Field-Flow Fractionation: Extensions to Nonspherical Particles and Wall Effects

Gajdos, Lawrence J.; Brenner, Howard

doi:10.1080/01496397808060221

Cited by 32 publications

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“…In attempting to solve the relevant particle continuity equation in 'To whom all correspondence should be addressed. lCurrent address: Box 164, Mellon Institute, CarnegieMellon University, Pittsburgh, PA 15213. bounded systems it is a nontrivial matter to explicitly account for the constraints imposed upon the translational and rotational particle motions by the presence of a nearby bounding wall (9). This problem is largely avoided when attention is restricted to spherical particles, since particle orientation effects are physically irrelevant for such shapes.…”

Section: Introductionmentioning

confidence: 99%

“…By recognizing the boundary as the seat of short-range forces and torques external to the particle it is possible to incorporate these forces and torques directly into the continuity (i.e., conservation) equation itself (via the addition of Smoluchowskitype external force and torque contributions to the conventional constitutive equations for the translational and rotational particle fluxes) (5,9,10,12). Such constitutive relations normally entail only diffusive and "piggy-backy'-type fluid-convective contributions.…”

Section: Introductionmentioning

confidence: 99%

“…When, however, the arena of interest is enlarged to include nonspherical particles, the physico-mathematical description of such common boundary conditions as "adsorption" of the particle at the surface, or "impenetrability" of the surface to the particle, acquires a more complex character owing to the need to supplement the usual positional variables with orientational ones. Geometrically, hydrodynamically, and dynamically, "coupling" (7,9,11) between translational and rotational particle motions invariably occurs in proximity to a boundary, even for spherical particles.…”

Section: Introductionmentioning

confidence: 99%

“…Our interest in this problem derives from questions relating to the boundary conditions to be imposed upon the solutions of the convective-diffusion equation involving the transport of orientable, i.e., nonspherical, Brownian solute particles (4-6) moving in proximity to surfaces (7)(8)(9)(10). In attempting to solve the relevant particle continuity equation in 'To whom all correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

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London – van der Waals forces and torques exerted on an ellipsoidal particle by a nearby semi-infinite slab

Brenner¹,

Gajdos²

1981

Can. J. Chem.

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A Hamaker-type integration of the pairwise en vacuo intermolecular forces is performed for a homogeneous triaxial ellipsoidal particle in proximity to a homogeneous semi-infinite slab bounded by a plane wall. The orientation of the ellipsoid relative to the plane is taken to be arbitrary, as too is its distance from the plane. The integrated potential energy function of the ellipsoid with respect to the slab is found to possess nonadditive positional and orientational contributions. This macroscopic potential is employed to compute the force and torque on the ellipsoid as functions of both its position and orientation relative to the plane.The novel integration scheme pertains to centrally-symmetric pairwise intermolecular potentials of arbitrary functional form. Specific results are derived for classical inverse-power intermolecular potentials possessing both attractive (r-") and repulsive (-r-"' ) additive components (with n > m). In stable equilibrium the ellipsoid aligns itself with the shortest of its three principal axes perpendicular to the bounding wall, and at a separation distance comparable to the length scale ofthe intermolecular potential itself.HOWARD BRENNER et LAWRENCE J. GAJDOS. Can. J. Chem. 59,2004Chem. 59, (1981. On a effectuk une integration du type Hamaker des forces intermoleculaires en vacuo prises deux a deux pour une particule Cllipsoidale triaxiale homogene au voisinage d'une plaque homogene semi-infinie reliee a un mur plan. On considere que l'orientation de I'ellipsoide par rapport au plan ainsi que sa distance par rapport ce plan sont arbitraires. On a trouve que la fonction d'energie potentielle integrte de I'ellipsoide par rapport 21 la plaque possede des contributions de position et d'orientation qui ne sont pas additives. On a employe cette propriete macroscopique pour calculer la force et la torsion appliquee i I'ellipsoide en fonction a la fois de sa position et de son orientation par rapport au plan.Le nouveau schema d'integration s'applique a des potentiels intermoleculaires centro-symetriques considerees sous forme de paire dont la forme fonctionnelle est arbitraire. On a dkduit des resultats specifiques pour des potentials intermoleculaires de puissance inverse classique possedant a la fois des composantes additives (r-") et repulsives ( -r m ) (avec n > m). En Cquilibre stable, I'ellipsoide s'aligne lui-mCme avec le plus court de ses trois axes perpendiculaires principaux par rapport au mur plan liant et la distance qui le &pare d'un mur se compare l'echelle de longueur du potentiel intermoleculaire lui-mCme.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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London – van der Waals forces and torques exerted on an ellipsoidal particle by a nearby semi-infinite slab

Brenner¹,

Gajdos²

1981

Can. J. Chem.

