Many biological fluids display shear-thinning rheology, where the viscosity decreases with an increasing shear rate. To better understand how this non-Newtonian rheology affects the motion of biological and artificial micro swimmers, recent efforts have begun to seek answers to fundamental questions about active bodies in shear-thinning fluids. Previous analyses based on a squirmer model have revealed non-trivial variations of propulsion characteristics in a shear-thinning fluid via the reciprocal theorem. However, the reciprocal theorem approach does not provide knowledge about the flow surrounding the squirmer. In this work, we fill in this missing information by calculating the non-Newtonian correction to the flow analytically in the asymptotic limit of small Carreau number. In particular, we investigate the local effect due to viscosity reduction and the non-local effect due to induced changes in the flow; we then quantify their relative importance to locomotion in a shear-thinning fluid. Our results demonstrate cases where the non-local effect can be more significant than the local effect. These findings suggest that caution should be exercised when developing physical intuition from the local viscosity distribution alone around a swimmer in a shear-thinning fluid.
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Tel Aviv Univ, Sch Mech Engn, IL-6997801 Tel Aviv, Israel
Soreq NRC, IL-8180000 Yavne, IsraelTel Aviv Univ, Sch Mech Engn, IL-6997801 Tel Aviv, Israel
Barmak, Ilya
Picchi, Davide
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Univ Brescia, Dept Mech & Ind Engn, Via Branze 38, I-25123 Brescia, ItalyTel Aviv Univ, Sch Mech Engn, IL-6997801 Tel Aviv, Israel
Picchi, Davide
Gelfgat, Alexander
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Tel Aviv Univ, Sch Mech Engn, IL-6997801 Tel Aviv, IsraelTel Aviv Univ, Sch Mech Engn, IL-6997801 Tel Aviv, Israel
Gelfgat, Alexander
Brauner, Neima
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Tel Aviv Univ, Sch Mech Engn, IL-6997801 Tel Aviv, IsraelTel Aviv Univ, Sch Mech Engn, IL-6997801 Tel Aviv, Israel
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Univ Bologna Alma Mater Studiorum, Dipartimento Ingn Civile Ambientale & Mat DICAM, I-40136 Bologna, ItalyUniv Bologna Alma Mater Studiorum, Dipartimento Ingn Civile Ambientale & Mat DICAM, I-40136 Bologna, Italy