Motion of a sphere parallel to plane walls in a Poiseuille flow. Application to field-flow fractionation and hydrodynamic chromatography

Pasol, Laurentiu; Martin, Michel; Ekiel-Jeżewska, Maria L.; Wajnryb, Eligiusz; Bławzdziewicz, Jerzy; Feuillebois, François

doi:10.1016/j.ces.2011.05.033

Cited by 35 publications

(30 citation statements)

References 20 publications

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“…The result is in good agreement with the expected drag coefficient for a perfect no-slip sphere in low Reynolds number flow in an unbounded fluid, ξ b = 6πµR = 781m/τ . Wall effects are negligible for a sphere of radius 8σ at the center of a channel of width 60σ: the correction to ξ b is only about 0.2% [25], and comparable to the statistical error. The discrepancy may be attributed to the particle's surface roughness, which introduces some uncertainty in the definition of radius; we could define a hydrodynamic radius equal to 7.74σ.…”

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confidence: 86%

Diffusivity and hydrodynamic drag of nanoparticles at a vapor-liquid interface

Koplik

Maldarelli

2017

Phys. Rev. Fluids

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Measurements of the surface diffusivity of colloidal spheres translating along a vapor/liquid interface show an unexpected decrease in diffusivity, or increase in surface drag (from the Stokes-Einstein relation) when the particles situate further into the vapor phase. However, direct measurements of the surface drag from the colloid velocity due to an external force find the expected decrease with deeper immersion into the vapor. The paradoxical drag increase observed in diffusion experiments has been attributed to the attachment of the fluid interface to heterogeneities on the colloid surface, which causes the interface, in response to thermal fluctuations, to either jump or remain pinned, creating added drag. We have performed molecular dynamics simulations of the diffusivity and force experiments for a nanoparticle with a rough surface at a vapor/liquid interface to examine the effect of contact line fluctuations. The drag calculated from both experiments agree and decrease as the particle positions further into the vapor. The surface drag is smaller than the bulk liquid drag due to the partial submersion into the liquid, and the finite thickness of the interfacial zone relative to the nanoparticle size. Contact line fluctuations do not give rise to an anomalous increase in drag.When a colloid particle breaches the interfacial zone between two adjoining immiscible fluid phases the interfacial energy of the particle changes, because the area of the fluid interface decreases and the contact areas of the particle with the bounding fluid phases are altered. For a particle which only partially wets both adjoining fluids, the change in interfacial energy is at a minimum when the colloid partially straddles both adjoining phases. For example, for a spherical colloid of radius R at a vapor/liquid interface of interfacial tension γ (Fig. 1a), the minimum free energy relative to the vapor phase is [1] ∆F = −πγR 2 (1 + cos θ) 2 where the contact angle θ is measured through the liquid. For particles of large enough size, ∆F can overwhelm the typical thermal energy k B T and the particle becomes trapped, as thermal fluctuations cannot dislodge the particle from the interface. Monolayers of strongly adsorbed colloids at the fluid interfaces of foams and emulsions provide steric barriers to coalescence of the dispersed phase, and find applications as foam and emulsion stabilizers (e.g. Pickering emulsions). Particle stabilized foams and emulsions are also used for the fabrication of colloid-based solid foams, gels, and bijels, and crystalline monolayers find applications as superhydrophobic or antireflection coatings, and templates for micro and nanostructured materials [2]. Central to these applications is the surface organization of the colloids, which is a balance between interparticle attractive and repulsive forces, external forces applied parallel to the interface, and the viscous resistance or surface drag due to the hydrodynamic motion of the colloids along the fluid surface. As we explain, the surface drag is not w...

