Session H23: Non-Newtonian Flows I

Dynamics of associative polymer solutions: Capillary break-up, jetting and rheology

Associative polymer solutions are used in extensively in the formulations for water-borne paints, food, inks, cosmetics, etc to control the rheology and processing behavior of multi-component dispersions. These complex dispersions are processed and used over a broad range of shear and extensional rates. Furthermore, the commercially relevant formulations use dilute solutions of associative polymers, which have low viscosity and short relaxation times, and hence their non-Newtonian response is not apparent in a conventional rheometer. In this talk, we explore several methods for systematically exploring the linear and nonlinear solution rheology of associative polymer dispersions, including: fractional model description of physical gelation, high frequency oscillatory tests at frequencies up to 10 kHz, microfluidic shear rheometry at deformation rates up to 1000000 /s and the influence of transient extensional rheology in the jet breakup. We show that high deformation rates can be obtained in jetting flows, and the growth and evolution of instability during jetting and break-up of these viscoelastic fluids shows the influence of both elasticity and extensibility.   

Designing a simple rheometer: Unsteady dam-break flows of power-law fluids

Many geophysical flows, such as mud slides, debris flows and avalanches, are non-Newtonian, and consequently exhibit complex flow behaviour. This is often due to an underlying microstructure within the flow -- for example, a suspension of particles within an interstitial fluid. We develop a method for determining the rheological parameters of a power-law fluid through the utilization of both numerical results and data from simple laboratory experiments. The model employed describes an unsteady dam-break flow of a viscous material within a rectangular channel, capturing the shape of the free surface and the streamwise velocity; a novel feature of this work is that it accounts for the effect of the containing side walls of a channel of any specified dimensions. Much of the previous work in this area has neglected this aspect of the physics, but here it can be shown that the side walls have an appreciable influence on the flow. The method relies on the numerical calculation of the flux through a cross-section of the channel, which has been done using both a finite element solver and a pseudo-spectral method, coupled to an evolution equation along the axis of the channel. Results from laboratory experiments will be shown in order to demonstrate the application, and effectiveness, of the method.   

Rheology of Concentrated Colloidal Suspensions in the Approach of the Glass Transition

Concentrated, non-crystallizing colloidal suspensions in their approach of the glass state exhibit distinct dynamics patterns. This is demonstrated with a model suspension at increased volume fraction of solid. The glass is defined by arrested motion of the spherical suspension particles. Dynamic mechanical experiments suggest a powerlaw rheological constitutive model for near-glass viscoelasticity as presented here. The rheological parameters used for this model originate in the Mode-Coupling Theory. The proposed constitutive model provides explicit expressions for the steady shear viscosity, the steady normal stress coefficient, the modulus-compliance relation, and the \textit{$\alpha $}-peak of $G$''. The relaxation pattern distinctly differs from gelation.   

Selective withdrawal as a method to measure extensional viscosity

The extensional viscosity of a liquid is a property that has shown to be very difficult to measure experimentally. We propose the use of the so-called selective withdrawal device to measure it. A viscous fluid layer is withdrawn from below with a tube. The suction deforms the free surface and generates an extensional ow at the entrance of the pipe. We conducted measurements of the extensional rate using PIV and related its value with the deformation of the free surface to determine the extensional viscosity. Some preliminary results will be presented and discussed for both Newtonian and viscoelastic liquids.   

Finite and Infinite Width Stokes Layers in a Power-Law Fluid

Self-similar solutions for the oscillatory boundary layer (the ``Stokes layer'') in a semi-infinite power-law fluid bounded by an oscillating wall (the so-called Stokes problem) are obtained and analysed. These semi-analytical solutions differ qualitatively from the classical solution for a Newtonian fluid, both in the non-sinusoidal form of the velocity oscillations and in the manner at which their amplitude decays with distance from the wall. In particular, for shear-thickening fluids the velocity reaches zero at a finite distance from the wall, and for shear-thinning fluids it decays algebraically with distance, in contrast to the exponential decay for a Newtonian fluid. We demonstrate numerically that these self-similar solutions provide a good approximation to the flow driven by a sinusoidally oscillating wall. Further details can be found in the recent paper by D.\ Pritchard, C.\ R.\ McArdle and S.\ K.\ Wilson entitled ``The Stokes boundary layer for a power-law fluid,'' in {\it Journal of Non-Newtonian Fluid Mechanics} {\bf 166}, 745--753 (2011).   

Britle failure of non-Newtonian, floating, extensional flows

Glacier ice is driven by gravity to flow from the land, where it is under shear, into the ocean, where it floats and extends. Owing to its non-Newtonian rheology, the ice can flow axisymmetrically over the bed but undergo brittle failure once it is floating on the ocean, as observed for example in crevassing of ice shelves. We model this coupled flow as an intrusion of a viscous gravity current into a denser ocean and study it both theoretically and experimentally. We have conducted laboratory experiments using a shear-thinning suspension that represents ice, and a denser inviscid fluid that represents an ocean. The non-Newtonian fluid was released at a constant flux through a cylindrical nozzle over a horizontal plane. The grounded, shear-dominated region of the flow was axisymmetric throughout the experiment, while past the transition line axisymmetry broke down into a seemingly ordered set of finger-like extensions (floating shelves) that demonstrated brittle behaviour. We have found that the width of the fingers as well as their radial extent increase with the flux. We attempt to explain these observations through a fingering instability that is driven by the dynamical differences between the two flow domains and by the material rheology, and we project that analysis to formulate a linkage between the material properties of ice and an upper bound on the width of ice shelves.   

Numerical Analysis of Gravity-driven Spreading of Viscoelastic Fluids: Investigation of the Effect of Shear-thinning and Elastic Behavior

Many complex fluids of interest exhibit viscoelastic hehavior. Polymeric drug delivery vehicles, such as anti-HIV topical microbicides, are among these fluids. For the optimal design of microbicides, the combined effect of shear-thinning and elastic behavior on the gravity-driven spreading of viscoelastic fluids is studied. We develop a 2D model to simulate the fluids spreading down an incline using ANSYS POLYFLOW software package. Arbitrary Lagrangian-Eulerian (ALE) method combined with Lagrangian remeshing is applied to track the moving free surface of fluids during spreading. Adaptive meshing method is used to generate high quality mesh for the remeshing process. Based on an elastic viscous split stress (EVSS) approach, several differential viscoelastic constitutive models are studied to investigate the combined effect of shear-thinning and elastic behavior. Mesh convergence test and constant volume check are studied to verify the new model. Moreover, the new model with zero elasticity is compared with previous studies of Newtonian and power-law fluids.   

Heat Transfer and Couette Flow of a Chemically-Reacting Non-Linear Fluid

The velocity, temperature, and concentration fields of a reacting fluid flowing in a channel are obtained. The fluid is assumed to flow between two parallel plates where one of the plates is sheared at constant speed whereas the other one is stationary. The plates are kept at constant hot and cold temperatures. Chemically reacting fluids are used in many industries and technologies such as combustion, catalysis, and biological systems and they usually show non-Newtonian behavior. The fluid is assumed to obey generalized power-law constitutive equation and its physical properties, i.e., viscosity, thermal conductivity and the diffusion coefficients are assumed to be a function of the concentration. The system is studied numerically for various parameters.