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Phoretic motion in active matter

Brady, John F. (2021) Phoretic motion in active matter. Journal of Fluid Mechanics, 922 . Art. No. A10. ISSN 0022-1120. doi:10.1017/jfm.2021.530.

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A new continuum perspective for phoretic motion is developed that is applicable to particles of any shape in ‘microstructured’ fluids such as a suspension of solute or bath particles. Using the reciprocal theorem for Stokes flow it is shown that the local osmotic pressure of the solute adjacent to the phoretic particle generates a thrust force (via a ‘slip’ velocity) which is balanced by the hydrodynamic drag such that there is no net force on the body. For a suspension of passive Brownian bath particles this perspective recovers the classical result for the phoretic velocity owing to an imposed concentration gradient. In a bath of active particles that self-propel with characteristic speed U₀ for a time τ_R and then change direction randomly, taking a step of size ℓ=U₀τ_R, at high activity the phoretic velocity is U∼−U₀ℓ∇ϕ_b, where ϕ_b is a measure of the ‘volume’ fraction of the active bath particles. The phoretic velocity is independent of the size of the phoretic particle and of the viscosity of the suspending fluid. Because active systems are inherently out of equilibrium, phoretic motion can occur even without an imposed concentration gradient. It is shown that at high activity when the run length varies spatially, net phoretic motion results in U∼−ϕ_bU₀∇ℓ. These two behaviours are special cases of the more general result that phoretic motion arises from a gradient in the swim pressure of active matter. Finally, it is shown that a field that orients (but does not propel) the active particles results in a phoretic velocity U∼−ϕ_bU₀ℓ∇Ψ, where Ψ is the (non-dimensional) potential associated with the field.

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Brady, John F.0000-0001-5817-9128
Additional Information:© The Author(s), 2021. Published by Cambridge University Press. Received 22 January 2021; revised 4 June 2021; accepted 8 June 2021. Published online by Cambridge University Press: 05 July 2021. The results were first presented in August 2019 at Stanford University at a birthday celebration symposium in honour of Professor E.S.G. Shaqfeh. This work was supported in part by the National Science Foundation (grant number 1803662). The author reports no conflict of interest.
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Record Number:CaltechAUTHORS:20210727-170713408
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Official Citation:Brady, J. (2021). Phoretic motion in active matter. Journal of Fluid Mechanics, 922, A10. doi:10.1017/jfm.2021.530
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110025
Deposited By: Tony Diaz
Deposited On:02 Aug 2021 17:28
Last Modified:02 Aug 2021 17:28

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