Hydrodynamic interactions of two nearly touching Brownian spheres in a stiff potential: Effect of fluid inertia

dc.contributor.authorRadiom, Miladen
dc.contributor.authorRobbins, Brianen
dc.contributor.authorPaul, Mark R.en
dc.contributor.authorDucker, Williamen
dc.date.accessioned2024-10-09T13:55:35Zen
dc.date.available2024-10-09T13:55:35Zen
dc.date.issued2015-02-26en
dc.description.abstractThe hydrodynamic interaction of two closely spaced micron-scale spheres undergoing Brownian motion was measured as a function of their separation. Each sphere was attached to the distal end of a different atomic force microscopy cantilever, placing each sphere in a stiff one-dimensional potential (0.08 Nm-1) with a high frequency of thermal oscillations (resonance at 4 kHz). As a result, the sphere's inertial and restoring forces were significant when compared to the force due to viscous drag. We explored interparticle gap regions where there was overlap between the two Stokes layers surrounding each sphere. Our experimental measurements are the first of their kind in this parameter regime. The high frequency of oscillation of the spheres means that an analysis of the fluid dynamics would include the effects of fluid inertia, as described by the unsteady Stokes equation. However, we find that, for interparticle separations less than twice the thickness of the wake of the unsteady viscous boundary layer (the Stokes layer), the hydrodynamic interaction between the Brownian particles is well-approximated by analytical expressions that neglect the inertia of the fluid. This is because elevated frictional forces at narrow gaps dominate fluid inertial effects. The significance is that interparticle collisions and concentrated suspensions at this condition can be modeled without the need to incorporate fluid inertia. We suggest a way to predict when fluid inertial effects can be ignored by including the gap-width dependence into the frequency number. We also show that low frequency number analysis can be used to determine the microrheology of mixtures at interfaces.en
dc.description.versionPublished versionen
dc.format.extent16 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifierARTN 022002 (Article number)en
dc.identifier.doihttps://doi.org/10.1063/1.4908295en
dc.identifier.eissn1089-7666en
dc.identifier.issn1070-6631en
dc.identifier.issue2en
dc.identifier.orcidPaul, Mark [0000-0002-0701-1955]en
dc.identifier.orcidDucker, William [0000-0002-8207-768X]en
dc.identifier.urihttps://hdl.handle.net/10919/121314en
dc.identifier.volume27en
dc.language.isoenen
dc.publisherAmerican Institute of Physicsen
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000350551300004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.relation.urihttp://dx.doi.org/10.1063/1.4908295en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.titleHydrodynamic interactions of two nearly touching Brownian spheres in a stiff potential: Effect of fluid inertiaen
dc.title.serialPhysics of Fluidsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherJournalen
pubs.organisational-groupVirginia Techen
pubs.organisational-groupVirginia Tech/Engineeringen
pubs.organisational-groupVirginia Tech/Engineering/Chemical Engineeringen
pubs.organisational-groupVirginia Tech/Engineering/Mechanical Engineeringen
pubs.organisational-groupVirginia Tech/All T&R Facultyen
pubs.organisational-groupVirginia Tech/Engineering/COE T&R Facultyen

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