Convective nonlinearity in non-newtonian fluids

In the limit of infinite yield time for stresses, the hydrodynamic equations for viscoelastic, non-Newtonian liquids such as polymer melts must reduce to that for solids. This piece of information suffices to uniquely determine the nonlinear convective derivative, an ongoing point of contention in the rheology literature.     

Mixing of non-Newtonian fluids in steadily forced systems

We investigate mixing in a viscoelastic and shear-thinning fluid-a very common combination in polymers and suspensions. We find that competition between elastic and viscous forces generates self-similar mixing, lobe transport, and other characteristics of chaos. The mechanism by which chaos is produced is evaluated both in experiments and in a simple model. We find that chaotic flow is generated by spontaneous oscillations, the magnitude and frequency of which govern the extent of chaos and mixing.     

Variational principle for flow of non-Newtonian fluids

A variational principle is formulated for finding stationary solutions of the equations of motion for an incompressible non-Newtonian fluid with constitutive equation of the Reiner-Rivlin type. The basic functional is related, but not identical to the rate of energy dissipation. It can be used for analyzing the stability of the stationary state against small perturbations.     

Study on bubble formation in non-Newtonian fluids by laser image technique

A laser image system for studying bubble formation at the orifice submerged in liquid was established. The process of bubble formation can be directly visualized and real-time recorded through computer by means of He–Ne laser as light source using the beam expanding and light amplification technique. The behaviors of bubble formation in polyacrylamide (PAM) aqueous solutions were investigated at temperature 293.15 K and orifice diameters 1, 1.5 and 2 mm, respectively, the chamber volume was 90 cm³ and the gas flowrate from 0.1 to 0.6 cm³/s. The influences of mass concentration of solution and orifice diameter on bubble detachment volume were investigated experimentally and the results show that bubble detachment volume increases with solution concentration and orifice diameter in the experimental range of this work.     

Miscible displacement of non-Newtonian fluids in a vertical tube

The influence of rheology on the miscible displacement of a viscous fluid by a less viscous, Newtonian one in a vertical tube is studied experimentally as a function of the flow velocity. For Newtonian displaced fluids the transient residual film thickness is nearly of the tube radius at large viscosity ratios between the two fluids in agreement with experimental and numerical results from the literature. For shear-thinning fluids with a zero yield stress (mostly xanthan-water solutions), decreases down to of the radius for the most concentrated solutions. For fluids with a non-zero yield stess, further decreases down to 24-25% of the radius. The orders of magnitude of these values can be obtained through numerical simulations (commercial code) for the various types of fluids. Instabilities of the film at its boundary develop downstream and lead to a reduction of the final thickness of the film at longer times: this reduction is larger for lower viscosity ratios and larger velocities.Received: 15 February 2003, Published online: 8 July 2003PACS: 47.20.Gv Hydrodynamic stability: Viscous instability - 83.60.Wc Rheology: Flow instabilities     

Nonlinear effects of non-Newtonian fluids on natural convection in a porous medium

This paper investigates the rheological effects of non-Newtonian fluids on the natural convection mechanism in a porous medium. A non-Newtonian behavior of power law fluid with a yield stress, saturating a porous medium, in which yield stress is temperature dependent, is considered. The cases of constant temperature boundary and constant heat flux boundary, along the heated vertical cylinder, are analyzed. The approximate similarity solutions in a closed form are shown, from which the velocity and temperature profiles are determined. The numerical solutions for a constant temperature boundary are also shown and discussed.     

Direct visualization of continuous simple shear in non-Newtonian polymeric fluids

Using a particle tracking velocimetric technique, we show direct evidence of nonlinear velocity profiles during simple-shear flow of an entangled polymer solution, offering new insight into the origins of such characteristics as stress overshoot. Upon a startup shear by imposing a constant velocity on one of the two surfaces that confine the sample, the velocity field evolves from the initial linearity across the gap to a final state with a shear rate gradient. The unexpected deviation from the widely assumed linear variation of the velocity along the gap direction is most plausibly due to the entangled polymer's ability to disentangle in the presence of high shear that can orient the polymer chains leading to anisotropy in their mutual constraint.     

Rheo-NMR of the secondary flow of non-Newtonian fluids in square ducts

We report the first real-time observations of the entire fully developed laminar secondary flow field of aqueous 2% Viscarin GP-209NF (a λ-carrageenan polysaccharide) in a square duct as made using a modest rheological NMR imaging (rheo-NMR) apparatus. Simulations using the Reiner-Rivlin constitutive equation verify the results. An included rheo-NMR flow rate quantification study assesses the measurement precision. Rheo-NMR resolves slow flows superimposed on primary flows about 300 times greater, making it a universally accessible technique by which full secondary flow field data may be systematically gathered.     

The inertial dynamics of thin film flow of non-Newtonian fluids

Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case where the viscosity depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general nonlinear dependence. The modelling allows for large changes in film thickness provided the changes occur over a relatively large enough lateral length scale. Modifying the surface boundary condition for tangential stress forms an accessible foundation for the analysis where flow with constant shear is a neutral critical mode, in addition to a mode representing conservation of fluid. Perturbatively removing the modification then constructs a model for the coupled dynamics of the fluid depth and the lateral momentum. For example, the results model the dynamics of gravity currents of non-Newtonian fluids when the flow is not creeping.