A note on the translation of a thin rod inside a cylinder

Manero, Ο.; Mena, B.; Vargas, Lourdes de

doi:10.1007/bf01329441

Cited by 6 publications

(1 citation statement)

References 2 publications

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“…The role of the aspect ratio of cylindrical rods has been studied in inelastic and elastic fluids, showing that drag coefficients reduce by about one order of magnitude over aspect ratios ranging from 1/150 to 1/10 [42]. Comparing these experimental result to semiempirical predictions, despite qualitative agreement, the drag coefficient was overestimated by theoretical predictions [43,44]. Comparable studies have also probed wall effects [39,45], different cross sections [46] and interactions between particles [47].…”

Section: Introductionmentioning

confidence: 99%

Empirical resistive-force theory for slender biological filaments in shear-thinning fluids

Riley

Lauga

2017

Phys. Rev. E

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Many cells exploit the bending or rotation of flagellar filaments in order to self-propel in viscous fluids. While appropriate theoretical modelling is available to capture flagella locomotion in simple, Newtonian fluids, formidable computations are required to address theoretically their locomotion in complex, nonlinear fluids, e.g. mucus. Based on experimental measurements for the motion of rigid rods in non-Newtonian fluids and on the classical Carreau fluid model, we propose empirical extensions of the classical Newtonian resistive-force theory to model the waving of slender filaments in non-Newtonian fluids. By assuming the flow near the flagellum to be locally Newtonian, we propose a self-consistent way to estimate the typical shear-rate in the fluid, which we then use to construct correction factors to the Newtonian local drag coefficients. The resulting non-Newtonian resistiveforce theory, while empirical, is consistent with the Newtonian limit, and with the experiments. We then use our models to address waving locomotion in non-Newtonian fluids, and show that the resulting swimming speeds are systematically lowered -a result which we are able to capture asymptotically and to interpret physically. An application of the models to recent experimental results on the locomotion of Caenorhabditis elegans in polymeric solutions shows reasonable agreement and thus captures the main physics of swimming in shear-thinning fluids.

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