Growth of adhesive contacts for Maxwell viscoelastic spheres

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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.

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