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 standards (from 2 to 50 μm in diameter) demonstrate that fast and relatively clean size separations are possible provided particles differ sufficiently in size and flow conditions are properly optimized. It is also shown that the system has the potential to quickly and gently separate blood cells from plasma.     

Optimization of Transport-Driven Continuous SPLITT Fractionation

Abstract

Continuous SPLITT fractionation (CSF) utilizes various forces acting across the thin dimension of a ribbonlike flow channel or cell to segregate suspended particles and macromolecules into different flow laminae. One or more splitters at the outlet of the channel then divide the differentially populated laminae into two or more substreams. The separation is rapid because of the extreme thinness (usually <0.5 mm) of the cell. The throughput/cell volume ratio is high because of the high separation speed. The purpose of this paper is to examine factors affecting resolution, speed, and throughput in transport-based CSF. The time of separation is roughly proportional to the path length of separation, giving CSF a >10²-fold advantage over many conventional techniques like gravitational sedimentation. The resolving power of CSF is related to the ratio of inlet substream flow rates, making possible the direct control of resolution. A straightforward tradeoff is found between resolution and throughput. The throughput is shown to be proportional to the concentration of particles in the feed stream, to the field strength, to the mobility range that can be tolerated for incompletely resolved material, and to the SPLITT cell area. However, throughput is independent of cell thickness. Optimization considerations suggest the desirability of working with very thin cells of high area and thus a high aspect ratio in CSF.     

Hydrodynamic Characterization of SPLITT Fractionation Cells

Abstract

The efficacy of SPLITT fractionation requires an absence of hydrodynamic mixing between laminae constituting the thin liquid film streaming through a SPLITT cell and it requires structural elements capable of splitting the film evenly along streamplanes. These requirements are examined here by both experimental tests and by a numerical analysis of flow properties near the inlet splitter. The experimental tests, involving dye injection and the injection of pulses of latex particles that may or may not be driven across flow laminae by gravity, show that SPLITT cell performance is close to that of ideal theory at low Reynolds numbers. The computer results verify an absence of mixing under these conditions, but when the Reynolds number and inlet flow asymmetry are both high, vortex motion is found near the inlet splitter edge, suggestive of mixing. The conditions leading to vortex formation are defined. It is shown that tapering the splitter edge suppresses vortex formation.     

Crossflow Gradients in Thin Channels for Separation by Hyperlayer FFF,SPLITT Cells,Elutriation, and Related Methods

Abstract

The formation and use of thin equilibrium layers or hyperlayers in separations are discussed and the advantages of developing such hyperlayers along the transverse coordinate of thin channels is described. It is shown how a new method for establishing crossflow gradients in thin permeable-wall channels can be combined with sedimentation or electrical forces to generate transverse hyperlayers free of gradient-forming materials. The sedimentation case is shown to be equivalent to elutriation, but with the advantages of increased speed and of flow uniformity and thus of improved resolution. A general theory describing the form of the transverse flow gradient is developed. This theory is applied to the special case of hyperlayer formation in a thin channel with one permeable and one impermeable wall.     

Rapid Separation of Micron-Sized Particles by Field-Flow Fractionation Using Earth's Gravitational Field

Abstract

This paper presents the rapid separation of latex particles of diameters 5–20 μm in a simple arrangement of the separation channel. Lift forces, which play an important role in the process, drive particles very quickly from the channel bottom, and they cause a decrease in retention times at first and then a deterioration of resolution when the flow rate increases. The magnitude of the lift forces depends on the flow rate and particle size among others. Several published observations concerning the lift forces are mentioned, and several suggested formulas for these forces are presented. Our experimental data are compared to the lift forces function which seems to be the most relevant: the function suggested by Vasseur and Cox and simplified by Kononenko and Shimkus that originates in inertial effects of the flow. The consequences of such a separation mechanism are discussed with respect to the limitations and advantages of lift forces activity.     

Continuous Separation in Split-Flow Thin (SPLITT) Cells: Potential Applications to Biological Materials

Abstract

We recently described a broad class of techniques in which separation is achieved over a submillimeter path extending along the thin dimension of a special separation cell termed a SPLITT cell. The separation is converted into a continuous process by flow through the cell, and the products are collected with the aid of flow splitters. The separation is rapid and predictable by virtue of the simple geometry of the cell. Separation can be based on differences in sedimentation coefficients, densities, electrophoretic mobilities, isoelectric points, diffusion coefficients, etc., depending on operating details. We describe here the principles of SPLITT cells and summarize our preliminary laboratory findings. We discuss various approaches for utilizing the SPLITT system to separate biological materials with components spanning the mass range from the extremes of biological cells down to that of simple amino acids.     

