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.

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Cited by in corpus (22)

• Bacterial hydrodynamics
• Squirming through shear-thinning fluids
• Exact solutions for hydrodynamic interactions of two squirming spheres
• Can the self-propulsion of anisotropic microswimmers be described by using forces and torques?
• Helical propulsion in shear-thinning fluids
• An active particle in a complex fluid
• The effect of gait on swimming in viscoelastic fluids
• Force moments of an active particle in a complex fluid
• The many-body reciprocal theorem and swimmer hydrodynamics
• A note on the reciprocal theorem for the swimming of simple bodies
• 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
• Jeffery's orbits and microswimmers in flows: A theoretical review
• Viscoelastic propulsion of a rotating dumbbell
• Higher-order force moments of active particles
• Diffusiophoretic propulsion of an isotropic active colloidal particle near a finite-sized disk embedded in a planar fluid-fluid interface
• Self-diffusiophoretic propulsion of a spheroidal particle in a shear-thinning fluid
• Biopolymer dynamics driven by helical flagella
• Jet-driven viscous locomotion of confined thermoresponsive microgels
• Viscoelastic levitation
• Pressure drop reduction due to coupling between shear-thinning fluid flow and a weakly deformable channel wall: A reciprocal theorem approach