Split-Flow Thin (SPLITT) Cell Separations Operating under Sink-Float

Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Split-Flow Thin (SPLITT) Cell Separations Operating under Sink-Float Mode Using Centrifugal and Gravitational Fields Bhajendra N. Barman,*,† P. Stephen Williams,‡ Marcus N. Myers,§ and J. Calvin Giddings§ Field-Flow Fractionation Research Center, Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, United States S Supporting Information *

ABSTRACT: Particles of two different densities can be continuously and rapidly separated by employing sink-float phenomenon in split-flow thin (SPLITT) cells using both centrifugal and gravitational fields. Separation of a binary mixture of submicron size latex beads differing in densities is achieved by feeding them as a suspension in a carrier liquid of intermediate density into a SPLITT cell subject to a centrifugal field. A steady state condition is rapidly achieved, and two particle types accumulate at opposing channel walls as they are carried by the laminar channel flow to two separate outlets. Similarly, micron size particles of two different densities are separated using a planar channel and the gravitational field. Equations are developed to predict throughput in terms of the number fractions of the separated particles determined by scanning electron microscopy. Experimental results from three SPLITT cell systems under different field and flow conditions are compared with theoretical predictions.

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INTRODUCTION The concept of separation across the thin dimension of splitflow thin (SPLITT) cells or channels introduced by Giddings1 in 1985 has found a wide range of applications. In such cells, the differential migration of component species can be induced by an applied field such as a gravitational field,2−7 a centrifugal field,8−12 an electrical field,13−15 a magnetic field,16,17 or hydrodynamic lift forces.18 The diffusion mode of SPLITT cell separation of low molecular weight materials from macromolecules was also demonstrated.19,20 The differential transport processes are rapid in a SPLITT cell because transport occurs across the thin channel dimension which is typically just a fraction of a millimeter. Besides Brownian motion which is often negligible or can be suppressed enough to be ignored, the particles within the SPLITT cell are subject to just two transport processes. They are transported along the flow axis by entrainment in the flowing carrier fluid. Simultaneously, particles that are influenced by the field applied perpendicularly to the flow axis migrate across the channel thickness. It is the latter which is responsible for separation in a SPLITT cell. The SPLITT cell separation methodology is an outgrowth of field-flow fractionation (FFF) although their operational modes are quite different. Both techniques make use of a thin elongated flow channel across the thickness of which a field or gradient is applied. The major difference lies in the direction of differential migration. FFF utilizes differential migration of components along the flow axis, and consequently, this method is applied for analytical or small scale batch separations.21,22 On the other hand, SPLITT methods where the separation occurs © XXXX American Chemical Society

across the thickness of the channel are intended for continuous and preparative scale separation.1,2 Usually, flow splitters at one or both ends of the SPLITT cell control the distribution of the incoming feed and outgoing fractionated products. Such flow splitters are not necessary for FFF separations, but may be used for other purposes such as hydrodynamic relaxation prior to separation23,24 or mitigating dilution of separated species at the channel outlet.23,25,26 There have been numerous applications of SPLITT cells based on gravitational and centrifugal fields using different channel designs and modes of operation. Gravitational SPLITT cell systems have been successfully applied to the continuous and rapid fractionation of 7−15 μm diameter polystyrene beads2 and 1−10 μm polydisperse glass beads into different narrow size distributions.3 An analytical SPLITT cell at 1 g has provided estimates of the abundance of oversized quartz particles and glass beads in given samples.4 A gravitational SPLITT cell has also been used to fractionate environmental samples,27 marine sediments,5 biological samples,28,29 and starch particles.30 A SPLITT cell operated in diffusion mode has been used to measure diffusion coefficients of proteins.31 A diffusion mode SPLITT cell system has also been used to purify proteins by depletion of low molecular weight contaminants.19,32 Centrifugal SPLITT cells have been employed in Received: October 16, 2017 Revised: January 18, 2018 Accepted: January 23, 2018

