Characterization of Effective Diffusion within Viscoelastic Fluids with Elastic Instabilities

We considered effective diffusion, characterized by magnitudes of effective diffusion coefficients, in order to quantify mass transport due to the onset and development of elastic instabilities. Effective diffusion coefficient magnitudes were determined using different analytic approaches, as they were applied to tracked visualizations of fluorescein dye front variations, as circumferential advection was imposed upon a flow environment produced using a rotating Couette flow arrangement. Effective diffusion coefficient results were provided for a range of flow shear rates, which were produced using different Couette flow rotation speeds and two different flow environment fluid depths. To visualize the flow behavior within the rotating Couette flow environment, minute amounts of fluorescein dye were injected into the center of the flow container using a syringe pump. This dye was then redistributed within the flow by radial diffusion only when no disk rotation was used, and by radial diffusion and by circumferential advection when disk rotation was present. Associated effective diffusion coefficient values, for the latter arrangement, were compared to coefficients values with no disk rotation, which were due to molecular diffusion alone, in order to quantify enhancements due to elastic instabilities. Experiments were conducted using viscoelastic fluids, which were based on a 65% sucrose solution, with different polymer concentrations ranging from 0 ppm to 300 ppm. Associated Reynolds numbers based on the fluid depth and radially averaged maximum flow velocity ranged from 0.00 to 0.5. The resulting effective diffusion coefficient values for different flow shear rates and polymer concentrations quantified the onset of elastic instabilities, as well as significant and dramatic changes to local mass transport magnitudes, which are associated with the further development of elastic instabilities.

Dehydration-induced mechanical instabilities in active elastic spherical shells

Active elastic instabilities are common phenomena in the natural world, where they have the character of sudden mechanical morphings. Frequently, the driving force of the instability mechanisms has a chemo-mechanical nature, which makes the instabilities very different from the standard elastic instabilities. In this paper, we describe and study the active elastic instability occurring in a swollen spherical closed shell, confining a water-filled cavity, during a dehydration process. We set up a few numerical experiments based on a stress-diffusion model to give an insight into the phenomenon. Then, we present a study that looks at the chemo-mechanical problem and, through a few simplifying assumptions, allows us to derive a semi-analytical model of the phenomenon. It takes into account both the stress state and the water concentration in the walls of the shell at the onset of the instability. Moreover, it considers the invariance of the cavity volume at the onset of instability, which is due to the impossibility of instantaneously changing the cavity volume filled with water. Eventually, it is shown that the semi-analytic model matches very well the outcomes of the numerical experiments far from the initial regime; the ranges of validity of the approximated analytical model are also discussed.

On the Interaction of Viscoelasticity and Waviness in Enhancing the Pull-Off Force in Sphere/Flat Contacts

Motivated by roughness-induced adhesion enhancement (toughening and strengthening) in low modulus materials, we study the detachment of a sphere from a substrate in the presence of both viscoelastic dissipation at the contact edge, and roughness in the form of a single axisymmetric waviness. We show that the roughness-induced enhancement found by Guduru and coworkers for the elastic case (i.e. at very small detachment speeds) tends to disappear with increasing speeds, where the viscoelastic effect dominates and the problem approaches that of a smooth sphere. This is in qualitative agreement with the original experiments of Guduru’s group with gelatin. The cross-over velocity is where the two separate effects are comparable. Viscoelasticity effectively damps roughness-induced elastic instabilities and makes their effects much less important. Graphical Abstract