Session HN: Non-Newtonian Flows II

Topological fluid mechanics of stirring in a non-Newtonian fluid

It is well known that laminar flows, both Newtonian and non-Newtonian, can be stirred effectively using chaotic advection, which produces exponential stretching and folding of material lines and surfaces. A recent development in this field is the concept of topological choas, in which the topology of the trajectories of moving rods can be used to predict a lower bound on the stretching of the surrounding fluid. We present the first analysis of topological chaos in a non-Newtonian fluid using experimental and computational tools. The power of this approach lies in the fact that a lower bound on the stretching is established independent of the fluid properties, making it possible to predict efficient stirring even when the fluid properties are quite complex and/or not well characterized.   

Visualization and microrheology of complex fluid/fluid interfaces

We describe a novel microrheological technique to measure the rheological properties of fluid/fluid interfaces, which can dramatically affect the flow properties and dynamics of multiphase materials (emulsions, foams, cells and organs). Such measurements can be particularly challenging, as one needs to measure the influence of molecularly thin, two-dimensional layers but be insensitive to the three-dimensional bulk fluids on either side. However, dimensionality helps here: interfacial forces on a probe are exerted along a contact perimeter, whereas the bulk forces are exerted on the contact area. Smaller probes thus increase the perimeter/area ratio, and therefore the relative sensitivity to interfacial viscoelasticity. We fabricate micron-scale ferromagnetic amphiphilic disks (with versatile surface chemistry), place them on the interface, use external electromagnets to exert a known torque (stress), and measure the resulting rotational displacement (strain). In addition to its sensitivity, our technique can measure frequency dependent linear/nonlinear viscoelastic properties and yield stresses. Simultaneous visualization of the interface by fluorescence microscopy allows us to correlate local dynamics withe measured rheology. We validate our technique and highlight its capabilities with measurements on a variety of systems, including two-dimensional colloidal monolayers, fatty acid and phospholipid monolayers.   

Formation of beads-on-a-string structures during the pinch-off of viscoelastic filaments

Breakup of liquid filaments is omnipresent in nature and technology. When a filament formed by placing a drop of syrup between a thumb and a forefinger is stretched by pulling apart the two fingers, it resembles a thinning cylinder. If the same experiment is repeated with saliva, the filament's morphology close to pinch-off resembles that of beads of several sizes interconnected by slender threads. Although there is general agreement that formation of such beads-on-a-string (BOAS) morphology only occurs for viscoelastic fluids, the mechanism behind this phenomenon remains unclear and controversial. The physics of formation of BOAS structures is probed here by simulation which reveals that viscoelasticity alone does not give rise to a small, satellite bead between two much larger main drops (beads) but that inertia is required for its formation. Viscoelasticity, however, enhances the growth of the satellite bead and delays pinch-off, which leads to a relatively long-lived, stable beaded filament. The new simulations also show the formation of second-generation sub-satellite beads in certain cases, as observed experimentally but not, heretofore, predicted theoretically.   

On the evolution of the drop-filament corner region during the pinch-off of viscoelastic fluids

Fluid pinch-off is important in applications involving the production of drops, e.g., ink-jet printing and atomization, and in the capillary breakup extensional rheometry (CaBER). A characteristic feature of fluid pinch-off is the formation of drops that are connected to thinning threads. In the pinch-off of viscoelastic fluids, the region that connects the drops to the threads develops into a sharp corner. Recently, Clasen {\em et al}.\ [J.\ Fluid Mech.\ {\bf 556}, 283 (2006)] showed that such a corner evolves self-similarly---a result which can be exploited in estimating accurately the extensional viscosity of fluids from CaBER experiments. However, the agreement between the similarity solution derived by Clasen {\em et al}.\ and experiments is only qualitative, and it may be due to their approximation of the dynamics in the corner region by a one-dimensional analysis. The evolution of the drop-filament corner region is elucidated here using theory and both one- and two-dimensional computations. A new similarity solution is obtained which describes better the shape of the liquid-gas interface in the corner region, and the dynamics in the corner region is demonstrated to be two-dimensional.   