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DOI: 10.1021/acs.iecr.7b04223 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research the fractionation of blood cells, platelets and plasma proteins,9 and pharmaceutical emulsions.12 In this work, centrifugal SPLITT cells were used for continuous separation of submicron size particles where the higher field enhanced the sedimentation process. Submicron particles can exhibit significant Brownian motion which tends to oppose the separation of the two particle populations in the thin channel. However, the enhanced field-driven transport of the particles in the centrifugal field counters Brownian transport and diminishes its disruptive effect on the separation.33 The centrifugal SPLITT cell in this study resembles a ribbon-like sedimentation FFF channel as shown in Figure 1. The channel circles a centrifuge rotor such that a

Figure 2. Mechanism of separation of lighter class 1 (○) and heavier class 2 (●) particles eluting from a single inlet and split outlet SPLITT channel. V̇ a and V̇ b are the volumetric flow rates at outlet a and outlet b, respectively. V̇ is the inlet flow rate, equal to V̇ a + V̇ b.

liquid accumulate at upper wall A, whereas those of class 2 with a density higher than that of the carrier liquid accumulate at lower wall B. In this work, wall A corresponds to the inner wall in a centrifugal SPLITT or top wall in a gravitational SPLITT system, and wall B corresponds to the outer wall in a centrifugal SPLITT or bottom wall in a gravitational SPLITT system. The class 1 and class 2 particles are carried down the channel by the fluid flow and subsequently elute through outlets a and b, respectively, as pure or enriched fractions depending on the experimental conditions. The SPLITT separation process therefore utilizes a simple sink−float phenomenon when particles accumulate at opposite walls because of different relative buoyancy. The speed of separation is aided by the relatively short transverse transport distances involved. Although the separation is based on particle buoyant density, the particle size as well as the strength of the applied field influence the rate at which particles reach their respective accumulation walls. A strong centrifugal field is generally required to enhance the rate of migration of submicron size particles. For micron size particles, a gravitational field is adequate to effect separation provided their densities differ sufficiently from that of the suspending fluid. The present SPLITT cells operate in an equilibrium mode where different particles approach different equilibrium positions across the channel thickness.34 A lack of hydrodynamic confinement of the sample stream by merging of inlet flow streams in these channels should not affect the separation because the equilibrium distributions within the thin dimension of the channel are independent of the initial particle positions at the inlet. A physical splitter in the outlet region of the SPLITT cell helps in preventing remixing of the two distinct layers formed at the two accumulation walls as they are carried to the outlets. An ideal physical splitter in a gravitational SPLITT channel is perfectly flat and parallel to the channel walls, and in a centrifugal SPLITT channel it has a slight curvature but remains exactly concentric with the curved channel walls. In either case, a virtual surface divides the fluid elements in the channel that exit the two different outlets. Ideally, this surface, known as the outlet splitting plane (OSP), is also parallel to the channel walls. Its position within the channel thickness depends on the ratio of the outlet flow rates V̇ a and V̇ b, where V̇ a and V̇ b are flow rates at outlets a and b, respectively.20 Any distortion of the stream splitter will result in a distortion of the OSP. This effect has been computationally modeled and experimentally explored for an annular SPLITT device.35,36 The same principles apply to the thin parallel-walled channels considered in this work. It is therefore important that the splitter be as well-constructed as possible. When an outlet

Figure 1. Schematic of a centrifugal SPLITT cell. Symbols u1 and u2 represent lateral transport velocities under field-induced migration of lighter class 1 and denser class 2 particles, respectively.

centrifugal field can be applied in a direction perpendicular to the flow of carrier liquid along the channel. This SPLITT cell has one inlet and two outlets. One of the channels was equipped with a flow splitter between the outlets to aid the smooth division of the flow streams at the end of the channel. The channel was used for the continuous fractionation of two classes of submicron size particles of different densities suspended in a carrier liquid of intermediate density. Experiments were also performed on the same binary particle suspension using a second channel without a physical outlet flow splitter. A gravitational SPLITT cell was used for the separation of micron size latex beads. It was made from a copper-clad Teflon spacer sandwiched between two glass plates. Similar to a conventional gravitational FFF channel, the ends of the channel were tapered and extend to the single inlet and two outlet ports located on the upper and lower walls at the outlet end of the channel. This channel included a physical flow splitter made of a Teflon spacer core mounted parallel to the channel walls between the outlet ports. A schematic of the separation of two classes (1 and 2) of particles is given in Figure 2. Shown in this figure are the axial flow carrying the particles in the z direction and lateral transport of the particles due to a field-induced migration in the x direction. The two classes of particles accumulate at the opposite walls depending on their densities relative to the carrier liquid that is arranged to have an intermediate density. The class 1 particles with density lower than that of the carrier B


