A mesoscopic rheological model of moderately concentrated colloids

•We present an extended model for concentrated soft colloids.•Model considers topological interactions and large non ellipsoidal deformations.•Rheological response has been studied in steady and oscillatory solicitation.

We extend the Maffettone–Minale model by including non-elliptical shapes of dispersed particles, a new family of internal forces controlling particle deformations, and particle–particle interactions. The last extension is made by transposing the way the chain-chain interactions are mathematically expressed in the reptation theory to suspensions. The particle–particle interactions are regarded as a confinement to cages formed by surrounding particles and by introducing a new dissipative motion (an analog of the reptation motion) inside the cages. Nonlinear responses to imposed shear and elongational flows are found to be in qualitative agreement with available experimental data.