Tunable adhesion using field-activated ``smart" fluids

We demonstrate experimentally that field-responsive magnetorheological fluids can adhere to non-magnetic substrates. The tunable adhesive performance is measured experimentally with pull-off tests, i.e. probe-tack experiments, in which the external magnetic field and fluid geometry are varied. The adhesive force is predicted by a lubrication model which treats the adhesive as a yield stress fluid with field-dependent and inhomogeneous yield stress (caused by the inhomogeneous external magnetic field). The peak adhesive force, the ``work of adhesion" and the mode of failure are all controlled by the field-responsive nature of the magnetorheological fluid forming the adhesive layer.   

Branching of an electrospinning fiber

The phenomenon of branching during the electrospinning of polymeric liquid has been studied using high-speed video imaging. Linear stability analysis of the electrified jet has been performed including non-Newtonian effects. The branching is only observed using very fine needles of diameters of approximately 100 microns. The onset of the branching is associated with the flattening of the jet, which occurs at stronger electric fields than used for regular fiber spinning. The branch emerges out of the jet where it has the highest azimuthal curvature. We have characterized the relationship between inter-branch distances and the operating parameters, such as the applied electric field and the physical properties of the liquid, such as the molecular weight of polymer and the nature of the solvent.   

Is there an elongational Flow State in Circular Couette Flow?

We investigate the behavior of dilute polymer solutions in a Taylor-Couette cell with independently rotatable cylinders. The focus of our interest concentrates on the examination of the elongation of the solved polymers and their response on the imposed flow. The elongation is imposed to the fluid by a special ratio of the cylinder rotation rates which create a non rotational circular Couette flow. This special flow state is numerically investigated concerning its effectiveness deforming dispersed material in the fluid. Experimental results show, that the flow state holds for Newtonian fluids but that it is changed for polymer solutions due to their power law shear thinning behaviour. In addition to the investigated polymer solutions including different types of polymers, concentrations and solvent viscosities an industrial manufactured emulsion has been tested.   

Is there a Relationship between the Elongational Viscosity and the First Normal Stress Difference in Polymer Solutions?

We investigate polymer solutions in shear and elongational flow. Shear flow is created in a cone-plate-geometry of a commercial rheometer. The capillary thinning of a filament of polymer solution in the Capillary Breakup Extensional Rheometer (CaBER) serves as an elongational flow. We compare the relaxation time and the elongational viscosity measured in the CaBER with the first normal stress difference and the relaxation time from the rheometer measurements. All these four quantities depend on different fluid parameters - the viscosity of the polymer solution, the polymer concentration within the solution, and the molecular weight of the polymers - and on the shear rate (in the shear flow measurements). Nevertheless, we found that the first normal stress coefficient depends quadratically on the CaBER relaxation time. A simple model is presented that explains this relation on a phenomenological level.   

An experimental investigation on transient change in viscoelasticity in mixing and reaction processes between a water-soluble polymer solution and a metal ion.

We have experimentally investigated mixing and reaction processes between a partially hydrolyzed polyacrylamide (PAM) solution and iron ion. We added a solution including iron ion to a vessel in which the PAM solution was stirred by an impeller at a constant rotational speed. We observed flow behavior in the vessel during and after the addition of the iron ion solution. We found transient flow behavior. After the addition of the iron ion solution, Weissenberg effect started to occur. It should be noted that Weissenberg effect is not observed before the addition in the present experimental condition. When the rotation of the impeller was kept, Weissenberg effect gradually disappeared and a free surface of the solution finally became flat. In order to elucidate mechanism for the observed transient phenomenon, some measurements by means of a rheometer have been performed. Finally, we propose the mechanism associated with interaction between iron ion and the polymer chain.