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Industrial & Engineering Chemistry Research stream splitter is not included between directly opposed outlets, there is a greater chance that the OSP will be distorted by asymmetry of the flow pattern at the channel outlets. Nevertheless, if the particles can be brought down to their respective channel walls as very thin layers and this can be aided by application of the centrifugal field, then a good separation may still be obtained.37 This possibility was experimentally explored in the work. It should also be mentioned that there is an alternative design for splitter-less SPLITT cells, known as the step-SPLITT device.38,39 At a step-SPLITT outlet, a fraction of the fluid exits the channel at a slot across the breadth of one wall just in front of a step reduction in channel thickness, with the remaining fluid proceeding past the step to a second outlet. The gathering of fluid from the first slot can take place in the dimension at right angles to the channel. While this design would not be susceptible to distortion under centrifugation, it would not be easily implemented for a centrifugal system. Also, the design does not eliminate the possible distortion of the OSP, as this would result from any imperfections in the slot or step geometry just as occurs with imperfection of a flow splitter. In this paper, experimental results for the continuous separation of binary latex mixtures of different densities are presented. Equations are derived to quantitatively describe the separation process in the SPLITT cell system. Effects of channel dimensions, field strength, densities of sample components and fluid, particle sizes, inlet flow rate, and the two outlet flow rates on the throughput and resolution are evaluated through these equations. Studies have been carried out to compare performances of SPLITT cells having a physical flow splitter between the outlets with theoretical predictions. Examples for the quality of separation of particles using a centrifugal SPLITT channel lacking a physical flow splitter are also provided.

ΔV2̇ = bLu 2 =

V 0u 2 w

(1)

where b is the channel breadth, L is the channel length, w is the channel thickness, and V0 is the channel volume. The second formulation on the right of eq 1 is included because the channel thickness is generally more certain than the channel breadth. The SPLITT channel volume may be determined by measuring the elution volume of a sodium benzoate injection, and its thickness is assumed to be equal to that of the spacer used in its construction. For a sedimentation process in the laminar flow regime, u2 for a spherical particle is given by u2 =

|Δρ2 |d 2 2G 18η

= s 2G

(2)

where Δρ2, as noted above, is the difference in the density between the class 2 particles (ρ2) and the carrier liquid (ρ0), G is the sedimentation field strength (acceleration), d2 is the class 2 particle diameter, and η is the viscosity of the carrier liquid. The symbol s2 represents the sedimentation coefficient of a class 2 particle.2 Using eqs 1 and 2, we obtain ΔV2̇ =

V0 s 2G w

(3)

For a SPLITT channel having a single inlet it may be assumed that particles are initially distributed uniformly across the full channel thickness. Considering class 2 particles again, it is evident that a fraction commence their migration along the channel from positions below the OSP, the plane dividing the fluid streams that exit the two outlets. This fraction will exit outlet b no matter how fast the flow velocity, provided the flow remains laminar. The remainder of the class 2 particles are initially located above the OSP, and depending on field and flow conditions, a fraction or possibly all of these may migrate across the OSP before exiting the channel. Those that do cross the OSP exit at outlet b, while those that do not have time to migrate this far exit at outlet a. If ΔV̇ 2 < V̇ a, the fraction of class 2 particles that exit outlet b is given by

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THEORY As mentioned earlier, a particle inside the SPLITT cell is subject to two transport processes, the flow and field induced migrations. In a centrifugal field, the enhanced field-induced migration of submicron particles can be so much greater than Brownian motion that the latter can be ignored. Figure 2 shows that migration due to axial flow takes place along the z axis (i.e., length of the channel) and field-induced migration occurs in the x direction (i.e., thickness of the channel). Let us consider the densities of lighter class 1 and denser class 2 particles are denoted by ρ1, and ρ2, respectively, and that the carrier liquid has density ρ0. It follows that ρ1 < ρ0 < ρ2; Δρ1 = ρ1 − ρ0 < 0; Δρ2 = ρ2 − ρ0 > 0. It will be assumed that the two classes of particle are monodisperse in size and density for the following discussion. For the separation process involving class 2 particles which tend to accumulate at the outer wall B and exit through outlet b, the class 2 particle starting at the topmost left position of the channel in Figure 2 moves toward the bottom outlet b with a lateral transport velocity u2 under the influence of the field. During the time of its migration along the length of the channel, it may not traverse the full channel thickness. In this case, it will cross volumetric flow elements corresponding to a flow rate ΔV̇ 2, which is less than the total volumetric flow rate V̇ along the channel. This volumetric flow rate ΔV̇ 2 is obtained by the simple equation2