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“…E lectrical field flow fractionation (EFFF) is an effective technique to separate a variety of solutes, including for example, proteins, DNA, and pharmaceuticals, among others (Wang and Flagan, 1990;Lee et al, 1991;Probstein, 1991;Giddings, 1993;Williams and Lee, 2006;Messaud et al, 2009;Gajdos and Brenner, 1978;Heller et al, 1994). However, there is still much work to be done regarding the effects of many of the variables that contribute to these processes.…”

Section: Introductionmentioning

confidence: 98%

Effect of wall velocities on the determination of optimal separation times in electrical field flow fractionation (EFFF)

2010

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Electrical field flow fractionation (EFFF) has two perpendicular driving forces that help to produce an optimal separation of solute in a mixture [Giddings, Science 1993; 260:1456-1465. For Couette flow based devices, the ratio of the velocity of the capillary walls offers an extra parameter that can be exploited to enhance the efficiency of EFFF applications. The analysis of the effects of this parameter on optimal times of separation is the subject matter of this contribution. The use of this additional parameter increases flexibility in the design of new devices for the improvement of the separation of solutes, such as proteins, DNA, and pharmaceuticals, as it will be illustrated with the results of this analysis Trinh et al., 1999). The analysis has been illustrated by selecting parameter values that represent a number of potential useful applications. A set of five parameters (i.e., z, the valence; , electrophoretic mobility; Pe, Peclet number; , the orthogonal applied electrical field; and R, the ratio of channel wall velocities) has been combined to obtain the best operating conditions for optimal separation of solutes. Results indicate that R, the ratio of the channel wall velocities, is actually the most important driving parameter.Le fractionnement de flux de champélectrique (EFFF) a deux forces motrices perpendiculaires qui aidentà produire une séparation optimale d'un soluté dans un mélange [Giddings, Science 1993; 260:1456-1465. Pour les systèmes basés sur le flux Couette, le ratio de la vélocité des parois capillaires offre un paramètre supplémentaire qui peutêtre exploité pour rehausser l'efficience des applications EFFF. L'analyse des effets de ce paramètre sur les temps optimaux de séparation est le thème de ce travail. L'utilisation de ce paramètre supplémentaire rehausse la flexibilité de la conception de nouveaux systèmes pour l'amélioration de la séparation des solutés tels que les protéines, l'ADN et les produits pharmaceutiques, comme cela sera illustré par les résultats de cette analyse. L'analyse aété illustrée en sélectionnant des valeurs de paramètres qui représentent un nombre d'applications utiles potentielles. Un ensemble de cinq paramètres (c.-à-d., z, la valence; la mobilitéélectrophorétique, ; Pe, nombre de Peclet; , le champélectrique orthogonal appliqué et R, le ratio des vélocités des parois de canal) aété combiné pour obtenir les meilleures conditions opératoires pour une séparation optimale des solutés. Les résultats indiquent que R, le ratio des vélocités des parois de canal, est en fait le paramètre moteur le plus important.

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Separations in conventional, hyperlayer, and steric field‐flow fractionation

Tomida¹,

McCoy²

1988

AIChE Journal

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Separation in field-flow fractionation is caused by the interaction of a longitudinal flow in a narrow channel with a transverse flow or flux (Giddings, 1985). The transverse flux is due to an imposed field--electrical, magnetic, or gravitational-acting on the particles or molecules to be separated. A transverse flow may be caused by a wall permeable to the solvent but impermeable to the particles to be separated. For conventional field-flow fractionation, the flux downward is counteracted by diffusion upward, giving rise to exponential distributions of the different species over the cross section of the channel formed between two closely spaced parallel surfaces, Figure 1. The longitudinal flow, which increases with distance from the confining walls, convects the components at different longitudinal rates, thus causing separation of solute bands. The process called steric field-flow fractionation separates particles of different diameter whose closest approach to the wall is their radius (Giddings and Myers, 1978).In hyperlayer field-flow fractionation (Giddings, 1983), particles are focused at a layer parallel to the boundary surfaces by, for example, a transverse density gradient. Giddings showed that Brownian motion about this layer induces a Gaussian concentration profile transversely across the channel, Figure 1, The layer is convected longitudinally at the rate of the velocity profile at that position, and separation of different layers can occur.Applications and fundamental ideas of field-flow fractionation were reviewed recently by Giddings (1985). Experimental studies by Schallinger et al. (1984) suggest that sedimentation field-flow fractionation is a rapid and quantitative method mild enough for bioproducts, such as DNA. Schunk et al. AIChE JournalFebruary 1988 separation of ultrafine particles and macromolecules has recently been announced (Blaine, 1986).As with chromatography, field-flow fractionation is a nonequilibrium separation process influenced by interacting transport phenomena. An early nonequilibrium treatment of fieldflow fractionation (Giddings, 19681, showed that the dispersion coefficient, and thus the height equivalent to a theoretical plate, could be expressed in terms of spatial averages of concentration and velocity. These essential ideas were implemented by Giddings et al. (1975) for parallel wall columns. Gajdos and Brenner (1978) extended the theory of field-flow fractionation to nonspherical particles and general power-series velocity profiles. Jayaraj and Subramanian (1978) discussed relaxation phenomena in field-flow fractionation. Lightfoot et al. (1981) provided a critical review of the foundations of the subject.The present study applies a temporal moment analysis to reveal the similarities among processes with different transverse concentration profiles, for example, conventional, steric, and hyperlayer field-flow fractionation. The hypothesis that longitudinal dispersion in field-flow fractionation is not substantially different from dispersion in the absence of the ext...

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Field-Flow Fractionation: Extensions to Nonspherical Particles and Wall Effects

Cited by 32 publications

References 20 publications

London – van der Waals forces and torques exerted on an ellipsoidal particle by a nearby semi-infinite slab

London – van der Waals forces and torques exerted on an ellipsoidal particle by a nearby semi-infinite slab

Effect of wall velocities on the determination of optimal separation times in electrical field flow fractionation (EFFF)

Separations in conventional, hyperlayer, and steric field‐flow fractionation

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