Fractional rheology of methylcellulose thermogelation

Methylcellulose is well known for its thermoreversible gelation. Here, we utilize a fractional viscoelastic constitutive framework to analyze the time-, temperature-, and concentration-dependent behavior of the thermorheologically complex system formed by methylcellulose in water. We characterize the viscoelastic moduli using small amplitude oscillatory shear tests conducted over a wide temperature range (15 ≤ T ≤ 80 °C), which captures the evolving rheological responses associated with fibrillar microstructure formation on heating and dissolution on cooling. Depending on the temperature, the measured rheological responses are well described by the Scott Blair model of a critical gel or the fractional Kelvin–Voigt spring model, which provide a compact description of the evolving viscoelastic properties of methylcellulose. Below the fibril formation temperature, we observe the rheological response of a “clear gel” sustained by transient hydrophobic associations. Upon fibril formation, we observe a substantial change in the viscoelastic properties; the storage modulus grows dramatically, leading to the formation of highly elastic fibrillar gels whose power-law rheology is well described by the Scott Blair model. These changes with temperature and frequency are represented using a Cole–Cole representation. A distinct thermal hysteresis is associated with the thermogelation transition, which depends on the heating or cooling rate imposed. Analysis of the evolution in the material properties with temperature and concentration shows that a phenomenological scaling law effectively describes the fibril formation and dissolution processes across a range of methylcellulose compositions. This scaling law simplifies the analysis of large datasets and provides physical interpretability of the observed thermogelation phenomena.