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Physics of Fluids
Article
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zbMATH Open
Article . 2005
Data sources: zbMATH Open
Physics of Fluids
Article . 2005 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2005
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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Brownian motion near a partial-slip boundary: A local probe of the no-slip condition

Brownian motion near a partial-slip boundary: a local probe of the no-slip condition
Authors: Lauga, Eric; Squires, Todd M.;

Brownian motion near a partial-slip boundary: A local probe of the no-slip condition

Abstract

Motivated by experimental evidence of violations of the no-slip boundary condition for liquid flow in micrometer-scale geometries, we propose a simple, complementary experimental technique that has certain advantages over previous studies. Instead of relying on externally induced flow or probe motion, we suggest that colloidal diffusivity near solid surfaces contains signatures of the degree of fluid slip exhibited on those surfaces. To investigate, we calculate the image system for point forces (Stokeslets) oriented perpendicular and parallel to a surface with a finite slip length, analogous to Blake’s solution for a Stokeslet near a no-slip wall. Notably, the image system for the point source and perpendicular Stokeslet contain the same singularities as Blake’s solution; however, each is distributed along a line with a magnitude that decays exponentially over the slip length. The image system for the parallel Stokeslet involves a larger set of fundamental singularities, whose magnitude does not decay exponentially from the surface. Using these image systems, we determine the wall-induced correction to the diffusivity of a small spherical particle located “far” from the wall. We also calculate the coupled diffusivities between multiple particles near a partially slipping wall. Because, in general, the diffusivity depends on “local” wall conditions, patterned surfaces would allow differential measurements to be obtained within a single experimental cell, eliminating potential cell-to-cell variability encountered in previous experiments. In addition to motivating the proposed experiments, our solutions for point forces and sources near a partial-slip wall will be useful for boundary integral calculations in slip systems.

Country
United States
Related Organizations
Keywords

diffusion, Fluid Dynamics (physics.flu-dyn), FOS: Physical sciences, Physics - Fluid Dynamics, Condensed Matter - Soft Condensed Matter, 530, 510, two-phase flow, colloids, slip flow, Fluid mechanics, boundary integral equations, Soft Condensed Matter (cond-mat.soft), Brownian motion

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    93
    popularity
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    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
93
Top 10%
Top 10%
Top 10%
Green
bronze