Hydrodynamic effects in driven soft matter

TL;DR

This paper reviews recent theoretical advances in understanding how hydrodynamic interactions influence the behavior of deformable soft matter systems in non-equilibrium conditions, highlighting new effects arising from elasticity-hydrodynamics coupling.

Contribution

It introduces new insights into the role of hydrodynamics in soft matter deformation and propulsion, emphasizing the coupling between elasticity and hydrodynamic torques in non-equilibrium states.

Findings

Elasticity induces orientation in sedimenting polymers.

Bending enables net propulsion in rotating elastic rods.

Shear flow deforms grafted polymers, altering hydrodynamic boundary conditions.

Abstract

Recent theoretical works exploring the hydrodynamics of soft material in non-equilibrium situations are reviewed. We discuss the role of hydrodynamic interactions for three different systems: i) the deformation and orientation of sedimenting semiflexible polymers, ii) the propulsion and force-rectification with a nano-machine realized by a rotating elastic rod, and iii) the deformation of a brush made of grafted semiflexible polymers in shear flows. In all these examples deformable polymers are subject to various hydrodynamic flows and hydrodynamic interactions. Perfect stiff nano-cylinders are known to show no orientational effects as they sediment through a viscous fluid, but it is the coupling between elasticity and hydrodynamic torques that leads to an orientation perpendicular to the direction of sedimentation. Likewise, a rotating stiff rod does not lead to a net propulsion in the Stokes limit, but if bending is allowed an effective thrust develops whose strength and direction is independent of the sense of rotation and thus acts as a rectification device. Lastly, surface-anchored polymers are deformed by shear flows, which modifies the effective hydrodynamic boundary condition in a non-linear fashion. All these results are obtained with hydrodynamic Brownian dynamics simulation techniques, as appropriate for dilute systems. Scaling analyses are presented when possible. The common theme is the interaction between elasticity of soft matter and hydrodynamics, which can lead to qualitatively new effects.