Abstract
Optimal gait design is important for micro-organisms and micro-robots that propel themselves in a fluid environment in the absence of external force or torque. The simplest models of shape changes are those that comprise a series of linked-spheres that can change their separation and/or their sizes. We examine the dynamics of three existing linked-sphere types of modeling swimmers in low Reynolds number Newtonian fluids using asymptotic analysis, and obtain their optimal swimming strokes by solving the Euler–Lagrange equation using the shooting method. The numerical results reveal that (1) with the minimal 2 degrees of freedom in shape deformations, the model swimmer adopting the mixed shape deformation modes strategy is more efficient than those with a single-mode of shape deformation modes, and (2) the swimming efficiency mostly decreases as the number of spheres increases, indicating that more degrees of freedom in shape deformations might not be a good strategy in optimal gait design in low Reynolds number locomotion.
Highlights
Swimming by shape changes at low Reynolds number (LRN) is widely used in biology and micro-robotic design
The results are presented as follows: in Section 2 we present a brief introduction of the LRN swimming problem; in Section 3 we review the three existing linked-sphere types of swimmers: NG 3-sphere, PMPY 2-sphere and VE 3-sphere models and discuss their optimization problems in Section 4; in Section 5 we discuss the optimization problem of models consisting of a chain of spheres
The numerical results of optimal strokes of a NG 3-sphere, PMPY 2-sphere and VE 3-sphere swimmers are given in Table 1 and Figure 2, where we take ε = A/L = 0.2 in all simulations
Summary
Swimming by shape changes at low Reynolds number (LRN) is widely used in biology and micro-robotic design. Various linked-sphere types of models have appeared, since their simple geometry permits both analytical and computational results [10,11,12,13,14,15,16,17] These analytical and numerical results have greatly inspired the designs of micro robotic devices, for example, swimmers with 2 and 3 rotatory cylinders have been built to study the hydrodynamic interaction between a wall and an active swimmer [18,19]. An important problem in LRN swimming is to find the optimized swimming stroke of the micro-swimmer, either (1) with respect to time, i.e., the stroke in one swimming cycle that moves the cell farthest, or (2) with respect to energy, i.e., among all strokes with designated starting and end points, find the one that consumes the least energy These are usually called the time optimal control and the energy optimal control problems, respectively. The results are presented as follows: in Section 2 we present a brief introduction of the LRN swimming problem; in Section 3 we review the three existing linked-sphere types of swimmers: NG 3-sphere, PMPY 2-sphere and VE 3-sphere models and discuss their optimization problems in Section 4; in Section 5 we discuss the optimization problem of models consisting of a chain of spheres
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
