Abstract
Abstract
Highlights
The squirmer model (Lighthill 1952; Blake 1971) has been widely adopted by mathematicians and physicists over the past decades to model ciliated micro-swimmers such as Opalina, Volvox and Paramecium (Lauga & Powers 2009)
We address the following broader question: Given an axisymmetric shape of a steady squirmer, what is the slip velocity that maximizes its swimming efficiency? The optimization problem, being quadratic, is reduced to a linear system of equations solved by a direct method, while forward exterior flow problems are solved using a boundary integral method
The optimal slip velocity for a particular prolate spheroid tested against the analytical solution given by Leshansky et al (2007) is shown in figure 2
Summary
The squirmer model (Lighthill 1952; Blake 1971) has been widely adopted by mathematicians and physicists over the past decades to model ciliated micro-swimmers such as Opalina, Volvox and Paramecium (Lauga & Powers 2009). Michelin & Lauga (2010) found the optimal swimming strokes of unsteady spherical squirmers by employing a pseudo-spectral method for solving the Stokes equations that govern the ambient fluid and a numerical optimization procedure. Their approach, does not readily generalize to arbitrary shapes. The work considered power loss inside the squirmer surface, which could be an order of magnitude higher than the outside power loss (Keller & Wu 1977; Ito, Omori & Ishikawa 2019) It assumed that the tangential force on the squirmer surface is linear to its local slip velocity, which is not always the case for micro-swimmers.
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