Session OI: Non-Newtonian Flows III

Flows of elastic liquids through planar hyperbolic micro contractions

Understanding and characterizing fluid elasticity in elongational flows remains a challenging area of complex liquid behaviour, and especially so for low viscosity solutions. In this experimental investigation, microfluidic devices featuring hyperbolic contractions are used to generate planar elongational flows. The extensional strain rate and total material strain are controlled by the dimensions of the microfluidic device. As a result of the small length scales ($10-50~\mu$m) very high deformation rates can be achieved. An approximately homogeneous streamwise velocity gradient is achieved by confining viscous shearing effects to boundary layers near the converging channel walls. The fluids studied include concentrated surfactant solutions ($\eta_{0}\sim10$~Pa$\cdot$s) and dilute aqueous solutions of polyethylene oxide ($\eta\sim0.01$~Pa$\cdot$s). The velocity and pressure fields in the hyperbolic converging flow regions are quantified using micro-PIV and a MEMS-based pressure sensor. The resulting information can then be used to evaluate the apparent extensional viscosity of these complex fluids.   

A Higher-Order Upwind Method for Viscoelastic Flow in Irregular Geometries

We present a high-resolution numerical method to capture elastic shear waves in incompressible viscoelastic fluids. The viscoelastic fluid is described by the Oldroyd-B constitutive equation for the polymer stress coupled to the incompressible Navier-Stokes equations. In our approach, we leverage the hyperbolic nature of the equations to make use of higher-order Godunov methods which have been previously used with much success in capturing shocks in compressible flow. The hyperbolic step also utilizes a new exact and efficient Riemann solver. Incompressibility is enforced through a projection method and a special partitioning of variables which leads to proper characteristic properties in the hyperbolic step. An embedded boundary method / volume-of-fluid method allows irregular geometries to be represented on Cartesian grids whereby the boundary cuts regular cells into irregular control volumes requiring special discretization stencils; away from boundaries standard finite differences are used. We demonstrate second-order accuracy for both highly elastic flows of a Maxwell fluid and steady-state flow of an Oldroyd-B fluid in the Newtonian limit.   

Laminar Tube Flow of Complex Fluids and Heat Transfer Enhancement

The flow structure and the heat transfer enhancement in steady pressure gradient driven flow of a class of non-affine non-linear viscoelastic fluids in straight tubes of arbitrary shape is analyzed analytically when the tube wall is maintained at constant temperature. Enhancement components due to constitutive elasticity as well as shear-thinning are identified. The former is due to secondary flows generated by the non-affine constitutive structure of the fluid and overwhelms the enhancement due to the latter with increasing inertia. Heat transfer enhancement increases as the strength of secondary flows increases with increasing elasticity or pressure gradient without any significant additional energy input to drive the secondary flows. Enhancement is an order of magnitude larger than its Newtonian counterpart under the same conditions. The variation of the average Nusselt number for each component of the enhancement with Weissenberg and Reynolds numbers in various non-circular cross-sections is presented. Work in progress concerning the possible implications on the heat transfer enhancement of the change of type of the vorticity equation is discussed.   

The effect of pre-shear on the extensional rheology of wormlike micelle solutions

With the increasing application of wormlike micelles as rheological modifiers in many consumer products, the predictions of the behavior of these solutions have become increasingly important in the recent years. A complete understanding of the fluid behavior requires the knowledge of both the shear and extensional rheology of the wormlike micellar solutions. In this talk, we present the results of our experimental measurements of the transient uniaxial extensional viscosity of a series of wormlike micelle solutions, both with and without the application of a known pre-shear prior to the onset of stretch. Both CTAB/NaSal and CPyCl/NaSal micellar solutions of varying concentrations were tested over a progressively increasing range of extension rates, pre-shear rates and pre-shear durations in order to acquire a better insight into the extensional rheology and the effect of pre-shear. Pre-shear was found to delay the onset of strain hardening and the delay was found to increase with increasing pre-shear rate and pre-shear duration. At large enough extension rate, the fluid filaments have been observed not to fail under capillary thinning, but to rupture at a critical value of the elastic tensile stress. This failure has been found to be independent of the imposed extension rate, but a strong function of the pre-shear.   

A rheological study of wormlike micelles flows in microchannel

Complex fluids show non linear properties under simple shear flows since they have various microstructures leading to flow induced phase transitions and instabilities. Such a coupling has widely been studied for wormlike micelles. Their flow curve exhibits a stress plateau separating high and low viscosity branches, corresponding to a shear-banding flow. Our aim is to understand the structure/concentration/flow coupling of wormlike micelles. A microfluidic chip is easy to couple with many analytical methods; it is hence well adapted to our study. We both perform particle image velocimetry and microscopy on a microfluidic chip consisting in a straight channel with dimensions: 250 $\mu $m large and 1 mm deep. Such a ``canyon'' geometry enables us to simply relate the measured velocity profiles to the local rheology. We evidence shear banding flow and slip at the walls. Strikingly there is no single rheological law that describes the velocity profiles at different pressure drops. Using microscopy, we point out turbid bands at the walls of the channels corresponding to the highly sheared bands. It seems that the shear induced phase has a lower concentration than the low sheared band. At low pressure drops, these bands are stable in time and their widths increase with increasing pressure until a limit where they fluctuate in space and time.   

Rheology of complex fluids by particle image velocimetry in microchannels

We use an experimental method to investigate the rheology of complex fluids. Here we propose to use microchannels to scan large dynamic ranges of shear rates observing the flow directly with a set-up developed in our group based on a micro-PIV technique. We image the flow of complex fluids in microchannels of controlled geometry using tracers. We show on model polymer solutions that the bulk nonlinear rheology can be extracted from velocity profiles. The spatial resolution allows us to access quantitatively slip effects that occur at the liquid -- solid interface. We have also used this technique to study wormlike micelles solutions. The macroscopic flow-curve of those fluids displays a constant stress plateau that suggests shear-banding effects. We indeed observe banding in the velocity profile when the shear stress imposed to the fluid reaches a critical value. This system exhibits large slip lengths (tens of microns) below the shear banding transition and smaller slip lengths (around one micron) when shear bands are present.