Spatial averaging of a dissipative particle dynamics model for active suspensions

TL;DR

This paper derives meso-scale stochastic continuum equations from a fine-scale dissipative particle dynamics model of active suspensions using spatial averaging, valid for highly concentrated systems and incorporating fluctuation forces.

Contribution

It introduces a spatial averaging method to derive continuum equations from DPD models of active particles without relying on kinetic theory, including a novel constitutive relation for fluctuation forces.

Findings

Derived stochastic continuum equations similar to Toner and Tu's models.

Included a constitutive equation for fluctuation forces dependent on local density.

Demonstrated the inclusion of nonlinear internal body forces despite lack of explicit alignment mechanisms.

Abstract

Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving--Kirkwood--Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields a stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.