P. Stephen Williams

Characterization of near-wall hydrodynamic lift forces using sedimentation field-flow fractionation

Abstract In field-flow fractionation (FFF), a family of high resolution techniques for the separation of particles and polymers, the measured retention time of entrained particles eluting through a thin (50-500 μm) parallel plate channel is determined by the transverse forces acting on the particles during their migration. For particles in the size range ∼l-100μm an applied transverse driving force (in the present case sedimentation) rapidly brings the particles into balance with hydrodynamic lift forces, so that the two force vectors are equal in magnitude but opposite in direction. By subjecting latex microspheres of known size and density to a specified rotation rate in a centrifuge, the applied sedimentation force is known and thus the magnitude of the lift forces is immediately obtained. The transverse particle position can be determined from the measured particle retention time. Thus lift forces can be determined as a function of particle size, transverse position, and flowrate. This strategy has be...

CHARACTERIZATION OF HYDRODYNAMIC LIFT FORCES BY FIELD-FLOW FRACTIONATION. INERTIAL AND NEAR-WALL LIFT FORCES

Abstract Sedimentation/steric FFF has been used to measure hydrodynamic lift forces exerted on 2-30 μm latex microspheresdnven by flow through a 95 cm long ribbonlike FFF channel of ∼ 127 um thickness. Following a previous study, lift forces are examined as a function of shear rate, distance from the wall, and sphere size. Here, in contrast to the earlier study, measured lift forces are extended downward into a range corresponding to theoretical values of the inertial lift force. After corrections are made for secondary relaxation, it is found, as before, that a near-wall lift force proportional to l/δ (where δ is the particle-wall distance) dominates lift effects at small δs. As δ increases and this force decays, the measured lift force assumes a value in good agreement with the inertial lift force predicted by the theory of Cox and Brenner as extended by subsequent workers. Over a broad range of conditions explored in almost 300 measurements, the results are consistent with a total lift force that equa...

Effect of viscosity on retention time and hydrodynamic lift forces in sedimentation/steric field-flow fractionation

Abstract Particles entrained in fluid flow between parallel bounding walls tend to be driven by hydrodynamic forces, acting perpendicular to the direction of flow, towards certain equilibrium positions between the walls. Sedimentation field-flow fractionation is a technique that is well suited to the measurement of these forces, particularly in the regions close to the walls. Forces much stronger than those due to fluid inertial effects are commonly observed in the near-wall regions. A study is presented here of the influence of carrier fluid viscosity on these hydrodynamic lift forces. The carrier viscosity is varied via two different methods: (1) various ternary mixtures of water, glycerol, and ethanol were used that varied in viscosity while being of constant density and (2) the temperature of the FFF system was raised, changing the carrier viscosity while not significantly altering its density. The near-wall lift forces are shown to be dependent on fluid viscosity. An empirical equation describing the apparent dependence is presented.

Theoretical Basis of Field-Flow Fractionation

In field-flow fractionation (FFF), macromolecular or particulate species (including colloids and particles up to about 50 μm) are separated in thin flow channels under the influence of a transverse external field. The separation relies on the non-uniform distribution of the species molecules or particles in the channel cross-section. In the ideal case corresponding to molecules or particles of negligible size and a uniform applied field, the migration toward one of the channel walls is countered by Brownian motion resulting in an exponential transverse concentration profile. This characterizes the Brownian, or normal, mode of operation in FFF. Interactions of species with nonuniform fields, transverse gradients, the flow of carrier fluid, and/or the channel walls may result in quite different transverse concentration profiles. These profiles distinguish the non-Brownian modes of operation.

Design of an asymmetrical flow field‐flow fractionation channel for uniform channel flow velocity

A new design for an asymmetrical flow field-flow fractionation (FFF) channel, having a breadth that decreases exponentially along its length, is presented. It is shown that such a channel may be operated under certain flow conditions to obtain a constant mean channel flow velocity throughout its effective length. This is not possible with trapezoidal channels, which were themselves introduced with the objective of reducing the variation of mean flow velocities along the channel length. It is also shown that when operated under other flow conditions, the resulting variation in mean flow velocity is reduced in comparison to that predicted for trapezoidal channels.xa0© 1997 John Wiley & Sons, Inc.xa0J Micro Sep9: 459–467, 1997

Separation of Cells and Cell-Sized Particles by Continuous SPLITT Fractionation Using Hydrodynamic Lift Forces

