The relationship between viscoelasticity and elasticity

Abstract

We consider models for elastic liquids, such as solutions of flexible polymers. They introduce a relaxation time λ into the system, over which stresses relax. We study the kinematics of the problem, and clarify the relationship between Lagrangian and Eulerian descriptions, thereby showing which polymer models correspond to a nonlinear elastic deformation in the limit λ → ∞. This allows us to split the change in elastic energy into reversible and dissipative parts, and thus to write an equation for the total energy, the sum of kinetic and elastic energies. As an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability, using novel numerical schemes based on our insights into the flow kinematics.

Capillary thinning of elastic and viscoelastic threads: From elastocapillarity to phase separation

“…Very recent theory by Snoeijer et al [25] and Eggers et al [26] investigates this question in detail. In the generic models for the flow of viscoelastic polymeric liquids, one has to adopt a Lagrangian reference frame: the polymers that are being stretched move with the fluid and are stretched by velocity gradients in the moving fluid.…”

“…The most striking conclusion is that in practice the instability is identical between purely elastic and viscoelastic materials. For instance, for the pertinent example of the BOAS structure the prediction is that the interface shapes connecting the filament (the string) to the drops (the beads) has an identical shape [25][26][27]. To test these proposals and investigate how the crossover between elastic and viscoelastic filaments happens we here investigate the capillary thinning of filaments of a biopolymer with a tunable elasticity, varying from an almost Newtonian liquid to a gel.…”