Large amplitude oscillatory shear study of a colloidal gel near the critical state

Abstract

A system undergoing sol-gel transition passes through a unique point, known as the critical gel state, where it forms the weakest space spanning percolated network. We investigate the nonlinear viscoelastic behavior of a colloidal dispersion at the critical gel state using large amplitude oscillatory shear (LAOS) rheology. The colloidal gel at the critical point is subjected to oscillatory shear flow with increasing strain amplitude at different frequencies. We observe that the first harmonic of the elastic and viscous moduli exhibits a monotonic decrease as the material undergoes a linear to nonlinear transition. We analyze the stress waveform across this transition, and obtain the nonlinear moduli and viscosity as a function of frequency and strain amplitude. The analysis of the nonlinear moduli and viscosities suggests intracycle strain stiffening and intracycle shear thinning in the colloidal dispersion. Based on the insights obtained from the nonlinear analysis, we propose a potential scenario of the microstructural changes occurring in the nonlinear region. We also develop an integral model using the time-strain separable K-BKZ constitutive equation with a power-law relaxation modulus and damping function obtained from experiments. The proposed model with slight adjustment of the damping function, inferred using a spectral method, compares well with experimental data at all frequencies.

The Method of Harmonic Balance for the Giesekus Model under Oscillatory Shear

“…Bayesian inference of model parameters [21], which requires the model to be evaluated thousands of times [56,57]. The goal of this work is to adopt a similar technique for differential constitutive models in LAOS.…”

“…Here, K is a N × N diagonal matrix with constant coefficients, f nl is a N × 1 vector of nonlinear functions of the dependent variable y, and f ex contains the external oscillatory forcing function. Substituting equation (21) into (27), and using equations ( 24) and ( 25), we obtain,…”

“…As γ 0 and ω increase, the behavior becomes increasingly nonlinear. Such large amplitude oscillatory shear (LAOS) measurements have been extensively used to study rheological phenomena including shear thinning/thickening and strain softening/hardening [1,2,3,4], timedependent structural buildup or breakage [5,6,7,8,9,10], pseudoplasticity and elastoviscoplasticity [11,12,8], shear banding [13,14,15,16], wall slip [17,18,19,20], gelation [21,22,23,24], chain stretch and entanglement in polymeric systems [25,26,27,28,29,30], etc. Several analytical approaches have been introduced to interpret experimental LAOS data including Fourier series [31], power series [32], Pade approximants [33], Chebyshev polynomi-als [34], stress decomposition methods [35,36], characterstic waveforms [19], weakly nonlinear intrinsic parameters [37], sequence of physical processes [38], etc.…”

Understanding Gel-Powers: Exploring Rheological Marvels of Acrylamide/Sodium Alginate Double-Network Hydrogels

“…In polymer processing, rheology bridges the molecular structure and processing properties. The guidance of rheology is widely used in industrial polymer chemistry and processing technology [ 41 ].…”

“…LAOS data analysis is crucial for interpreting complex rheological behavior, and various methods, such as Lissajous curves and Fourier transforms, have been used. LAOS characterization of biopolymers provides a better understanding of rheological behavior and can simulate actual polymer processing conditions [ 40 , 41 , 47 , 55 , 60 , 61 , 64 , 65 , 66 , 67 , 68 ].…”