Abstract The use of hydrodynamic lift forces for the separation of particles according to size by continuous SPLITT fractionation is explored. The mechanism for particle separation in the transport mode of SPLITT fractionation is first explained. This is followed by a discussion of the hydrodynamic lift forces that act upon particles entrained in fluid flow between the parallel bounding walls of the SPLITT cell. The effect of the bounding walls on particle motion both parallel and perpendicular to the direction of flow is explained. Computer simulations of particle trajectories are presented that predict extremely high size selectivity for the method. A parallel experimental study was carried out using both polystyrene latex particles and red blood cells. The experimental selectivity was found to be smaller than that predicted theoretically. This discrepancy is attributable to nonidealities in the construction of the SPLITT cell. Nonetheless, the results are promising. Suspensions of polystyrene particle ...

Rapid breakthrough measurement of void volume for field-flow fractionation channels

A peak breakthrough technique is described and evaluated for measuring the void volume of field-flow fractionation (FFF) channels, particularly those used for flow FFF. This technique uses a high-molecular-mass macromolecular or particulate probe that can be displaced rapidly by flow through the FFF channel with minimal transverse diffusion. The particles that emerge first are those carried through the entire length near the channel centerline at the apex of the parabolic flow profile. These particles generate a sharp breakthrough profile. The measured breakthrough time is two thirds of the void time, thus making it possible to calculate both the void time and the associated void volume. This method, although applicable to all FFF channels (and capable of extension to open tubes), is particularly useful for flow FFF because conventional low-molecular-mass void probes can diffuse into the permeable walls and thus distort void measurements. The theoretical basis of the breakthrough technique and an explanation for the sharpness of the breakthrough front are given. A method for compensating for deviations from perfect sharpness is developed in which the breakthrough time is identified with the time needed to reach 85-88% of the breakthrough peak maximum. Preliminary experimental results are shown using various protein probes in four different FFF channel systems.

Influence of accumulation wall and carrier solution composition on lift force in sedimentation/steric field-flow fractionation

Abstract Sedimentation/steric field-flow fractionation is an established analytical technique for characterizing particulate materials by size in the approximate diameter range 1–100 μm. Particles are eluted through a thin, parallel-walled channel by a flow of a carrier liquid while a centrifugal field is applied across the thin dimension perpendicular to the flow. During elution, particles are driven towards equilibrium positions between the channel walls where the force due to the applied field is balanced by hydrodynamic lift forces. These lift forces are not yet fully characterized, and calibration using latex standards is at present a necessary prerequisite for size characterization of unknown materials. A greater understanding of the forces involved will ultimately eliminate this need for calibration. The elution of latex standards under various field strength and carrier flow rate regimes yields information on lift force as a function of particle size, flow velocity, position within the channel, and any other controllable system property. The work presented here examines the influence of channel wall and carrier solution composition (ionic strength and pH) on overall lift. It is shown that the observed lift may be described as the sum of a force due to the effects of fluid inertia, an empirical near-wall lift force inversely dependent on particle distance from the wall, and a force due to electrostatic repulsion.

Fractionating Power in Sedimentation Field-Flow Fractionation with Linear and Parabolic Field Decay Programming

Abstract Following an earlier treatment of exponentially programmed field decay in field-flow fractionation (FFF), expressions have been derived for retention time and fractionating power Fdfor linear and two types of parabolic programmed field decay. The particular case of sedimentation FFF has been considered and plots of both retention time and Fdas functions of particle diameter are generated by computer in order to illustrate the influence of the various experimental parameters. Approximate analytical expressions have been derived for retention time and Fd in each case, and from these the means of calculating both the initial field strength and the program time necessary to obtain a desired level of Fd at some particular particle size have been obtained. Finally the special properties and possible uses of these programs have been discussed.

Comparison of power and exponential field programming in field-flow fractionation

Field programming in field-flow fractionation has the purpose of expanding the molecular weight or particle diameter range subject to a single analytical run. The two most widely used field programs are those in which the field strength decays with time according to an exponential function and a power function, respectively. The performances of these two programming functions are compared by obtaining limiting equations showing how retention time tr, standard deviation in retention sigma t, and fractionating power Fd vary with particle diameter d. It is shown that uniform fractionating power (Fd independent of d) can be obtained with power programming but that in exponential programming Fd is always non-uniform, varying as d-1/2. In exponential programming a linear relationship arises between tr and log d. This particular relationship is impossible to realize in power programming but an alternative linear relationship can be obtained by plotting tr versus dt/3. These results are made more concrete by plotting and comparing field strength, relative field strength, Fd and tr for specific programming cases.