Direct measurement of cohesion

Investigation into the cohesiveness of bulk solids may proceed in two complementary ways. 

One way which relies upon the fundamental knowledge of the stress-strain-volume behaviour of bulk solids is dependent upon the development of testers such as the biaxial and triaxial shear testers as well as the now universally accepted Jenike shear cell, or the standard shear test tester. Other instruments, such as the annular shear cells and the cross-sectional Peschl and Colijn (1977) tester, use the same stress-strain-volume principle. These annular shear cells may also be used to evaluate a bulk powder flow function. The powder flow function, having been discussed previously, still requires a family of yield loci before cohesion can be evaluated. 

In view of the experimental errors normally affecting shear cell measurements and the amount of personal judgement required to draw Mohr stress circles tangential to a curved yield locus, there is always some uncertainty in the flow function derived from the Jenike-type shear yield loci method. A direct measurement therefore offers considerable advantage and, besides possibly giving better accuracy, may prove to be more rapid and reproducible. 

The second way relies upon the development of specific powder testers, which will permit the straightforward measurement of cohesiveness and/or tensile strength of difficult flowing and poorly mixed cohesive powders. 

The instruments available for direct measurements are mainly associated with two classes of devices. One class measures the torque or stress on an immersed vaned paddle in a bed of powder compressed at a known bulk density, whilst the other class is the mould or column failure method. The more practical mould devices are those based on the formation of a powder column in a cylindrical container (sometimes split into two halves) (see Section 1.7.3.2). The container walls are then removed to leave a freestanding cylindrical column of powder, which is then subjected to loads placed on the top of the column imtil the column fails. 

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In the case of concentrated (structured) disperse systems the essential features that are usually of interest are their mechanical and rheological properties and behavior. The main parameter describing these features is the cohesive force, F, px in Chapter IX), or the strength of immediate contacts between particles. Stability is manifested as a correlation between the applied mechanical stress, P, and the sum of strengths of individual contacts, i.e. as the %FX product, where x is the number of contacts per unit area [35].In this case one only needs to evaluate the force in the immediate contact, without distance measurements. The experimental devices for such measurements may be extremely soft (pliable),which makes them very sensitive towards the measured forces. Corresponding methods and highly sensitive instruments for direct measurements of cohesive forces between individual particles of any nature in any media were developed by the authors and their co-workers [38-41], and are described in Chapter IX. 

The corresponding techniques and instruments, suitable for direct measurements of cohesive forces (CF) between individual macroscopic particles of any nature placed into any media, were designed and developed by Shchukin and co-workers [17-19,27,28], The key element in this technique is the magnetoelectric galvanometer used as a precision dynamometer (Fig. IX-17). One of the macroscopic particles, e.g., a glass bead, a in Fig. IX-17) is attached to the arm connected to the core of the galvanometer, while the... 

N = 0 value. This is an unfortunate drawback of the experimental technique the estimate for the Nq is essential for an understanding of the mechanisms of the influence of surfactants and polymers on the friction between fibers and on the pulp rheology. This estimate can be obtained from direct measurements of cohesive forces in contacts between crossed fibers. The molecular component of the cohesion, p, in the contact between two fibers can be obtained as the force necessary to rupture the fiber-fiber contact. The shear friction force can then be determined as the product of the previously determined friction coefficient, p, and the normal force Nq. In the absence of an external load, the value of Nq is solely the result of the molecular attraction forces, that is, F = iNq = pp. 

Israelachvili, J. N., Intermodular and Surface Forces, 2d ed., Academic Press, New York, 1991. (Graduate and undergraduate levels. An excellent source for the relation between molecular-level van der Waals interactions and macroscopic properties and phenomena such as surface tension, cohesive energies of materials, adhesion, and wetting. Also discusses direct measurement of van der Waals forces using the surface force apparatus.)... 

The surface tension of a pure liquid is a direct measure of the free energy or cohesion. For a solid, the surface free energy, which has the same dimensions as surface tension, is the measure of free energy of cohesion. Thus, for Substance i... 

James, A. E., Williams, D. J. A., and Williams, P. R. 1987. Direct measurement of static yield properties of cohesive suspensions. Rheol. Acta 26 437-446. 

For conditions of constant craze thickening rate, agreement between prediction and experiment is already very encouraging, particularly at higher speeds. There are still refinements to be made to the experimental method, and drop-weight striker speeds of less than 0.5 m/s will remain inherently difficult to control. Nevertheless, the Full Notch Impact test provides a promising direct method for the measurement of cohesive properties in tough polymers. 

A number of tests such as contact angle, bulk density, and tap density are relatively simple tests that, though not direct measurements of flow, have been found often to be predictive of the flow characteristics of materials. This is because these measurements are highly dependent on particle size and shape and the cohesive nature of the material, all of which are chief variables in the flowability of solids. These tests are commonly used in combination and are still routinely being conducted and related to flow in every-day pharmaceutical development. 

In addition to the direct measurements of tensile strength and cohesion, there are a number of other, indirect ways of assessing cohesiveness. These are discussed in sections 3, 5.2.4 and 4.8 which deal with categories of powders, Hausner ratio and flow-ability respectively. 

