The shear stress in a suspension arises from the cumulative contributions of individual particle stresses. In concentrated suspensions of soft particles—such as micelles, microgels, and emulsions—these stresses are inherently distributed. Even at rest, such suspensions exhibit a range of positive and negative particle stresses that, on average, sum to zero. We introduce a Smoluchowski model to predict the distribution of particle stresses under three conditions: at rest, under steady shear, and during the transition from rest to steady shear. The model accounts for both the applied shear and the kinetics of stress transitions between particle states. These transition rates are critical for accurately capturing the observed stress distributions across flow regimes. A key feature of the model is an Arrhenius-type transition rate, governed by the free energy difference between the initial and final stress states of a particle. By applying Taylor dispersion theory, we reformulate the kinetic model as an advection-diffusion equation, where stress mobility is proportional to a single kinetic rate constant, and the effective temperature corresponds to the average elastic energy of interparticle contacts. At equilibrium, the model predicts a Boltzmann distribution of particle stresses. It also successfully captures the transient evolution of shear stress during startup flows, including the characteristic stress overshoot. Potential extensions to other types of concentrated suspensions are discussed.
