Brownian dynamics simulation on the parallel superposition rheology of a colloidal gel

Parallel superposition rheology has been explored using Brownian dynamics simulations on a model colloidal gel by imposing a small amplitude probing oscillation parallel to the main shear flow. This study aims to investigate the constituting principles behind the material functions in parallel superposition rheometry (PSR) and to elucidate the principles behind the structure responses. The viscoelastic spectra under frequency sweeps show that in a high-frequency region, each curve can be superimposed onto a single master curve using horizontal shift factors equal to viscosity which is a reminiscence of time-shear rate superposition in orthogonal superposition rheometry. This corresponds to the region where a parallel superposition analysis can be adequately performed as the shear rate controls the viscoelastic spectra of the gel independently from probing perturbation. On the other hand, in the low-frequency region, this principle breaks down and even negative storage modulus is observed due to the strong flow coupling effect, which is also found in experiments. By introducing the spatial moduli, it is found that the negative modulus originates from the attractive potential region. In the flow conditions where negative modulus occurs, the shear force is strong enough to break down every surface bond between the particles. In this state, the increase in structural factor in response to the rise in the shear rate dominates particle stress, even within the attractive potential region. This arises because the isolated particles have more opportunities to interact with other particles as the shear rate of the imposed perturbation increases. This structural response, influenced by the attractive potential, results in a negative storage modulus and a positive loss modulus after performing Fourier transformation. This paper, for the first time by a simulation approach, demonstrates the essential characteristics of the material functions obtained using PSR. Also, this study is expected to enhance our understanding on the flowing materials and suggest a criterion for the reliable application of superposition rheology using a viscoelastic master curve.