A System Based on Split-Flow Lateral-Transport Thin (SPLITT) Separation Cells for Rapid and Continuous Particle Fractionation

Abstract

In this paper we introduce a versatile separation system based on the operation of some rather simple separation cells termed SPLITT cells. These thin cells are capable of acting singly or in linked arrays depending on the problem at hand. Separation in the cells can be driven by sedimentation, electrical, and related forces, by diffusion, and by various gradients. SPLITT cells resemble FFF channels and are subject to similar methods of construction, except for the requirement for various split-flow elements in different parts of the SPLITT system. The separation path, across the narrow dimension of the thin SPLITT cells, is extremely short (often <1 mm), leading to rapid separation. The system is capable of continuous operation. The combination of continuous processing and rapid separation is anticipated to provide a relatively high throughput, despite the low volume of the cells. The optimization of throughput is discussed. Because separation takes place without the distortion accompanying some continuous methods, resolution is expected to be reasonably high (peak capacity ～2–20 or more) despite the short path and high speed.     

Continuous separation of particles from macromolecules in split-flow thin (SPLITT) cells

A split-flow thin (SPLITT) cell with a perpendicular driving force of one gravity has been utilized for the rapid separation of micron-sized particles from macromolecules. The procedure involves the simultaneous use of two transport mechanisms and thus two operating modes: a sedimentation process controls the displacement of the particles across the thickness of the thin channel, while diffusion controls the displacement of macromolecules. The theoretical equations for these two operating modes are summarized and it is shown how the two modes can be combined to yield specified recovery factors. The theory was tested on a mixture of 10 μm polystyrene latex beads and three different proteins. The observed separation was in excellent agreement with theory. Attempts to fractionate red blood cells and plasma proteins from whole blood were only partially successful as a consequence of the weak sedimentation of red blood cells. Various remedies to this problem are suggested, the most promising of which is the use of a SPLITT cell subject to mild centrifugal forces.     

Relative importance of the lift force on heavy particles due to turbulence driven secondary flows

Saffman lift forces on dense particles due to gradients in both streamwise and cross-stream velocities in a downward, fully developed turbulent square duct flow at Re_τ = 360 are studied using large eddy simulations. Volume fraction of the dispersed phase is low enough (≤ 10^− 5) that the one-way coupling approach is reasonable, i.e., two-way coupling and particle-particle collisions are not considered. Eulerian and Lagrangian approaches are used to treat the continuous and dispersed phases, respectively. Subgrid stresses are modeled with the dynamic subgrid kinetic energy model of Kim and Menon [W.W. Kim and S. Menon. Application of the localized dynamic subgrid-scale model to turbulent wall-bounded flows, AIAA 97-0210, 1997.]. The particle equation of motion includes drag, lift forces due to both the streamwise and cross-stream velocity gradients, gravity, and is integrated using the fourth-order accurate Runge-Kutta scheme. Dependence of particle drag and lift forces on duct cross-sectional location and particle response time is demonstrated using the mean value contours and probability density functions (PDFs) of particle forces. It is shown that the streamwise component of the mean drag force experienced by particles of all response times is a deceleration force, i.e. on average, fluid streamwise velocity lags the particle streamwise velocity. Secondly, the two wall-normal (or lateral) components of the mean drag force are oriented such that the particles experience a net mean force toward the duct corners. PDFs of particle drag force components show that smaller response time particles experience a wider range of drag force about the mean value, as compared to the more inertial particles. Contours of mean wall-normal lift forces due to streamwise velocity gradients show that this force predominantly acts toward the duct walls and that the maximum lift force occurs close to the walls. PDFs of lift force due to streamwise velocity gradients show that the range of fluctuations increases with particle response time, but the dependence on particle response time is weaker compared to drag force. Lift forces due to cross-stream velocity gradients are at least an order of magnitude smaller than lift forces due to streamwise velocity gradients and are found to decrease in their range of fluctuations with particle response time. It is demonstrated that lift forces due to secondary flow velocity gradients are not as important as those due to streamwise velocity gradients in a square duct flow.     

Continuous Separation of Proteins in Electrical Split-Flow Thin (SPLITT) Cell with Equilibrium Operation

Abstract

The continuous separation of charged species in an electrical split-flow thin (SPLITT) cell is described. By operating the electrical SPLITT system in an equilibrium mode at a solution pH lying between the isoelectric points of two proteins, a mechanism is available for the rapid and complete separation of the proteins. The theoretical conditions necessary for such a separation are established. The apparatus constructed to test this concept is described. Preliminary experimental results are reported for several proteins, and the complete resolution of a binary mixture of ferritin and cytochrome C is demonstrated.     

