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Life around the scallop theorem
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lauga, Eric |
| Copyright Year | 2018 |
| Abstract | Swimming cells, such as bacteria (prokaryotes) or spermatozoa (eukaryotes), represent the prototypical example of active soft matter. They are active as they transform chemical energy (ATP for eukaryotes, ion flux for prokaryotes) into mechanical work [1] and, as a result, are able to continuously change shape and move in viscous environments [2]. As mechanical entities, cells belong to the world of soft matter, displaying complex rheological properties on a range of time and spatial scales and responding to external forcing in a time-dependent and nonlinear fashion [3]. In their micron-size environment, the fluid forces acting on swimming cells are dominated by the effect of viscous dissipation [4, 5]. Seminal papers in the 1950s laid the ground work for detailed investigations on the hydrodynamics of cell locomotion [6–9], with the main goal of predicting cell kinematics, energetics, the interactions with their environment, and the general importance of fluid forces in biological form and function [10–15]. In 1977, Purcell's influential paper “Life at low Reynolds number” put a somewhat different spin on a field which was already mature [16]. In it, Purcell brought to light the counter-intuitive physical and mathematical constraints arising from locomotion in an inertialess world. He demonstrated that for organisms moving in very viscous fluids, there exists a class of shape change that can never be used for locomotion, a result beautifully summarized under the name “scallop theorem”, borrowing the name of such an organism — a hypothetical microscopic scallop — which could not locomote in the absence of inertia. In this short review, we look back at the scallop theorem, and pose the question: What are the basic ingredients necessary to design swimmers able to move on small scales? What are the different ways offered by physics to get around the constraints of the theorem? After stating the various assumptions for the theorem to be valid (§II), we show how non-reciprocal shape changes (§III), inertia (§IV), hydrodynamic interactions (§V), and coupling with the physical environment (§VI) can all be exploited to provide locomotion on small scales. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://export.arxiv.org/pdf/1011.3051 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
