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Recent experiments imaging fluid flow around swimming microorganisms haverevealed complex time-dependent velocity fields that differ qualitatively fromthe stresslet flow commonly employed in theoretical descriptions of activematter. Here we obtain the most general flow around a finite sized activeparticle by expanding the surface stress in irreducible Cartesian tensors. Thisexpansion, whose first term is the stresslet, must include, respectively,third-rank polar and axial tensors to minimally capture crucial features of theactive oscillatory flow around translating Chlamydomonas and the activeswirling flow around rotating Volvox. The representation provides explicitexpressions for the irreducible symmetric, antisymmetric and isotropic parts ofthe continuum active stress. Antisymmetric active stresses do not conserveorbital angular momentum and our work thus shows that spin angular momentum isnecessary to restore angular momentum conservation in continuum hydrodynamicdescriptions of active soft matter.

Irreducible Representations Of Oscillatory And Swirling Flows In Active Soft Matter