A Continuum Framework for Dense Suspensions of Self-Propelled Elongated Particles

We derive a thermodynamically consistent continuum model for a dense suspension of active elongated particles in a fluid by spatially averaging the microscopic equations of motion. The active particles are modeled as Janus particles that generate self-propulsion through prescribed surface stresses at the microscopic scale. Short-range forces and torques induce local alignment of the particles, represented by a unit vector field describing both their orientation and swimming direction. Following a common approach in nematic liquid crystal modeling, we represent spatial distortions of the orientation field and the related elastic energy using the Oseen–Frank energy, which quantifies the energetic cost of non-uniform alignment. Unclosed terms, such as the particle-phase stress and the interphase interaction force, are expressed in terms of microscopic quantities like surface forces exerted by the fluid or neighboring particles. Closure relations are then derived based on the second law of thermodynamics. The resulting two-phase description couples a classical fluid (solvent) with a micropolar fluid (particle phase), incorporating rotational degrees of freedom. We apply the resulting model to a relatively simple flow configuration and solve it numerically. The novelty of the model is its ability to capture the essential properties of active suspensions by allowing distinct velocities for the fluid and particle phases, resulting in a more accurate description of dense suspensions.