A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)

Rheological properties of some polymer solutions in both the linear and non-linear regions have been investigated. The solutions include poly(vinyl alcohol) solution (with and without sodium borate), hyaluronic acid solution, and xanthan gum solution; some of which form microstructures depending on their deformation history, and thus can be classed as complex fluids. Among the rheological properties, the large amplitude oscillatory shear (LAOS) behavior was found to be very sensitive to the interactions or the shear-induced formation of microstructures. Depending on the interactions between the microstructures, it was found that there exist at least four types of LAOS behavior: type I, strain thinning (G′, G″ decreasing); type II, strain hardening (G′, G″ increasing); type III, weak strain overshoot (G′ decreasing, G″ increasing followed by decreasing); type IV, strong strain overshoot (G′, G″ increasing followed by decreasing). It is suggested that the LAOS behavior can be effectively used as a tool for classifying the complex fluids.

Large amplitude oscillatory shear as a way to classify the complex fluids

The performance of the open source multiphase flow solver, interFoam, is evaluated in this work. The solver is based on a modified volume of fluid (VoF) approach, which incorporates an interfacial compression flux term to mitigate the effects of numerical smearing of the interface. It forms a part of the C + + libraries and utilities of OpenFOAM and is gaining popularity in the multiphase flow research community. However, to the best of our knowledge, the evaluation of this solver is confined to the validation tests of specific interest to the users of the code and the extent of its applicability to a wide range of multiphase flow situations remains to be explored. In this work, we have performed a thorough investigation of the solver performance using a variety of verification and validation test cases, which include (i) verification tests for pure advection (kinematics), (ii) dynamics in the high Weber number limit and (iii) dynamics of surface tension-dominated flows. With respect to (i), the kinematics tests show that the performance of interFoam is generally comparable with the recent algebraic VoF algorithms; however, it is noticeably worse than the geometric reconstruction schemes. For (ii), the simulations of inertia-dominated flows with large density ratios yielded excellent agreement with analytical and experimental results. In regime (iii), where surface tension is important, consistency of pressure–surface tension formulation and accuracy of curvature are important, as established by Francois et al (2006 J. Comput. Phys. 213 141–73). Several verification tests were performed along these lines and the main findings are: (a) the algorithm of interFoam ensures a consistent formulation of pressure and surface tension; (b) the curvatures computed by the solver converge to a value slightly (10%) different from the analytical value and a scope for improvement exists in this respect. To reduce the disruptive effects of spurious currents, we followed the analysis of Galusinski and Vigneaux (2008 J. Comput. Phys. 227 6140–64) and arrived at the following criterion for stable capillary simulations for interFoam: where . Finally, some capillary flows relevant to atomization were simulated, resulting in good agreement with the results from the literature.

https://iopscience.iop.org/article/10.1088/1749-4699/5/1/014016/pdf

Evaluating the performance of the two-phase flow solver interFoam

The deformations and stresses during squeeze flows are evaluated for a wider class of materials than previously covered in articles on this subject. These include generalised Newtonian fluids, yield stress fluids, as well as elastic and viscoelastic materials. Wherever possible, results are given in a compact mathematical form. The effect of different boundary conditions (no slip, perfect slip and partial slip) and how these interact with different types of material behaviour to give a variety of macroscopic responses is also discussed. The significance of this in using squeeze flow as a rheometry method is highlighted and a state-of-the-art view of squeeze flow rheometry is given.

Squeeze flow theory and applications to rheometry: A review

A mathematical analysis of bubble growth in an expanding foam is presented. The analysis is based on a cell model whereby the foam is divided into spherical microscopic unit cells of equal and constant mass, each consisting of a liquid envelope (or shell) and a concentric spherical gas bubble. Expansion occurs by diffusion of a dissolved gas from the supersaturated envelope into the bubble. This cell model is capable of describing important qualitative features of a real system of numerous bubbles growing in close proximity to one another, and is intended as the building block of a global analysis of macroscopic foam expansion. The coupled algebraic and differential equations governing the growth of a cell are derived and solved numerically. Five dimensionless parameters are identified for the case of constant temperature and pressure outside the cell, and their effects are demonstrated through computer simulations of the system. Of these parameters, surface tension and initial radius prove to be of relatively little importance in the practical cases considered. The other parameters are the thermodynamic driving force, the cell mass (inversely proportional to the number density of bubbles), and the ratio of characteristic times for mass and momentum transport.

A study of the dynamics of foam growth: Analysis of the growth of closely spaced spherical bubbles

Dynamic oscillatory shear testing has been used to study the rheology of xanthan gum in the moderate concentration regime (500 2000 ppm but decrease substantially at lower xanthan gum concentrations. The broth sample is relatively insensitive to salt addition (especially for c>2000 ppm), and maintains higher levels of dynamic moduli at low concentrations in high salt, than the powdered sample. However, for c>2000 ppm in high salt, the dynamic properties of the broth sample are lower than those of the powdered sample. The indication is that the broth sample has a higher apparent molecular weight. Detailed studies of the effects of salt, temperature, and high shear on 5000 ppm xanthan gum solutions in dynamic, steady,...

Rheology of Xanthan Gum: Salt, Temperature, and Strain Effects in Oscillatory and Steady Shear Experiments

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/bit.260170218

Shear modification of enzyme kinetics

A theory for roll coating of a fluid onto a moving sheet is developed utilizing the usual “lubrication approximations.” The effects of fluid and operating parameters on coating thickness and pressure distribution are determined for a Newtonian fluid, and for a purely viscous non-Newtonian fluid obeying the Power Law. The results for these cases are obtained analytically, and are rather straightforward.



A viscoelastic fluid is considered, of a type which shows typical non-Newtonian shear behavior observed in polymer melts and solutions and which also exhibits normal stress behavior. Analytical solutions are not possible, but a perturbation method, using a viscoelastic perturbation parameter related to a Deborah number, yields an approximate solution. Only terms to first order in the perturbation parameter are given. Subject to that degree of approximation, the following conclusions are drawn: 

1
Non-Newtonian shear behavior reduces the pressure distribution, and increases the coating thickness.

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Elasticity of the type usually observed in polymer solutions makes only a minor contribution to the roll-separating (load-carrying) force. The contribution is positive, but smaller than the corresponding negative contribution due to the non-Newtonian shear effects.

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An increase in load-carrying capacity would require a different viscoelastic fluid than the type considered here—one that is essentially Newtonian in shear but, independently, capable of developing significant normal stresses.

A theory of roll coating of viscous and viscoelastic fluids

Air entrainment in a roll coating system

General expressions for determining the pressure coefficient and axial distribution of the viscosity and pressure in capillary flow are derived for Newtonian and shear-thinning fluids. The pressure-dependent viscosity model is obtained from the WLF equation as derived from Doolittle's free volume theory. The model has also been derived from Eyring's hole theory for viscosity. Poiseuille's equation is modified to correct for the pressure effect on viscosity. A Newtonian, low-molecular-weight polystyrene and a shear-thinning, high-molecular-weight polystyrene were tested in an Instron capillary rheometer. The axial velocity distribution was found to be negligibly affected by pressure whereas the viscosity was shown to increase markedly with a decrease in volume. The resulting pressure effects on the viscosity of both samples were analyzed by using the derived expressions.

Stanley Middleman

Papers

Rheology of Xanthan Gum: Salt, Temperature, and Strain Effects in Oscillatory and Steady Shear Experiments

Shear modification of enzyme kinetics

A theory of roll coating of viscous and viscoelastic fluids

Air entrainment in a roll coating system

Determination of the pressure coefficient and pressure effects in capillary flow