**A Review of Nonlinear Oscillatory Shear Tests: Analysis and Application of Large Amplitude Oscillatory Shear (LAOS)**

By Hyun, K., Wilhelm, M., Klein,
C.O., Cho, K.S., Nam, J.G., Ahn, K.H., Lee, S.J., Ewoldt, R.H. and McKinley,
G.H.

Dynamic oscillatory shear tests
are common in rheology and have been used to investigate a wide range
of soft matter and complex fluids including polymer melts and
solutions, block copolymers, biological macromolecules,
polyelectrolytes, surfactants, suspensions, emulsions and beyond. More
specifically, Small Amplitude Oscillatory Shear (SAOS) tests have
become the canonical method for probing the linear viscoelastic
properties of these complex fluids because of the firm theoretical
background [1-4] and the ease of implementing suitable test protocols.
However, in most processing operations the deformations can be large
and rapid: it is therefore the nonlinear material properties that
control the system response. A full sample characterization thus
requires well-defined nonlinear test protocols. Consequently there has
been a recent renewal of interest in exploiting Large Amplitude
Oscillatory Shear (LAOS) tests to investigate and quantify the
nonlinear viscoelastic behavior of complex fluids. In terms of the
experimental input, both LAOS and SAOS require the user to select
appropriate ranges of strain amplitude (γ

_{0}) and frequency
(ω). However, there is a distinct difference in the analysis of
experimental output, i.e. the material response. At sufficiently large
strain amplitude, the material response will become nonlinear in LAOS
tests and the familiar material functions used to quantify the linear
behavior in SAOS tests are no longer sufficient. For example, the
definitions of the linear viscoelastic moduli G΄(ω) and G˝(ω) are based
inherently on the assumption that the stress response is purely
sinusoidal (linear). However, a nonlinear stress response is not a
perfect sinusoid and therefore the viscoelastic moduli are not uniquely
defined; other methods are needed for quantifying the nonlinear
material response under LAOS deformation. In the present review
article, we first summarize the typical nonlinear responses observed
with complex fluids under LAOS deformations. We then introduce and
critically compare several methods that quantify the nonlinear
oscillatory stress response. We illustrate the utility and sensitivity
of these protocols by investigating the nonlinear response of various
complex fluids over a wide range of frequency and amplitude of
deformation, and show that LAOS characterization is a rigorous test for
rheological models and advanced quality control.

Keywords: LAOS (Large amplitude oscillatory shear), nonlinear response, FT-Rheology, Stress Decomposition