Generalized Navier-Stokes equations for active suspensions

TL;DR

This paper introduces a generalized version of the Navier-Stokes equations to model active suspensions, incorporating nonlocal stress effects to better understand the fluid dynamics driven by active components.

Contribution

It proposes a novel nonlocal extension of the stress tensor in the Navier-Stokes framework for active suspensions, with analytical and numerical analysis of stability and spectral properties.

Findings

The model captures the influence of active components on solvent flow.

Stability analysis reveals conditions for flow behavior.

Numerical simulations demonstrate the model's applicability.

Abstract

We discuss a minimal generalization of the incompressible Navier-Stokes equations to describe the solvent flow in an active suspension. To account phenomenologically for the presence of an active component driving the ambient fluid flow, we postulate a generic nonlocal extension of the stress-tensor, conceptually similar to those recently introduced in granular media flows. Stability and spectral properties of the resulting hydrodynamic model are studied both analytically and numerically for the two-dimensional (2D) case with periodic boundary conditions. Future generalizations of this momentum-conserving theory could be useful for quantifying the shear properties of active suspensions.