Stretching of viscoelastic drops in steady sliding

Abstract

The sliding of non-Newtonian drops down planar surfaces results in a complex, entangled balance between interfacial forces and non-linear viscous dissipation, which has been scarcely inspected. In particular, a detailed understanding of the role played by the polymer flexibility and the resulting elasticity of the polymer solution is still lacking. To this aim, we have considered polyacrylamide (PAA) solutions of different molecular weights, suspended either in water or in glycerol/water mixtures. In contrast to drops of stiff polymers, drops of flexible polymers exhibit a remarkable elongation in steady sliding. This difference is most likely attributed to variation of viscous bending as a consequence of variation of shear thinning. Moreover, an "optimal elasticity" of the polymer seems to be required for this drop elongation to be visible. We have complemented experimental results with numerical simulations of a viscoelastic FENE-P drop. This has been a decisive step to unraveling how a change of the elastic parameters (e.g. polymer relaxation time, maximum extensibility) affects the dimensionless sliding velocity.

Droplet breakup driven by shear thinning solutions in a microfluidic T-junction

“…Measurements are currently in progress on the generation of oil droplets in polyacrylamide (PAA) solutions [40,65], characterized by strong elastic effects, while showing only weak shear thinning properties, a situation complementary to this study. Another interesting aspect for future studies could be the assessment of the validity of the effective Capillary number to rescale and predict droplet size upon changing the channel geometry, while keeping the same flow rate magnitudes.…”

“…First, we notice that the effective shear rate γeff is here imposed via the geometrical lengthscale δ and the average velocity U av . This differs from the definition adopted in the analysis of non-Newtonian sliding droplets [30,40], where a "phenomenological" lengthscale was introduced only a posteriori, and whose value was derived by imposing that the non-Newtonian data match the Newtonian ones for small Capillary numbers and small driving forces. There are also some technical differences in the definition of the effective Capillary number, if compared with the definition adopted in a recent study by Roumpea and coworkers [41]: first, we use the prefactor 3 in front of the effective shear rate, while the definition in ref.…”

Electroosmotic Flow of Viscoelastic Fluid through a Constriction Microchannel

“…For different types of viscoelastic fluids, various constitutive models have been developed to relate the polymeric stress tensor τ and the deformation rate of the fluid, including WhiteMetzner model [14], which is commonly used for shear-thinning fluid; PTT model [17], which has good performance for prediction of viscosity at low shear rates; Giesekus model [19], which is suitable for concentrated polymer solutions; and OB model [16], which is suitable for dilute polymer solutions. Since OB model can properly fit the rheological behavior of aqueous PAA solutions [45], OB model is adopted in this study. In the OB model, the polymeric stress tensor, τ, is described as [16],…”

An adaptive solver for viscoelastic incompressible two-phase problems applied to the study of the splashing of weakly viscoelastic droplets

“…Each of these models can better suit the particular solvent-polymer solution or melt employed in a particular problem. For example, either the Oldroyd-B or the FENE-type seems to fit properly the rheological behaviour of aqueous solutions of polyacrylamide (PAA) [37,38]. Both the FENE-P and FENE-CR models correct the more simple Oldroyd-B model by imposing a maximum stretch that cannot be exceeded (FENE stands for Finitely Extensible Nonlinear Elastic), with the difference between them being the statistical closure used for the restoring force; P denotes the Peterlin's closure [34] and CR follows from the closure proposed by Chilcott & Rallison [35].…”