Numerical Study of Particle Behaviour in Split-Flow Thin-Channel Fractionation Using the Discrete Element Method

Abstract

This study examines the usefulness of the discrete element method (DEM) for studying particle motion in SPLITT fractionation. The method was tested against the conventional SPLITT theory and published experimental data for particle sizes 7, 10, and 15 µm at various run conditions and good agreement was achieved. Illustrative studies presented in this paper show that particle collisions occur at concentrations as low as 0.05%(v/v); and particle trajectory deviates from theory more notably for larger particles, 15 µm diameter and greater. The finding suggests the DEM can be useful in SPLITT calculations for modeling the influence of particle-particle interactions.     

Effect of Sub-Grid Scales on Large Eddy Simulation of Particle Deposition in a Turbulent Channel Flow

Large-eddy simulations (LES) of particle transport and deposition in turbulent channel flow were presented. Particular attention was given to the effect of subgrid scales on particle dispersion and deposition processes. A computational scheme for simulating the effect of subgrid scales (SGS) turbulence fluctuation on particle motion was developed and tested. Large-eddy simulation of Navier-Stokes equations using a finite volume method was used for finding instantaneous filtered fluid velocity fields of the continuous phase in the channel. Selective structure function model was used to account for the subgrid-scale Reynolds stresses. It was shown that the LES was capable of capturing the turbulence near wall coherent eddy structures.

The Lagrangian particle tracking approach was used and the transport and deposition of particles in the channel were analyzed. The drag, lift, Brownian, and gravity forces were included in the particle equation of motion. The Brownian force was simulated using a white noise stochastic process model. Effects of SGS of turbulence fluctuations on deposition rate of different size particles were studied. It was shown that the inclusion of the SGS turbulence fluctuations improves the model predictions for particle deposition rate especially for small particles. Effect of gravity on particle deposition was also investigated and it was shown that the gravity force in the stream wise direction increases the deposition rate of large particles.     

Particle Motion in Simple Shear Flow with Gravity

The motion of aerosol particles in simple shear flow, subject to gravity, is analyzed. The combination of gravity and shear-induced lift is shown to give rise to particle drift. It is shown that in shear flow near a wall, when gravity points in the direction of flow, particles drift towards the wall, while for gravity pointing against the flow the drift is away from the wall. These results are also demonstrated experimentally, with fair qualitative agreement between analysis and experiments.     

Investigations of Performance Characteristics Including Limitations Due to Flow Instabilities in Continuous SPLITT Fractionation

Abstract

An investigation of SPLITT fractionation is conducted to improve its overall performance. Particular attention is devoted to factors which degrade separation resolution in the thin SPLITT channels, including the development of instabilities due to unstable stratification of density. The presence of these instabilities is quantified using the Richardson number (Ri) and the flow-rate ratio [Vdot] (a)/[Vdot] (a′), where [Vdot](a) and [Vdot] (a′) are volumetric flow rates at the top outlet substream and the top inlet feed substream, respectively. The stability boundary separating the stable and unstable flow domains is identified in terms of these parameters. Based on these criteria, the region most suitable for operation of SPLITT fractionation corresponds to [Vdot] (a)/[Vdot] (a′) ≥ 8, and Ri in the range of 0.001 to 0.0055, depending upon the value of [Vdot] (a)/[Vdot] (a′) Experimental verification is provided by the successful separation of a sample of glass bead particles using a multistage fractionation system.     

Aerosol Particle Removal and Re-entrainment in Turbulent Channel Flows – A Direct Numerical Simulation Approach

Aerosol particle removal and re-entrainment in turbulent channel flows are studied. The instantaneous fluid velocity field is generated by the direct numerical simulation (DNS) of the Navier – Stokes equation via a pseudospectral method. Particle removal mechanisms in turbulent channel flows are examined and the effects of hydrodynamic forces, torques and the near-wall coherent vorticity are discussed. The particle resuspension rates are evaluated, and the results are compared with the model of Reeks. The particle equation of motion used includes the hydrodynamic, the Brownian, the shearinduced lift and the gravitational forces. An ensemble of 8192 particles is used for particle resuspension and the subsequent trajectory analyses. It is found that large-size particles move away roughly perpendicular to the wall due to the action of the lift force. Small particles, however, follow the upward flows formed by the near-wall eddies in the low-speed streak regions. Thus, turbulent near-wall vortical structures play an important role in small particle resuspension, while the lift is an important factor for reentrainment of large particles. The simulation results suggests that small particles (with τ _p ⁺ ≤ 0.023) primarily move away from the wall in the low-speed streaks, while larger particles (with τ _p ⁺ ≥ 780) are mostly removed in the high-speed streaks.     

