Anke Lindner

Viscous fingering in non-Newtonian fluids

We study the viscous fingering or Saffman–Taylor instability in two different dilute or semi-dilute polymer solutions. The different solutions exhibit only one non-Newtonian property, in the sense that other non-Newtonian effects can be neglected. The viscosity of solutions of stiff polymers has a strong shear rate dependence. Relative to Newtonian fluids, narrower fingers are found for rigid polymers. For solutions of flexible polymers, elastic effects such as normal stresses are dominant, whereas the shear viscosity is almost constant. Wider fingers are found in this case. We characterize the non-Newtonian flow properties of these polymer solutions completely, allowing for separate and quantitative investigation of the influence of the two most common non-Newtonian properties on the Saffman–Taylor instability. The effects of the non-Newtonian flow properties on the instability can in all cases be understood quantitatively by redefining the control parameter of the instability.

Cohesive failure of thin layers of soft model adhesives under tension

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.

Adhesive and Rheological Properties of Lightly Crosslinked Model Acrylic Networks

The viscoelastic and adhesive properties of a series of model, lightly crosslinked acrylic polymer networks have been investigated. The model networks were statistical copolymers of 2-ethyl-hexyl acrylate and acrylic acid or terpolymers of 2-ethyl-hexyl acrylate, acrylic acid, and stearyl acrylate synthesized in solution. All were lightly crosslinked after the polymerization was completed to obtain typical properties of pressure-sensitive adhesives. The bulk rheological properties of the networks were characterized by dynamical mechanical spectroscopy and in uniaxial extension. Their adhesive properties were tested with an instrumented probe tester fitted with a cylindrical steel probe. The presence of acrylic acid in the copolymer caused an increase in both elastic modulus and resistance to interfacial crack propagation characterized by the critical energy-release rate 𝒢 c and the incorporation of stearyl acrylate caused a decrease in both modulus and 𝒢 c . In both cases, however, the modification of 𝒢 c controlled the overall behavior. The analysis of the nonlinear elastic properties of the adhesives with the Mooney–Rivlin model provided new insights on the role played by the ratio between entanglements and crosslink points in controlling the formation and extension of the bridging fibrils observed upon debonding.

Viscous fingering in a shear-thinning fluid

We study the Saffman–Taylor instability in a rectangular Hele-Shaw cell. The driven fluid is a dilute (or semidilute) polymer solution, with a viscosity that exhibits shear thinning. Other non-Newtonian properties such as elastic effects are negligible under the present experimental conditions; the system thus allows for separate investigation of the influence of shear thinning on the instability. The experiments show that, for weak shear-thinning, the results for the width of the fingers as a function of the capillary number collapse onto the universal curve for Newtonian fluids, provided the shear-thinning viscosity is used to calculate the capillary number. For stronger shear thinning, narrower fingers are found. The experiment allows also for a study of the applicability of Darcy’s law to shear thinning fluids. For Newtonian fluids, this law gives the finger velocity as a function of the pressure gradient. For weakly shear-thinning fluids, we find that an effective Darcy’s law, in which the constant v...

Non-Newtonian viscosity of Escherichia coli suspensions.

The viscosity of an active suspension of E. coli bacteria is determined experimentally as a function of the shear rate using a Y-shaped microfluidic channel. From the relative suspension viscosity, we identify rheological thickening and thinning regimes as well as situations at low shear rate where the viscosity of the bacteria suspension can be lower than the viscosity of the suspending fluid. In addition, bacteria concentration and velocity profiles in the bulk are directly measured in the microchannel.

How to obtain the elongational viscosity of dilute polymer solutions

Measurement of the resistance to a stretching motion, the so-called elongational viscosity ηe, has proven to be difficult for dilute polymer solutions, although it is important for a large number of applications. We attempt to deduce ηe of dilute solutions of flexible polymers in two different ways. First, ηe can be inferred from measurements of the shear viscosity η and the first normal stress difference N1, invoking an appropriate constitutive equation. Second, it is measured in the opposing jet elongational viscometer. Although the results of the latter method have been much debated they agree reasonably well with those from the first method. The combination of the two methods thus allows to obtain the correct order of magnitude of ηe.

Inclined plane rheometry of a dense granular suspension

We present a new method to measure the viscosity of a dense model suspension using an inclined plane rheometer. The suspension is made of mono-disperse, spherical, non-Brownian polystyrene beads immersed in a density matched silicon oil. We show that with this simple set-up, the viscosity can be directly measured up to volume fractions of ϕ=61% and that particle migration can be neglected. The results are in excellent agreement with local viscosity measurements obtained by magnetic resonance imaging techniques by Ovarlez et al. [J. Rheol. 50(3), 259–292 (2006)]. In the high density regime, we show that the viscosity is within the tested range of parameters, independent of the shear rate and the confinement pressure. Finally, we discuss deviations from the viscous behavior of the suspensions.

Accelerated drop detachment in granular suspensions

We experimentally study the detachment of drops of granular suspensions using a density matched model suspension with varying grain volume fraction (ϕ = 15% to 55%) and grain diameter (d = 20 μm to 140 μm). We show that at the beginning of the detachment process, the suspensions behave as an effective fluid. The detachment dynamics in this regime can be entirely described by the shear viscosity of the suspension [R. J. Furbank and J. F. Morris, Int. J. Multiphase Flow 33(4), 448–468 (2007)]. At later stages of the detachment, the dynamics become independent of the volume fraction and are found to be identical to the dynamics of the interstitial fluid. Surprisingly, visual observation reveals that at this stage, particles are still present in the neck. We suspect rearrangements of particles to locally free the neck of grains, causing the observed dynamics. Close to the final pinch off, the detachment of the suspensions is further accelerated, compared to the dynamics of pure interstitial fluid. This accele...

Stretch flow of thin layers of Newtonian liquids: Fingering patterns and lifting forces

We study the stretch flow of a thin layer of Newtonian liquid constrained between two circular plates. The evolution of the interface of the originally circular bubble is studied when lifting one of the plates at a constant velocity and the observed pattern is related to the measured lifting force. By comparing experimental results to numerical simulations using a Darcy’s law model we can account for the fully nonlinear evolution of the observed fingering pattern. One observes an initial destabilization of the interface by growth of air fingers due to a Saffman–Taylor-like instability and then a coarsening of the pattern toward a circular interface until complete debonding of the two plates occurs. Numerical simulations reveal that when relating the observed patterns to the lifting force not only the number of fingers but also the amplitude of the fingering growth has to be taken into account. This is consistent with the experimental observations.

Buckled in translation

We report experiments on the deformation and transport of an elastic fiber in a viscous cellular flow, namely a lattice of counter-rotative vortices. We show that the fiber can buckle when approaching a stagnation point. By tuning either the flow or fiber properties, we measure the onset of this buckling instability. The buckling threshold is determined by the relative intensity of viscous and elastic forces, the elasto-viscous number Sp. Moreover we show that flexible fibers escape faster from a vortex (formed by closed streamlines) compared to rigid fibers. As a consequence, the deformation of the fiber changes its transport properties in the cellular flow.