Boundary integral methods for multicomponent fluids and multiphase materials

In this article, a connection is made between the behavior of thin layers of Newtonian liquids under tensile loading conditions and the behavior of highly deformable elastic or viscoelastic solids, which are more commonly used as adhesives. The behavior of Newtonian liquids is understood in the most quantitative detail and serves as a starting point for understanding the origins of fingering and cavitation instabilities that appear when the tensile deformation rates applied to these layers are sufficiently large. Similar instabilities appear in solid systems and can be attributed to common features of the stress distribution for incompressible liquids and solids. A unifying treatment is presented that can be used to understand the overall deformation behavior and adhesive performance of a wide variety of solid and liquid systems that are typically applied as thin layers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4023–4043, 2004

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/polb.20258

Deformation behavior of thin, compliant layers under tensile loading conditions

The cohesive failure of soft adhesives is studied using a yield stress fluid as a model adhesive, which allow to relate the viscoelastic properties of the fluid directly to its adhesive performance. We derive a theoretical expression for the force—distance curve as a function of the yield stress, which describes our experimental results very well. The theoretical prediction is obtained by assuming a circular air—adhesive interface; surprisingly, good agreement between theory and experiment is also obtained when strong fingering instabilities are observed in the experiment. This result is confirmed by the fact that we do not find a significant reduction in the work of adhesion when fingering instabilities are present. In addition, we discuss the morphology of the fingering instabilities.

Cohesive failure of thin layers of soft model adhesives under tension

Numerical simulation of 3D viscoelastic flows with free surfaces

We perform traction experiments on viscous liquids highly confined between parallel plates, a geometry known as the probe-tack test in the adhesion community. Direct observation during the experiment coupled to force measurement shows the existence of several mechanisms for releasing the stress: while fingering is favored for low traction velocities, low confinement and low viscosity, nucleation of bubbles occurs in the opposite conditions. It is possible to quantitatively predict the transition between the two regimes and, in many respects, describe the shape of the force response. Using a model for purely viscous fluids, we also present a phase diagram for the different force peak regimes that remarkably accounts for the data. Our results show that conspicuous features of the traction curve commonly thought to be characteristic of soft viscoelastic solids like adhesives are already encountered in liquid materials.

Force response of a viscous liquid in a probe-tack geometry: fingering versus cavitation.

We consider flow in a Hele - Shaw cell for which the upper plate is being lifted uniformly at a specified rate. This lifting puts the fluid under a lateral straining flow, sucking in the interface and causing it to buckle. The resulting short-lived patterns can resemble a network of connections with triple junctions. The basic instability - a variant of the Saffman - Taylor instability - is found in a version of the two-dimensional Darcy's law, where the divergence condition is modified to account for the lifting of the plate. For analytic data, we establish the existence, uniqueness and regularity of solutions when the surface tension is zero. We also construct some exact analytic solutions, both with and without surface tension. These solutions illustrate some of the possible behaviours of the system, such as cusp formation and bubble fission. Further, we present the results of numerical simulations of the bubble motion, examining in particular the distinctive pattern formation resulting from the Saffman - Taylor instability, and the effect of surface tension on a bubble evolution that in the absence of surface tension would fission into two bubbles. AMS classification scheme numbers: 76E30, 76D45

https://iopscience.iop.org/article/10.1088/0951-7715/10/6/005/pdf

Krzysztof Wlodarski

Papers

Hele-Shaw flow and pattern formation in a time-dependent gap