Transport and Deposition of Angular Fibers in Turbulent Channel Flows

Transport and deposition of angular fibrous particles in turbulent channel flows were studied. The instantaneous fluid velocity field was generated by the direct numerical simulation (DNS) of the Navier-Stokes equation via a pseudo-spectral method. An angular fibers was assumed to consist of two elongated ellipsoids attached at their tips. For a dilute suspension of fibers, a one-way coupling assumption was used in that the flow carries the fibers, but the coupling effect of the fiber on the flow was neglected. The particle equations of motion used included the hydrodynamic forces and torques, the shear-induced lift and the gravitational forces. The hydrodynamic interactions of the high aspect ratio linkage were assumed to be negligibly small. Euler's four parameters (quaternions) were used for describing the time evolution of fiber orientations. Ensembles of fiber trajectories and orientations in turbulent channel flows were generated and statistically analyzed. The results were compared with those for spherical particles and straight fibers and their differences were discussed. Effects of fiber size, aspect ratio, fiber angle, turbulence near wall eddies, and various forces were studied. The DNS predictions were compared with experimental data for straight fibers and a proposed empirical equation model.     

Phase Distribution Measurements during Transient Bubbly Two‐Phase Flow in a Vertical Pipe

An experimental procedure for investigating transient bubble flow for an adiabatic air/water system with vertical upward flow in a pipe is presented. The results of the measured local transient two‐phase flow parameters are shown along a pipe length of approx. four meters. From the measured radial phase distributions under steady and under transient conditions one can draw conclusions about the interfacial forces. Here, the effects indicate the action of forces such as a transverse lift force and a time dependent force like the virtual mass force during the transient. For modelling the transverse lift force which seems to play a dominant role for that flow regime the formulation of Zun was chosen and it was implemented into the commercial CFD‐Code Fluent Release 4.4.4 via user‐defined subroutines. Finally, results from the simulation of the steady states of start and end conditions of an experimental measured transient are shown.     

Buoyancy-Driven Continuous SPLITT Fractionation: A New Technique for Separation of Microspheres

Abstract

A new method of Continuous Fractionation using a SPLITT cell is conceived, developed, and tested, and is demonstrated to be useful for separation of collections of particles with different sizes and densities. With this previously uninvestigated mode of operation, this is accomplished for particles by buoyancy-driven separation. Some of the capabilities of this system are illustrated by successful separations of different-sized fluorescent polymer microspheres, with different carrier densities. The resulting experimentally-measured fraction recovery variations are then in good agreement with theoretical calculation from buoyancy-driven SPLITT theory.     

Hydrodynamic forces on monodisperse assemblies of axisymmetric elongated particles: Orientation and voidage effects

We investigate the average drag, lift, and torque on static assemblies of capsule-like particles of aspect ratio 4. The performed simulations are from Stokes flow to high Reynolds numbers (0.1 ≤ Re ≤ 1,000) at different solids volume fraction (0.1 ≤ ɛ_s ≤ 0.5). Individual particle forces as a function of the incident angle ϕ with respect to the average flow are scattered. However, the average particle force as a function of ϕ is found to be independent of mutual particle orientations for all but the highest volume fractions. On average, a sine-squared scaling of drag and sine-cosine scaling of lift holds for static multiparticle systems of elongated particles. For a packed bed, our findings can be utilized to compute the pressure drop with knowledge of the particle-orientation distribution, and the average particle drag at ϕ = 0° and 90°. We propose closures for average forces to be used in Euler–Lagrange simulations of particles of aspect ratio 4.     

Euler/Lagrange computations of pneumatic conveying in a horizontal channel with different wall roughness

The present study is related to the particle behaviour and the pressure drop in a particle-laden six meter long horizontal channel with rectangular cross-section from both experimental and numerical perspectives. Experiments and calculations are carried out for different spherical glass beads with diameters between 60 and 625 μm and mass loadings up to 1.0 (kg particles/kg gas). Additionally, stainless steel walls with different wall roughness are considered. In all experiments the air volume flow rate is constant in order to maintain a fixed gas average velocity of 20 m/s. As a result, the pressure drop in the channel is strongly influenced by wall roughness. Higher wall roughness implies higher pressure drop because of the increase in wall collision frequency, whereby momentum is extracted from the fluid due to two-way coupling. The numerical computations were performed by the Euler/Lagrange approach accounting for two-way and four-way coupling. For the calculation of the particle motion all relevant forces (i.e. drag, transverse lift and gravity), inter-particle collisions and wall collisions with wall roughness were considered. The agreement of the computations with the experiments was found to be very good for the gas and particle velocities as well as the pressure drop.