Higher-order force moments of active particles

TL;DR

This paper extends the modeling of active particles in fluids by including higher-order force moments, providing more accurate flow field predictions for arbitrarily-shaped particles beyond the leading-order approximations.

Contribution

It introduces explicit formulas for second-order force moments and applies them to derive improved flow models for various particle shapes.

Findings

Derived explicit formulas for stresslet dipole, rotlet dipole, and potential dipole.

Provided modified Faxén laws for active spherical particles.

Resolved higher-order moments for active rod-like particles.

Abstract

Active particles moving through fluids generate disturbance flows due to their activity. For simplicity, the induced flow field is often modeled by the leading terms in a far-field approximation of the Stokes equations, whose coefficients are the force, torque and stresslet (zeroth and first-order force moments) of the active particle. This level of approximation is quite useful, but may also fail to predict more complex behaviors that are observed experimentally. In this study, to provide a better approximation, we evaluate the contribution of the second-order force moments to the flow field and, by reciprocal theorem, present explicit formulas for the stresslet dipole, rotlet dipole and potential dipole for an arbitrarily-shaped active particle. As examples of this method, we derive modified Fax\'en laws for active spherical particles and resolve higher-order moments for active rod-like particles.