Article

# Pumping by flapping in a viscoelastic fluid.

Department of Mechanical and Aerospace Engineering, University of California-San Diego, 9500 Gilman Drive, La Jolla, California 92093-0411, USA.

Physical Review E (Impact Factor: 2.31). 03/2010; 81(3 Pt 2):036312. DOI: 10.1103/PhysRevE.81.036312 Source: arXiv

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**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.10/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**In the absence of inertia, a reciprocal swimmer achieves no net motion in a viscous Newtonian fluid. Here, we investigate the ability of a reciprocally actuated particle to translate through a complex, "structured" fluid using tracking methods and birefringence imaging. A geometrically polar particle, a rod with a bead on one end, is reciprocally rotated using magnetic fields. The particle is immersed in a wormlike micellar solution that is known to be susceptible to shear banding and the formation of local anisotropic structures. Results show that the nonlinearities present in this structured fluid break time-reversal symmetry under certain conditions, and enable propulsion of an artificial "swimmer." We find three regimes dependent on the Deborah number (De): net motion towards the bead at low De, net motion towards the rod at intermediate De, and no propulsion at high De. At low De, we believe propulsion is caused by an imbalance in the first normal stress differences between the two ends of the particle (bead and rod). However, at De~1, we observe network anisotropy near the rod using birefringence imaging, indicating alignment of the micellar structure, which is "locked in" due to the shorter timescale of the particle relative to the fluid. The development of these structures reverses the direction and magnitude of the imbalance in first normal stress differences, and suggests the particle is actively remodeling the microstructure, thus providing the nonlinearity required for propulsion.02/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**Microorganisms such as bacteria often swim in fluid environments that cannot be classified as Newtonian. Many biological fluids contain polymers or other heterogeneities which may yield complex rheology. For a given set of boundary conditions on a moving organism, flows can be substantially different in complex fluids, while non-Newtonian stresses can alter the gait of the microorganisms themselves. Heterogeneities in the fluid may also be characterized by length scales on the order of the organism itself leading to additional dynamic complexity. In this chapter we present a theoretical overview of small-scale locomotion in complex fluids with a focus on recent efforts quantifying the impact of non-Newtonian rheology on swimming microorganisms.10/2014;

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