J.C. Williams, A.H. Birks and D. Bhattacharya, The direct measurement of the failure function of a cohesive powder, Powder Technology, 4 (1970/71), 328-37. 

In spite of the importance of Pj studies in understanding liquid state behavior, there has been suprisingly little done since Hildebrand and coworkers in 1928. It has been over 50 years since their initial work, and since that time direct measurements of Pj for only about 50 materials have been made. The experimental data available show that P and cohesive energy density are not equivalent, as shown in the review by Allen, Gee, and Wilson (30). They tabulated, for a wide range of liquids, values of n, the ratio of P to CED, following Hildebrand and Carter (31). and n was found to vary from 0.32 to 1.3. 

The force of cohesion, i.e. the maximum value of attractive force between the particles, may be determined by a direct measurement of force, F required to separate macroscopic (sufficiently large) particles of radius r, brought into a contact with each other. Such a measurement yields the free energy of interaction (cohesion) in a direct contact, A (h0) = Ff n r,. Due to linear dependence of F on r, one can then use F, to evaluate the cohesive force F2 = (r2/r )Fx, acting between particles in real dispersions consisting of particles with the same physico-chemical properties but of much smaller size, e.g. with r2 10 8 m (i.e. in the cases when direct force measurements can not be carried out). At the same time, in agreement with the Derjaguin equation... 

The energy required to expand one mole of a fluid from its original state to infinite volume at constant temperature is the cohesive energy of the fluid. This is a direct measure of the strength of the intermolecular forces between the fluid molecules and for a liquid, can be broken down into two contributing steps vaporization of the liquid to its saturated vapor followed by expansion of that vapor to infinite volume ... 

The wettability characteristics of an adhesive/adherend pair are determined by the relative values of surface tension of the adhesive and adherend. Surface tension of a liquid is a direct measurement of intermolecular forces and is half of the free energy of molecular cohesion. Surface tension is commonly represented by -q (gamma), and is measured in dynes/cm. The value of the surface tension of the solid substrate, or adherend, is called the critical surface tension, To ensure that the surface of the adherend will be wetted by an adhesive, an adhesive whose surface tension is less than the critical surface tension should be selected, so that... 

The processes leading to the formation of phase contacts can be studied experimentally by direct measurement of the cohesive forces between the particles. Such studies were described in studies carried out by Amelina [25-27] and Kontorovich [34-36] and will be discussed in detail further in this chapter. Throughout the book, we have described techniques and instrumentation for measuring small cohesive forces. These measurements also yield the energetic and geometric parameters of the process, such as the size of the critical nucleus of contact and its woik of formation. 

Novosad, J. (1990) Proc. 2nd World Congress Particle Technology. Kyoto, Japan, Part 1, p. 54 Part 111, p. 167. Orband, J.L.R. Geldart, D. (1997) Direct measurement of powder cohesion using a torsional device. Powder Technol, 92(1), 25-33. 

In view of the difficulties related to the correlation of the Relative Density to the Cone resistance values (see Section S.4.3.5), rather than using literature correlations, a practical way forward could be to setup a site specific correlation. A tempting approach could be to correlate CPT test results with density measurements on undisturbed samples originated from adjacent boreholes. This is however not possible since undisturbed samples cannot be retrieved from boreholes in non-cohesive soils. Therefore, when setting up a site specific Relative Density - correlation, calibration chamber tests are required. New promising developments with nuclear density probes allow for direct measurement of densities (see Appendix B.2.3.2). 

In order to characterize this bonding tendency, the flow function of a material must be deterrnined. Data on flow function can be generated in a testing laboratory by measuring the cohesive strength of the bulk soHd as a function of consoHdation pressure appHed to it. Such strength is directly related to the abihty of the material to form arches and ratholes in bins and hoppers. 

Measurement of the free energies of monolayer desorption from the rates of desorption depends on whether equilibrium exists between the monolayer and a thin region of solution immediately beneath the film. The relation which tests this condition (Equation 8) must correctly predict the dependence of the rate constant for desorption, k8, on 7r. For the sulfate, phosphonate, and carboxyl films in this study Equation 8 is obeyed within the range of experimental error (2 to 5%). Therefore, it is reasonable to assume that the necessary equilibrium condition does exist. The cohesive forces in the monolayer follow directly from the evaluation of the free energies of desorption. 

It would be desirable to have simple tests capable of characterising the fluidisation behaviour or flowability of particulate materials on the basis of their bulk properties. To this end, Carr19 developed a system to characterise bulk solids with respect to flowability. Table 6 summarises the properties which are determined. In Carr s method a numerical value is assigned to the results of each of these tests, and is summed to produce a relative flowability index for that particular bulk material. Given the extensive use of these empirical techniques in academia and industry, a brief review on the subject is reported here. Nevertheless, it should be emphasised that these techniques allow measurements of the flow-ability or cohesion of materials solely in their stationary or compressed status and at ambient conditions. A direct relationship between these... 

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