F2(b) =

Vḃ + ΔV2̇ Vȧ + Vḃ

(4)

and if ΔV̇ 2 ≥ V̇ a then F2(b) = 1.0. The fraction F2(b) is known as the predicted fractional retrieval of class 2 particles at outlet b. If ΔV̇ 2 < V̇ a, the fraction of class 2 particles that exit outlet a is given by F2(a) =

Vȧ − ΔV2̇ = 1 − F2(b) Vȧ + Vḃ

(5)

and of course, if ΔV̇ 2 ≥ V̇ a then F2(a) = 0.0. The same logic applies to the consideration of buoyant class 1 particles where it is similarly shown that, with ΔV̇ 1 = V0s1G/ w, the predicted retrieval fraction of class 1 particles in outlet a is given by F1(a) =

Vȧ + ΔV1̇ Vȧ + Vḃ

(6)

which is valid for ΔV̇ 1 < V̇ b. For ΔV̇ 1 ≥ V̇ b we have F1(a) = 1.0. It also follows that

F1(b) = 1 − F1(a) C

(7) DOI: 10.1021/acs.iecr.7b04223 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research It is apparent from these equations that if conditions are arranged such that V̇ a = ΔV̇ 2 and V̇ b = ΔV̇ 1 then it would be theoretically predicted that F2(b) = 1.0 and F1(a) = 1.0, and a complete separation of the particle classes would be obtained. It follows that the maximum sample flow rate V̇ max for which complete separation is theoretically possible is given by ̇ Vmax

V 0G = ΔV1̇ + ΔV2̇ = (s1 + s2) w

Analogous equations can be obtained for predicted particle number fractions exiting from outlet a. These may be written as f2(a) =

̇ N2(b) ̇ + N2(b) ̇ N1(b)

=

(12)

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EXPERIMENTAL SECTION A centrifugal SPLITT apparatus based on a modified sedimentation FFF instrument and a conventional gravitational SPLITT channel were used in this study. A basic description of a sedimentation FFF instrument can be found elsewhere.21 The centrifugal SPLITT system employed an FFF-type channel with a single inlet and two outlet ports on opposite channel walls at the outlet end. The channel is wrapped around the centrifuge basket, and the distance between the channel and its axis of rotation was 15.3 cm. For this centrifugal SPLITT system, the fluid streams from the two outlets must be kept separate from one another as well as from the inlet stream, and these are conducted to and from the spinning channel via a rotating seal modified to accommodate the additional outlet stream.34 SPLITT cells with and without physical splitters are shown schematically in Figure 3a,b, respectively.

Figure 3. Schematics of SPLITT cells. (a) Channel with a physical outlet flow splitter and (b) channel without a physical splitter.

SPLITT Cell 1. Centrifugal SPLITT Cell with a Physical Outlet Stream Splitter. The channel spacer was fabricated from RT/Duroid material from the Rogers Corporation (Chandler, AZ). This material was a glass microfiber reinforced polytetrafluoroethylene (Teflon) composite with electrodeposited copper foil on both sides. The total thickness of the laminate was 0.0380 cm. The thickness of copper layer on each side of the laminate was 0.0068 cm. For this SPLITT channel, there is a triangular inlet endpiece for the single inlet, but the outlet end is cut square a short distance from the outlets (see Figure 3a). The copper layer on each side of the laminate was

(9)

where F1(b) and F2(b) in this equation are predicted fractional retrievals calculated using eqs 2−7. The predicted number fraction of class 1 particles in the b outlet is then given by f1(b) = 1 − f2(b)

(11)

Experimental number fractions of particles exiting outlets a and b may be defined in a similar way, so that f1(a) = N1(a)/(N1(a) + N2(a)) and f 2(a) = N2(a)/(N1(a) + N2(a)), where N1(a) and N2(a) represent the number counts of class 1 and 2 particles, respectively, in an electron micrograph of a sample collected at outlet a. For outlet b, we similarly obtain f1(b) = N1(b)/(N1(b) + N2(b)) and f 2(b) = N2(b)/(N1(b) + N2(b)). It is assumed that the ratio of particle classes exiting a given outlet per unit time is equal to the ratio of particle counts in the micrographs.

