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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 $$U_0$$ for a time $$\tau _R$$ and then change direction randomly, taking a step of size $$\ell = U_0 \tau _R$$ , at high activity the phoretic velocity is $$\boldsymbol {U} \sim - U_0 \ell \boldsymbol {\nabla } \phi _b$$ , where $$\phi _b$$ 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 $$\boldsymbol {U} \sim - \phi _b U_0 \boldsymbol {\nabla } \ell$$ . 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 $$\boldsymbol {U} \sim - \phi _b U_0 \ell \boldsymbol {\nabla }\varPsi$$ , where $$\varPsi$$ is the (non-dimensional) potential associated with the field.
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Autophoresis of two adsorbing/desorbing particles in an electrolyte solution
Classical diffusiophoresis describes the motion of particles in an electrolyte or non-electrolyte solution with an imposed concentration gradient. We investigate the autophoresis of two particles in an electrolyte solution where the concentration gradient is produced by either adsorption or desorption of ions at the particle surfaces. We find that when the sorption fluxes are large, the ion concentration near the particle surfaces, and consequently the Debye length, is strongly modified, resulting in a nonlinear dependence of the phoretic speed on the sorption flux. In particular, we show that the phoretic velocity saturates at a finite value for large desorption fluxes, but depends superlinearly on the flux for adsorption fluxes, where both conclusions are in contrast with previous results that predict a linear relationship between autophoretic velocity and sorption flux. Our theory can also be applied to precipitation/dissolution and other surface chemical processes.
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- Award ID(s):
- 1740630
- PAR ID:
- 10113079
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 865
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- 440 to 459
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2019.61
