“…It must be noted that the Reynolds numbers here are significantly larger than in most previous studies dealing with the skin friction on a flapping foil (Ehrenstein and Eloy, 2013;Ehrenstein et al, 2014;Das et al, 2016Das et al, , 2022Gross et al, 2021). These computationally works for 𝑅𝑒 ≲ 10 3 confirmed the Bone-Lighthill boundary layer thinning hypothesis for uniform flow past oscillatory plates, with skin friction drag coefficients proportional to 𝑅𝑒 −1∕2 , like in Blasius flat plate, but multiplied by a factor proportional to the square root of the ratio of the transverse and longitudinal velocities.…”
Section: Numerical Results Modeling the Unsteady Viscous Dragsupporting
confidence: 71%
“…Labasse et al (2020) considered 𝑅𝑒 = 2000 for different 𝛼 0 , finding that Blasius-type scaling is not reliable, without providing any scaling law. Gross et al (2021) also considered the range 𝑅𝑒 ≳ 10 3 -10 4 , but neglected the viscous drag for these larger Reynolds numbers, considering only a constant pressure drag coefficient. Here, we use the expression (16) for the timeaverage viscous drag, while all the pressure forces, of any sign, will be modeled with analytical expressions from linear inviscid theory (Section 5 below).…”
Section: Numerical Results Modeling the Unsteady Viscous Dragmentioning
“…It must be noted that the Reynolds numbers here are significantly larger than in most previous studies dealing with the skin friction on a flapping foil (Ehrenstein and Eloy, 2013;Ehrenstein et al, 2014;Das et al, 2016Das et al, , 2022Gross et al, 2021). These computationally works for 𝑅𝑒 ≲ 10 3 confirmed the Bone-Lighthill boundary layer thinning hypothesis for uniform flow past oscillatory plates, with skin friction drag coefficients proportional to 𝑅𝑒 −1∕2 , like in Blasius flat plate, but multiplied by a factor proportional to the square root of the ratio of the transverse and longitudinal velocities.…”
Section: Numerical Results Modeling the Unsteady Viscous Dragsupporting
confidence: 71%
“…Labasse et al (2020) considered 𝑅𝑒 = 2000 for different 𝛼 0 , finding that Blasius-type scaling is not reliable, without providing any scaling law. Gross et al (2021) also considered the range 𝑅𝑒 ≳ 10 3 -10 4 , but neglected the viscous drag for these larger Reynolds numbers, considering only a constant pressure drag coefficient. Here, we use the expression (16) for the timeaverage viscous drag, while all the pressure forces, of any sign, will be modeled with analytical expressions from linear inviscid theory (Section 5 below).…”
Section: Numerical Results Modeling the Unsteady Viscous Dragmentioning
Magnetically actuated miniature robots have attracted the attention of the scientific community over the past two decades, but the confined workspace of their manipulation system (typically a tri-axial coil or eight electromagnetic coils) and the low efficiency of propulsion have limited their utility. Here, we describe a highly efficient NiFe nanorod-based magnetic miniature swimmer that can be manipulated in 3D spaces using two pairs of coils placed in the x−y horizontal plane. In the new swimmer, the shape symmetry is broken along its body, and the asymmetry in magnetizations is introduced perpendicular to the long axis of its body simultaneously. Such a combined asymmetry design offers favorable controllability in planar magnetic fields, which relaxes the multi-axial coil requirement of the commonly used manipulation system and thus reduces the restriction on the shape and size of the workspaces. The new swimmers display efficient 3D propulsion, with a speed of over 5000 μm s −1 (∼3 body length s −1 ) and powerful locomotion in biological media such as raw human blood. The fuel utilization efficiency of the swimmer, defined as the ratio of the distance to the net input work in one period, was estimated to be approximately from 10 −2 to 10 −3 m/J, which is significantly higher than that of magnetic motors with a slender body. Moreover, to provide practical support for further potential use, we demonstrated that the swimmer is able to perform incision operations as a minimally invasive microsurgical tool. Such a swimmer actuation strategy provides a simple and efficient way for 3D manipulation of magnetic miniature robots, offering great potential for future biomedical and other applications.
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