skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: A reexamination of the Cox–Merz rule through the lens of recovery rheology
Empirical rules play a crucial role in industrial and experimental settings for efficiently determining the rheological properties of materials, thereby saving both time and resources. An example is the Cox–Merz rule, which equates the steady-shear viscosity with the magnitude of the complex viscosity obtained in oscillatory tests. This empirical rule provides access to the steady-shear viscosity that is useful for processing conditions without the instabilities associated with experiments at high shear rates. However, the Cox–Merz rule is empirical and has been shown to work in some cases and fail in others. The underlying connection between the different material functions remains phenomenological and the lack of a comprehensive understanding of the rheological physics allows for ambiguity to persist in the interpretation of material responses. In this work, we revisit the Cox–Merz rule using recovery rheology, which decomposes the strain into recoverable and unrecoverable components. When viewed through the lens of recovery rheology, it is clearly seen that the steady-shear viscosity comes from purely unrecoverable acquisition of strain, while the complex viscosity is defined in terms of contributions from both recoverable and unrecoverable components. With recovery tests in mind, we elucidate why the Cox–Merz rule works only in a limited set of conditions and present an approach that could allow for universal comparisons to be made. This work further highlights the significance of recovery rheology by showing how it is possible to extend beyond phenomenological approaches through clear rheophysical metrics obtained by decomposing the material response into recoverable and unrecoverable components.  more » « less
Award ID(s):
1847389
PAR ID:
10508404
Author(s) / Creator(s):
; ;
Publisher / Repository:
AIP Publishing
Date Published:
Journal Name:
Journal of Rheology
Volume:
68
Issue:
3
ISSN:
0148-6055
Page Range / eLocation ID:
381 to 396
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Aqueous foams are ubiquitous; they appear in products and processes that span the cosmetics, food, and energy industries. The versatile applicability of foams comes as a result of their intrinsic viscous and elastic properties; for example, foams are exploited as drilling fluids in enhanced oil recovery for their high viscosity. Recently, so-called capillary foams were discovered: a class of foams that have excellent stability under static conditions and whose flow properties have so far remained unexplored. The unique architecture of these foams, containing oil-coated bubbles and a gelled network of oil-bridged particles, is expected to affect foam rheology. In this work, we report the first set of rheological data on capillary foams. We study the viscoelastic properties of capillary foams by conducting oscillatory and steady shear tests. We compare our results on the rheological properties of capillary foams to those reported for other aqueous foams. We find that capillary foams, which have low gas volume fractions, exhibit long lasting rheological stability as well as a yielding behavior that is reminiscent of surfactant foams with high gas volume fractions. 
    more » « less
  2. Graphene oxide (GO) has attracted attention in materials science and engineering due to its large aspect ratio and dispersibility in polar solvent including water. It has recently been applied to direct-ink-writing (DIW) printing to realize the fabrication of three-dimensional structures, suggesting a wide variety of potential applications. Without post-processing, DIW printing requires yield stress fluids to fully build three-dimensional objects. The key properties of these inks are the yield stress and the viscoelastic properties during yielding. DIW ink rheology has therefore received significant interest in materials science, as well as mechanical and chemical engineering. Despite this interest, the yielding process has not been clearly elucidated and understanding yielding remains an outstanding problem. In this study, we discuss the yielding behavior of GO colloids via oscillatory rheology by decomposing the total strain into the recoverable and unrecoverable parts through iterative experimental techniques. The recoverable and unrecoverable responses represent viscoelastic solid and plastic properties, respectively, and they are used to determine the averaged storage and dissipation of energies. By mapping these contributions, we more clearly elucidate the yielding behavior of the GO colloids and suggest guidelines for energy efficiency. Beyond the specific lessons learned regarding the DIW-relevant rheology of GO colloids, our study contributes to an evolving development of material-centric and energy-focused methods for understanding the out-of-equilibrium rheological physics associated with the yielding of soft materials. 
    more » « less
  3. We probe the microstructural yielding dynamics of a concentrated colloidal system by performing creep/recovery tests with simultaneous collection of coherent scattering data via X-ray Photon Correlation Spectroscopy (XPCS). This combination of rheology and scattering allows for time-resolved observations of the microstructural dynamics as yielding occurs, which can be linked back to the applied rheological deformation to form structure–property relations. Under sufficiently small applied creep stresses, examination of the correlation in the flow direction reveals that the scattering response recorrelates with its predeformed state, indicating nearly complete microstructural recovery, and the dynamics of the system under these conditions slows considerably. Conversely, larger creep stresses increase the speed of the dynamics under both applied creep and recovery. The data show a strong connection between the microstructural dynamics and the acquisition of unrecoverable strain. By comparing this relationship to that predicted from homogeneous, affine shearing, we find that the yielding transition in concentrated colloidal systems is highly heterogeneous on the microstructural level. 
    more » « less
  4. Materials that exhibit yielding behavior are used in many applications, from spreadable foods and cosmetics to direct write three-dimensional printing inks and filled rubbers. Their key design feature is the ability to transition behaviorally from solid to fluid under sufficient load or deformation. Despite its widespread applications, little is known about the dynamics of yielding in real processes, as the nonequilibrium nature of the transition impedes understanding. We demonstrate an iteratively punctuated rheological protocol that combines strain-controlled oscillatory shear with stress-controlled recovery tests. This technique provides an experimental decomposition of recoverable and unrecoverable strains, allowing for solid-like and fluid-like contributions to a yield stress material’s behavior to be separated in a time-resolved manner. Using this protocol, we investigate the overshoot in loss modulus seen in materials that yield. We show that this phenomenon is caused by the transition from primarily solid-like, viscoelastic dissipation in the linear regime to primarily fluid-like, plastic flow at larger amplitudes. We compare and contrast this with a viscoelastic liquid with no yielding behavior, where the contribution to energy dissipation from viscous flow dominates over the entire range of amplitudes tested. 
    more » « less
  5. Understanding the yielding of complex fluids is an important rheological challenge that affects our ability to engineer and process materials for a wide variety of applications. Common theoretical understandings of yield stress fluids follow the Oldroyd–Prager formalism in which the material behavior below the yield stress is treated as solidlike, and above the yield stress as liquidlike, with an instantaneous transition between the two states. This formalism was built on a quasi-static approach to the yield stress, while most applications, ranging from material processing to end user applications, involve a transient approach to yielding over a finite timescale. Using stress-controlled oscillatory shear experiments, we show that yield stress fluids flow below their yield stresses. This is quantified through measuring the strain shift, which is the value about which the strain oscillates during a stress-controlled test and is a function of only the unrecoverable strain. Measurements of the strain shift are, therefore, measurements of flow having taken place. These experimental results are compared to the Herschel–Bulkley form of the Saramito model, which utilizes the Oldroyd–Prager formalism, and the recently published Kamani–Donley–Rogers (KDR) model, in which one constitutive equation represents the entire range of material responses. Scaling relationships are derived, which allow us to show why yield stress fluids will flow across all stresses, above and below their yield stress. Finally, derivations are presented that show strain shift can be used to determine average metrics previously attainable only through recovery rheology, and these are experimentally verified. 
    more » « less