Locomotion in complex fluids: Integral theorems

Abstract

The biological fluids encountered by self-propelled cells display complex microstructures and rheology. We consider here the general problem of low-Reynolds number locomotion in a complex fluid. {Building on classical work on the transport of particles in viscoelastic fluids,} we demonstrate how to mathematically derive three integral theorems relating the arbitrary motion of an isolated organism to its swimming kinematics {in a non-Newtonian fluid}. These theorems correspond to three situations of interest, namely (1) squirming motion in a linear viscoelastic fluid, (2) arbitrary surface deformation in a weakly non-Newtonian fluid, and (3) small-amplitude deformation in an arbitrarily non-Newtonian fluid. Our final results, valid for a wide-class of {swimmer geometry,} surface kinematics and constitutive models, at most require mathematical knowledge of a series of Newtonian flow problems, and will be useful to quantity the locomotion of biological and synthetic swimmers in complex environments.

References in corpus (8)

• The hydrodynamics of swimming microorganisms
• Propulsion in a viscoelastic fluid
• Swimming speeds of filaments in nonlinearly viscoelastic fluids
• Theory of swimming filaments in viscoelastic media
• Fluid elasticity increases the locomotion of flexible swimmers
• Locomotion by tangential deformation in a polymeric fluid
• Flapping motion and force generation in a viscoelastic fluid
• Pumping by flapping in a viscoelastic fluid

Cited by in corpus (7)

• Can the self-propulsion of anisotropic microswimmers be described by using forces and torques?
• Helical propulsion in shear-thinning fluids
• Force moments of an active particle in a complex fluid
• Swimming efficiency in a shear-thinning fluid
• Autophoretic locomotion in weakly viscoelastic fluids at finite Péclet number
• The mechanism of propulsion of a model microswimmer in a viscoelastic fluid next to a solid boundary
• Biopolymer dynamics driven by helical flagella