Effect of contact deformations on the adhesion of particles
TL;DR: In this article, it was shown that despite the van der Waals' forces being capable of increasing the elastic contact area between the ball and the plane, the force that is required to overcome the molecular forces arising when the contact is broken does not increase thereby.
About: This article is published in Journal of Colloid and Interface Science.The article was published on 1975-11-01. It has received 3951 citations till now. The article focuses on the topics: Non-contact force & Contact area.
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TL;DR: The atomic force microscope (AFM) is not only used to image the topography of solid surfaces at high resolution but also to measure force-versus-distance curves as discussed by the authors, which provide valuable information on local material properties such as elasticity, hardness, Hamaker constant, adhesion and surface charge densities.
3,281 citations
TL;DR: In this paper, the authors review the fundamentals, applications and future tendencies of dynamic atomic force microscopy (AFM) methods and present a detailed quantitative comparison between theoretical simulations and experiment.
1,908 citations
01 Apr 1992
TL;DR: In this article, the energy release rate G is computed by the J-integral and the equilibrium is given by G = w. To avoid self consistent numerical calculations based on a specific interaction model (Lennard-Jones potential for example) we have used a Dugdale model, which allows analytical solutions.
Abstract: In the Johnson-Kendall-Roberts (JKR) approximation, adhesion forces outside the area of contact are neglected and elastic stresses at the edge of the contact are infinite, as in linear elastic fracture mechanics. On the other hand, in the Derjaguin-Muller-Toporov (DMT) approximation, the adhesion forces are taken into account, but the profile is assumed to be Hertzian, as if adhesion forces Could not deform the surfaces. To avoid self consistent numerical calculations based on a specific interaction model (Lennard-Jones potential for example) we have used a Dugdale model, which allows analytical solutions. The adhesion forces are assumed to have a constant value σO, the theoretical stress, over a length d at the crack tip. This internal loading acting in the air gap (the external crack) leads to a stress intensity factor Km, which is cancelled with the stress intensity factor KI due to the external loading. This cancellation suppresses the stress singularities, ensures the continuity of stresses, and fixes the radius c and the crack opening displacement δt. The energy release rate G is computed by the J-integral and the equilibrium is given by G = w. The equilibrium curves a(P), a(δ), and P(σ), the adherence forces at fixed load or fixed grips, the profiles, and the stress distributions can therefore be drawn as a function of a single parameter λ. When λ increases from zero to infinity there is a continuous transition from the DMT approximation to the JKR approximation. Furthermore the value of G for the DMT approximation is derived. It is shown that it is not physically consistent to have tensile stresses in the area of contact and no adhesion forces outside or no tensile stresses in the area of contact and adhesion forces outside. In the JKR approximation the distribution of adhesion forces is reduced to a singular stress at r = a+. The total attraction force outside the contact being zero, the integral of stresses in the contact is equal to the applied load P and negative applied loads are supported by the elastic restoring forces. In the DMT approximation the adhesion stresses tend toward zero to have a continuity with the stress at r = a−, but their integral is finite and the total attraction force outside the contact is 2πwR. In the area of contact the distribution of stresses is Hertzian, and their integral is P + 27πwR. Negative applied loads are sustained by adhesion forces outside the contact.
1,808 citations
TL;DR: This paper reviews the work in this area with special reference to the discrete element method and associated theoretical developments, and covers three important aspects: models for the calculation of the particle–particle and particle–fluid interaction forces, coupling of discrete elements method with computational fluid dynamics to describe particle-fluid flow, and the theories for linking discrete to continuum modelling.
1,563 citations
TL;DR: Atomic force microscopy (AFM) force-distance curves have become a fundamental tool in several fields of research, such as surface science, materials engineering, biochemistry and biology.
1,559 citations
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01 Jan 1934
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Abstract: Chapter 1: Stresses and Strains Chapter 2: Foundations of Plasticity Chapter 3: Elasto-Plastic Bending and Torsion Chapter 4: Plastic Analysis of Beams and Frames Chapter 5: Further Solutions of Elasto-Plastic Problems Chapter 6: Theory of the Slipline Field Chapter 7: Steady Problems in Plane Strain Chapter 8: Non-Steady Problems in Plane Strain
20,724 citations
TL;DR: In this article, the London-v.d. interaction between two spherical particles is computed as a function of the diameters and the distance separating them, and a table is calculated which enables numerical application of the formulae derived.
3,484 citations
TL;DR: In this article, an Adhasionstheorie fester Korper entwickelt, die die molekularen Anziehungskrafte berucksichtigt and zwei verschiedene Formen fur folgende beiden Falle annimmt: Fur Fall 1 wird eine ganz allgemeine Formel abgeleitet, nach der die Adhasionskraft konvexer Korper proportional ist der auf die Flacheneinheit bezogenen Abreis ar
Abstract: Es wird eine Adhasionstheorie fester Korper entwickelt, die die molekularen Anziehungskrafte berucksichtigt und zwei verschiedene Formen fur folgende beiden Falle annimmt:
Fur Fall 1 wird eine ganz allgemeine Formel abgeleitet, nach der die Adhasionskraft konvexer Korper proportional ist der auf die Flacheneinheit bezogenen Abreis arbeit ebener Oberflachen. Durch Berucksichtigung des Einflusses der Phase (3), die den Zwischenraum zwischen den Korpern ausfullt, wird man dazu gefuhrt, Falle von Abstosung zwischen den Korpern zuzulassen, die eng mit der Lyosorption verbunden ist. Fur Fall 2 wird eine Korrektion zur Hertzschen Formel abgeleitet, die aquivalent ist dem Vorhandensein einer von der Kontaktflache s unabhangigen Adhasionskraft; bei s=0 besteht eine gewisse Unstimmigkeit zwischen den beiden Formen der Adhasionstheorie. Ferner wird der Einflus einer vierten Phase betrachtet, die in der Nahe der Beruhrungsstelle der beiden Korper kapillar festgehalten wird (z. B. infolge von Kapillarkondensation). Wenn die Randwinkel, die von der Trennungsflache der Phasen (3) und (4) und den festen Oberflachen eingeschlossen werden, ungleich Null sind, so beeinflust das Vorhandensein einer kapillar festgehaltenen Phase (4) die Adhasionskraft (mit Berucksichtigung des Laplace'schen Druckdefektes) nicht, im entgegengesetzten Fall nimmt die Adhasionskraft ab. In dem Fall, wenn die Phase (4) die sich beruhrenden Oberflachen zu trennen sucht, kann die Kapillarkondensation die zur volligen Trennung der Oberflachen (mit Zerreisen der Kapillarschicht) notwendige Kraft vergrosern; diese Kraft schliest die „wahre“ Adhasionskraft nicht mehr in sich ein.
1,536 citations
TL;DR: In this paper, an expression for the cohesive force between two unequal spheres in geometrical contact is derived and the surface energy of the solid may be computed from the constant in this expression.
Abstract: Summary An expression is obtained for the cohesive force between two unequal spheres in geometrical contact From the constant in this expression the surface energy of the solid may be computed Results are obtained in agreement with the theory The surface energies of freshly fused surfaces of quartz and sodium pyroborate are 33·8 and 69 ergs per sq cm In the case of borate spheres, however, the cohesion is probably due to a surface film of water
446 citations
285 citations