strength. Another approach is to adjust the thermal expansion coefficient of the adhesive to a value that is nearer to that of the substrate. This is generally accomplished by selection of a different adhesive or by formulating the adhesive with specific fillers to tailor the thermal expansion. A third possible solution is to coat one or both substrates with a primer. This substance can provide either resiliency at the interface or an intermediate thermal expansion coefficient that will help reduce the overall stress in the joint. 

The improvements in adhesive strength of cured epoxy joints that are attributable to fillers are not as much related to the improved cohesive characteristics of the adhesive as to the reduction in internal stress due to modification of the coefficient of thermal expansion, shrinkage, etc. 

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