Growth of adhesive contacts for Maxwell viscoelastic spheres

Abstract

Coalescence of a Maxwell viscoelastic sphere to a frictionless and flat rigid plane is analyzed to study the transition from initial elastic adhesion to viscous sintering. Deformation is driven by surface tractions due to the surface energy. The formulation for surface forces consistently combines direct van der Waals attraction across the gap ahead of the contact edge with curvature-based tractions normal to the sphere surface. These two contributions to the surface traction result in two different modes of contact growth. The initial elastic contact and the early stage of time-dependent contact growth are in a zipping mode of contact closure dominated by direct attractive forces. The later stage of sintering is by stretching of the contact and is dominated by curvature-based tractions. The transition from the initial elastic contact to the zipping mode of contact growth is viscoelastic. For a given sphere radius, kinetics of the zipping mode of contact growth scale with a characteristic viscous sintering time. However, this mode is not part of the existing sintering models because direct attractive tractions were neglected in previous analyses of sintering. This stage of coalescence does not have unique scaling with sphere radius. The transition from the zipping to stretching mode of contact growth occurs at a contact radius that depends on sphere radius. The stretching mode of contact growth is in good agreement with previous analyses of viscous sintering.

The Role of Viscoelastic Adhesive Contact in the Sintering of Polymeric Particles

“…An interesting result of Jagota et al (20) is that, at short times when viscoelastic adhesive contact dominates, the contact growth behaves as a simple power law in time after the initial elastic JKR contact, i.e., a ∝ t 1/5 , remarkably different from the viscous flow model [1] that predicts a ∝ t 1/2 . Also, Jagota's numerical results showed that contact growth depends not only on R but also on another length scale, which has to do with the nature of intersurface attractions.…”

Elastocapillarity: Surface Tension and the Mechanics of Soft Solids

“…General purpose computational (e.g., finite element) methods [31,34,37,[116][117][118]. These methods typically represent the role of surface stress in a modular way, say as a surface finite element, which allows surface stress effects to be combined with nearly any form of bulk mechanical behavior.…”

Origins and Applications of London Dispersion Forces and Hamaker Constants in Ceramics

“…On the other hand, forces at a sintering neck, which is essentially an exterior crack, usually have been modeled based on surface tension and local curvature. 134 The difference between the two is illustrated in Fig. 17.…”

“…Moreover, there may be a regime of particle size in which sintering is controlled by direct attractive forces across the gap ahead of the neck, rather than by surface tension. 145 By combining both surface tension and direct attractive interactions, Jagota et al 134 have studied the problem of sintering of a Maxwell viscoelastic sphere to a rigid half space. Their analysis retrieves the known limits: initial elastic adhesion driven by direct attractive forces and final contact growth driven by surface tension.…”