(8)

F2(b)f2(i) F1(b)f1(i) + F2(b)f2(i)

F1(a)f1(i) + F2(a)f2(i)

f1(a) = 1 − f2(a)

and the required V̇ b/V̇ would be given by ΔV̇ 1/V̇ max. Of course, for eq 8 to be valid, it is necessary that the OSP be perfectly parallel to the channel walls. If conditions do not allow for complete separation of the particle classes, then it is possible to predict the theoretical level of contamination of each of the outlet streams. It is convenient to predict cross-contamination of the outlet streams in terms of number fractions. The degree of cross-contamination will be shown to be a function of the number fractions of class 1 and class 2 particles in the sample feed as well as the system dimensions and field and flow parameters. Equations 1 and 8 suggest that V̇ max, the maximum theoretical throughput of the SPLITT cell, increases with b, L, G, and both s1 and s2 that are in turn inversely proportional to η. The flow rates ΔV̇ 1 and ΔV̇ 2 are independent of channel thickness when Brownian motion is ignored. To estimate the extent of cross-contamination due to V̇ a being in excess of ΔV̇ 2 and/or V̇ b being in excess of ΔV̇ 1, it is useful to derive equations in terms of easily observable experimental parameters such as the number fraction of each particle class present in the feed as well as fractionated products. When the class 1 and class 2 particles are monodisperse in both size and density but differ in size, the fraction of each particle type in the feed, and eluents collected from the two outlets can be determined by counting particles of each size in their electron micrographs. Let f1(i) and f 2(i) be the number fractions of class 1 and class 2 particles, respectively, in the sample introduced at the channel inlet. After separation in the channel, the number fractions of class 1 and class 2 particles collected from outlet a are denoted by f1(a) and f 2(a), respectively. The corresponding number fractions at outlet b are denoted by f1(b) and f 2(b). Let us assume that Ṅ 1(i) class 1 particles and Ṅ 2(i) class 2 particles are introduced per unit time at the inlet of the SPLITT cell. Let us also assume that Ṅ 1(a) and Ṅ 2(a) represent the respective numbers of particles exiting outlet a per unit time, with Ṅ 1(b) and Ṅ 2(b) exiting at outlet b. It follows that f1(i) = Ṅ 1(i)/(Ṅ 1(i) + Ṅ 2(i)) and f 2(i) = Ṅ 2(i)/(Ṅ 1(i) + Ṅ 2(i)). It is also apparent that under steady state conditions F1(a) = Ṅ 1(a)/Ṅ 1(i), and similar relationships hold for F1(b), F2(a), and F2(b). It follows that under steady state conditions a predicted number fraction for class 2 particles in the b outlet may be determined via the equation f2(b) =

F2(a)f2(i)

(10) D


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Industrial & Engineering Chemistry Research