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confidence: 86%

Diffusivity and hydrodynamic drag of nanoparticles at a vapor-liquid interface

Koplik

Maldarelli

2017

Phys. Rev. Fluids

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“…Particles are assumed to migrate along the channel length at velocities equal to that of undisturbed fluid at the cross-channel positions of their centers. This assumption is not strictly valid when a particle is very close to a bounding wall [29][30][31], but for a diffuse layer of particles, in which there is a constant exchange of positions, particles will spend very little time next to the wall and the assumption is likely to be acceptable. The assumption becomes more valid as α decreases relative to λ.…”

Section: Assumptions Regarding Fluid Flow and Particle Migrationmentioning

confidence: 99%

Retention ratio and nonequilibrium bandspreading in asymmetrical flow field-flow fractionation

Williams

2015

Anal Bioanal Chem

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In asymmetrical flow field-flow fractionation (As-FlFFF), only the membrane-covered accumulation wall is permeable to fluid; the opposite channel wall is impermeable. Fluid enters the channel at the inlet and exits partly through the membrane-covered accumulation wall and partly through the channel outlet. This means that not only does the volumetric channel flow rate decrease along the channel length as fluid exits through the membrane but also the cross-channel component to fluid velocity must approach zero at the impermeable wall. This dependence of cross-channel fluid velocity on distance across the channel thickness influences the equilibrium concentration profile for the sample components introduced to the channel. The concentration profile departs from the exponential profile predicted for the ideal model of field-flow fractionation. This influences both the retention ratio and the principal contribution to bandspreading--the nonequilibrium contribution. The derivation of an equation for the nonequilibrium bandspreading parameter χ in As-FlFFF is presented, and its numerical solution graphed. At high retention, it is shown that the solutions for both retention ratio R and χ converge on those for the ideal model, as expected. At lower levels of retention, the departures from the ideal model are significant, particularly for bandspreading. For example, at a level of retention corresponding to a retention parameter λ of 0.05, R is almost 4% higher than for the ideal model (0.28047 as compared to 0.27000) but the value of χ is almost 60% higher. The equations presented for both R and χ include a first-order correction for the finite size of the particles--the steric exclusion correction. These corrections are shown to be significant for particle sizes eluting well before steric inversion. For example, particles of half the inversion diameter are predicted to elute 25% slower and to show almost 40% higher bandspreading when steric effects are not accounted for. The work presented contributes to the fundamental theory of As-FlFFF and allows quantitative prediction of both retention and bandspreading at all levels of retention.

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“…66 The PF in 2D is characterized by a parabolic velocity profile of the form, v x ðzÞ ¼ v 0 ð1 À ðz=wÞ 2 Þ, where v 0 is the maximum velocity of the flow. Details of the influence of the channel walls on the parabolic profile 67 are not included in our model. In fact, taking into account the other conditions of a wide channel and low Peclet number employed here, they are expected to be insignificant anyway, and the main focus here is on the role of D(z).…”

Section: D and 3d Microchannelsmentioning

confidence: 99%

Spatially dependent diffusion coefficient as a model for pH sensitive microgel particles in microchannels

2016

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Solute transport and intermixing in microfluidic devices is strongly dependent on diffusional processes. Brownian Dynamics simulations of pressure-driven flow of model microgel particles in microchannels have been carried out to explore these processes and the factors that influence them. The effects of a pH-field that induces a spatial dependence of particle size and consequently the self-diffusion coefficient and system thermodynamic state were focused on. Simulations were carried out in 1D to represent some of the cross flow dependencies, and in 2D and 3D to include the effects of flow and particle concentration, with typical stripe-like diffusion coefficient spatial variations. In 1D, the mean square displacement and particle displacement probability distribution function agreed well with an analytically solvable model consisting of infinitely repulsive walls and a discontinuous pHprofile in the middle of the channel. Skew category Brownian motion and nonGaussian dynamics were observed, which follows from correlations of step lengths in the system, and can be considered to be an example of so-called "diffusing diffusivity." In Poiseuille flow simulations, the particles accumulated in regions of larger diffusivity and the largest particle concentration throughput was found when this region was in the middle of the channel. The trends in the calculated cross-channel diffusional behavior were found to be very similar in 2D and 3D. Published by AIP Publishing. [http://dx

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Motion of a sphere parallel to plane walls in a Poiseuille flow. Application to field-flow fractionation and hydrodynamic chromatography

Cited by 35 publications

References 20 publications

Diffusivity and hydrodynamic drag of nanoparticles at a vapor-liquid interface

Diffusivity and hydrodynamic drag of nanoparticles at a vapor-liquid interface

Retention ratio and nonequilibrium bandspreading in asymmetrical flow field-flow fractionation

Spatially dependent diffusion coefficient as a model for pH sensitive microgel particles in microchannels

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