The performance of discrete models of low Reynolds number swimmers.

Hans G Othmer,Qixuan Wang

doi:10.3934/mbe.2015.12.1303

Abstract

Swimming by shape changes at low Reynolds number is widely used in biology and understanding how the performance of movement depends on the geometric pattern of shape changes is important to understand swimming of microorganisms and in designing low Reynolds number swimming models. The simplest models of shape changes are those that comprise a series of linked spheres that can change their separation and/or their size. Herein we compare the performance of three models in which these modes are used in different ways.

Highlights

Single-cell organisms use a variety of strategies for translocation, including crawling, swimming, drifting with the surrounding flow, and others
Other cells can be more flexible in that they either crawl by transient attachments to their surroundings – often called the mesenchymal mode, or by shape changes – called the amoeboid mode [13]. The former may involve strong adhesion to the substrate or the extracellular matrix (ECM) via integrin-mediated adhesion complexes, while the latter depends less on force transmission to the ECM or to the surrounding fluid, and instead involves shape changes to exploit spaces in the ECM to move through it
Since a swimming stroke is a closed path in the v1 − v3 plane or equivalently, a closed path in the a1 − a3 plane, we find the following relation between the differential displacement dx and the differential controls from (24)

Summary

Introduction

Single-cell organisms use a variety of strategies for translocation, including crawling, swimming, drifting with the surrounding flow, and others. If u denotes the velocity field in the fluid exterior to Ω, a standard LRN self-propulsion problem is : given a cyclic shape deformation specified by v, solve the Stokes equations subject to σ · n = 0, r ∧ (σ · n) = 0, u|∂Ω(t) = V = v + U , u|x→∞ = 0 (5). In order to treat general shape changes of a cell defined by Ω(t) ∈ R3 with boundary ∂Ω(t), one must solve the exterior Stokes equations (4) for u, with a prescribed velocity v(t) on ∂Ω(t) and subject to the decay conditions u ∼ 1/r and p ∼ 1/r2 for r → ∞. We have the following conclusion, which applies to the PMPY swimmer

Conclusion

Discussion