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Journal of Chemical Physics / Volume 136 / Issue 6 / ARTICLES / Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

J. Chem. Phys. 136, 064508 (2012); http://dx.doi.org/10.1063/1.3681143 (15 pages)

Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer

Benedikt Sabass and Udo Seifert

II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany

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(Received 9 September 2011; accepted 11 January 2012; published online 9 February 2012)

Active diffusiophoresis—swimming through interaction with a self-generated, neutral, solute gradient—is a paradigm for autonomous motion at the micrometer scale. We study this propulsion mechanism within a linear response theory. First, we consider several aspects relating to the dynamics of the swimming particle. We extend established analytical formulae to describe small swimmers, which interact with their environment on a finite lengthscale. Solute convection is also taken into account. Modeling of the chemical reaction reveals a coupling between the angular distribution of reactivity on the swimmer and the concentration field. This effect, which we term “reaction induced concentration distortion,” strongly influences the particle speed. Building on these insights, we employ irreversible, linear thermodynamics to formulate an energy balance. This approach highlights the importance of solute convection for a consistent treatment of the energetics. The efficiency of swimming is calculated numerically and approximated analytically. Finally, we define an efficiency of transport for swimmers which are moving in random directions. It is shown that this efficiency scales as the inverse of the macroscopic distance over which transport is to occur.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. MODEL DESCRIPTION
  3. THE LINEARIZED, NON-DIMENSIONAL EQUATIONS
  4. SWIMMING SPEED AND THE ROLE OF THE INTERACTION POTENTIAL
    1. Analytical approximations
    2. Numerical results
    3. Comparison with passive diffusiophoresis
  5. REACTION INDUCED CONCENTRATION DISTORTION
    1. Boundary conditions for the concentration field
    2. Analytical approximations
    3. Numerical results
  6. ENERGETICS
    1. Energy balance
    2. Efficiency of swimming
    3. Analytical approximation for the efficiency of swimming
    4. Numerical results for the efficiency of swimming
    5. Efficiency of transport
  7. DISCUSSION AND CONCLUSION

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KEYWORDS and PACS

Keywords

biodiffusion, biomechanics, convection, distortion, irreversible thermodynamics

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3681143

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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