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Drift of a semi-permeable vesicle through an osmotic gradient: anomalous velocity amplification due to a proximate wall

Published online by Cambridge University Press:  13 May 2025

Ehud Yariv Open the ORCID record for Ehud Yariv [Opens in a new window]
Ehud Yariv*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
Corresponding author: Ehud Yariv, yarivehud@gmail.com
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Abstract

A spherical vesicle is made up of a liquid core bounded by a semi-permeable membrane that is impermeable to solute molecules. When placed in an externally imposed gradient of solute concentration, the osmotic pressure jump across the membrane results in an inward trans-membrane solvent flux at the solute-depleted side of the vesicle, and and outward flux in its solute-enriched side. As a result, a freely suspended vesicle drifts down the concentration gradient, a phenomenon known as osmophoresis. An experimental study of lipid vesicles observed drift velocities that are more than three orders of magnitude larger than the linearised non-equilibrium prediction (Nardi et al., Phys. Rev. Lett., vol. 82, 1999, pp. 5168–5171). Inspired by this study, we analyse osmophoresis of a vesicle in close proximity to an impermeable wall, where the vesicle–wall separation $a\delta$ is small compared with the vesicle radius $a$. Due to intensification of the solute concentration gradient in the narrow gap between the membrane and the wall, the ‘osmophoretic’ force and torque on a stationary vesicle scale as an irrational power, $1/\sqrt {2}-1\ (\approx -0.29289\ldots )$, of $\delta$. Both the rectilinear velocity $\mathcal V$ and the angular velocity $\unicode {x1D6FA}$ of a freely suspended vesicle scale as the ratio of that power to $\ln \delta$. In contrast to the classical problem of sedimentation parallel to a wall, where the ratio $a\unicode {x1D6FA}/\mathcal V$ approaches $1/4$ as $\delta \to 0$, here the ratio approaches unity, as though the vesicle performs pure rigid-body rolling without slippage. Our approximations are in excellent agreement with hitherto unexplained numerical computations in the literature.

JFM classification

Biological Fluid Dynamics: Capsule/cell dynamics Mass Transport: Coupled diffusion and flow Low-Reynolds-number flows: Lubrication theory

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1011 , 25 May 2025 , A18
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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