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Bypassing slip velocity: rotational and translational velocities of autophoretic colloids in terms of surface flux

Published online by Cambridge University Press:  03 August 2016

Paul E. Lammert Open the ORCID record for Paul E. Lammert [Opens in a new window] ,
Vincent H. Crespi  and
Amir Nourhani
Paul E. Lammert*
Affiliation:
Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA
Vincent H. Crespi
Affiliation:
Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA Department of Chemistry, The Pennsylvania State University, University Park, PA 16802, USA
Amir Nourhani*
Affiliation:
Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA
*
†Email addresses for correspondence: lammert@psu.edu, nourhani@psu.edu
†Email addresses for correspondence: lammert@psu.edu, nourhani@psu.edu
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Abstract

A standard approach to propulsion velocities of autophoretic colloids with thin interaction layers uses a reciprocity relation applied to the slip velocity although the surface flux (chemical, electrical, thermal, etc.), which is the source of the field driving the slip, is often more accessible. We show how, under conditions of low Reynolds number and a field obeying the Laplace equation in the outer region, the slip velocity can be bypassed in velocity calculations. In a sense, the actual slip velocity and a normal field proportional to the flux density are equivalent for this type of calculation. Using known results for surface traction induced by rotating or translating an inert particle in a quiescent fluid, we derive simple and explicit integral formulas for translational and rotational velocities of arbitrary spheroidal and slender-body autophoretic colloids.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics

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Papers
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Journal of Fluid Mechanics , Volume 802 , 10 September 2016 , pp. 294 - 304
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© 2016 Cambridge University Press 

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