Abstract
Abstract
Highlights
There has been a great deal of work on studying locomotion in complex fluids, because, most biological fluids exhibit non-Newtonian behaviour owing to the presence of large biomolecules embedded within them (Spagnolie 2015; Patteson, Gopinath & Arratia 2016)
Though, no one to date has yet considered if the squirmer model itself is mathematically well-behaved in the context of the nonlinear constitutive models commonly used to model viscoelastic fluids such as the upper-convected Maxwell (UCM), Oldroyd-B, Giesekus and finite-extensibility nonlinear elastic model with the Peterlin approximation (FENE-P) models
We show that the radius of convergence of asymptotic, perturbation, solutions in terms of the Weissenberg number, Wi, applied to squirming in elastic fluids is very small, necessitating the use of techniques that accelerate the convergence of series (Housiadas 2017), where Wi, defined in § 2, gives a measure of the elasticity of the ambient fluid
Summary
There has been a great deal of work on studying locomotion in complex fluids, because, most biological fluids exhibit non-Newtonian behaviour owing to the presence of large biomolecules embedded within them (Spagnolie 2015; Patteson, Gopinath & Arratia 2016). The velocity at the surface of a micro-swimmer is expressed as v (S) = This simplification is made since, in a Newtonian fluid, the swimming speed is determined solely by the value of B1, while B2 is the only coefficient that appears in the force that the fluid exerts on the particle. As is well known, the velocity of the micro-swimmer in a simple Newtonian fluid under creeping conditions is two-thirds of the coefficient of the first polar mode (Lighthill 1952; Blake 1971), i.e. V = 2B1/3 in dimensional units, and the rotation rate is ω = −C1/R3 (obviously, ω = 0 for C1 = 0). At the poles of the spherical coordinate system, the flow is purely extensional in character
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