Fractional rheology of colloidal hydrogels with cellulose nanofibers

Colloidal gels are soft solids composed of particles dispersed in a fluid phase. Their rheological behavior highly depends on the particle concentration, but establishing a relationship can be challenging. This article showcases the potential of fractional rheology to model and predict linear viscoelastic responses of colloidal hydrogels containing TEMPO-oxidized cellulose nanofibers. Cellulose nanofiber hydrogels are soft solids whose rheology is directly related to the particle concentration. Therefore, this work defined the rheological behavior of the hydrogels using a fractional order derivative analytically solved to determine rheological responses in frequency, stress relaxation, and creep. Using two parameters, it evaluated the rheology of cellulose nanofiber hydrogels and established tests that predict rheological behaviors for given particle concentrations. The findings suggested that the fractional approach could become a standard method for characterizing cellulose nanofiber hydrogels in the reported concentration regime. The two parameters of the fractional model build a comparison framework to assess the rheology of different viscoelastic materials.