Micron size latex beads, nominally 15 μm PS (Duke Standards, Palo Alto, CA) and 5 μm PMMA (from Seradyn Diagnostics) were obtained as 1% and 10% suspensions by weight, respectively. Using electron micrographs of PS beads taken at a magnification of 800×, the diameter of these beads was found to be 13.48 ± 0.81 μm. Micrographs for PMMA beads at a magnification of 3000× provided a diameter of 4.04 ± 0.21 μm. A total of 5 mL of PS and 25 μL of PMMA were added to 1000 mL of 18.0% sucrose solution to carry out experiments using the gravitational SPLITT cell 3. SPLITT Separation Procedures. As shown schematically in Figure 3, a mixture of particles suspended in the sucrose solution was continuously introduced to the inlet of the channel using a Gilson peristaltic pump (Middleton, WI). Under the influence of a centrifugal or gravitational field and depending on their densities, particles accumulate at the opposite channel walls as they are carried by the axial flow to outlets a and b. The ratio of volumetric flow rates at the two outlets was controlled using coiled flow restrictors made from 0.05 cm i.d. stainless steel tubing. For a fixed sample flow rate, the ratio of the outlet flow rates could be varied by changing the lengths of the two flow restrictors. The degree of cross contamination could then be determined as a function of V̇ b/V̇ for fixed V̇ by examination of micrographs of collected outlet streams. To equilibrate the SPLITT system with a new colloidal suspension at a specific sample flow rate, a volume equivalent to 10−20 times the channel volume was allowed to flow under a centrifugal field for submicron size particles or gravitational field for micron size particles. The eluent at each outlet was only then collected. To re-equilibrate for a different flow regime, a volume of suspension equivalent to 3−5 times the channel volume was allowed to flow through the channel before collection of eluents. All experiments were carried out at ambient laboratory temperature of 293 ± 2 K. Electron Microscopy. In this work, the quality of separation was determined by subjecting each collected colloidal suspension to scanning electron microscopy. For this, each collected fraction was stirred well, and about 2 mL was filtered through a 0.1 μm pore size Nucleopore membrane filter (Pleasanton, CA). The filtered particles were washed with distilled water to remove any adsorbed sucrose crystals and then air-dried. A cut from the filter paper containing particulates was used as the specimen for electron microscopy. Each specimen was first coated with gold using a Technico Hummer III sputter coater (Alexandria, VA) and then observed under a Hitachi S-450 scanning electron microscope (Tokyo, Japan) working at a 15 kV accelerating voltage and a 5 mm working distance. Typical magnifications used were 3000× for submicron-size particles and 400× for micron-size particles. At least two micrographs from two different areas of the filter were taken for each specimen. Usually, each of these micrographs contained from 600 to 2300 particles for centrifugal SPLITT separations. When the total number of particles counted was less than 600 from a single micrograph, particle counts from two micrographs were combined. Typically, multiple micrographs from each specimen provided number fractions for the classes of particles, differing by 3% or less. For gravitational SPLITT separations, because of the larger particle sizes, particle counts of 600 or more were achieved for only half of the times, even with combination of two micrographs. For this mode, total particle counts from 250 to 1225 were used to calculate number fractions. The particle counts and number fractions for

then etched using dilute nitric acid, into the triangular forms leading to the two outlets. The exposed Teflon composite core serves as the flow splitter. The edge of the splitter was carefully cut and polished with fine sand paper. Three small strips of copper on each side of the splitter were left in place to firmly locate the splitter at the channel midpoint when the channel spacer was secured inside a centrifuge basket. They also helped to prevent the distortion of the splitter during centrifugation. The spacer was sandwiched between two polished Hastelloy C strips which serve as the channel walls as shown in Figure 1, and the three layers were clamped together within the centrifuge basket. The breadth of the channel and channel tip-to-tip length were 1.5 and 90.5 cm, respectively. The channel volume measured as the elution volume of a sodium benzoate peak was 5.00 mL. SPLITT Cell 2. Centrifugal SPLITT Cell without a Physical Outlet Stream Splitter. This was constructed using a Mylar spacer of 0.0254 cm thickness. The complete channel outline, including both triangular inlet and outlet endpieces, was cut from the Mylar spacer. This channel had a breadth of 2.0 cm and tip-to-tip length of 90.5 cm. The channel volume was found to be 4.50 mL. SPLITT Cell 3. Gravitational SPLITT Cell with a Physical Outlet Stream Splitter. This channel had a tip-to tip length of 26.0 cm, breadth of 2.0 cm, and thickness of 0.0380 cm. The channel was made using a copper-clad Teflon spacer similar to that used for SPLITT cell 1. This was sandwiched between two glass plates that were clamped together between two Plexiglas blocks using nuts and bolts. The glass plates served as channel walls, and the SPLITT cell was used in its horizontal position. Inlet and outlet flows passed through small holes drilled through the glass plates and Plexiglas blocks. The volume of this channel was found to be 2.03 mL. Carrier Liquids. For the separation of submicron-size particles under centrifugal fields, SPLITT cells 1 and 2 were employed. Experiments were performed on a binary mixture of latex beads suspended in 21.6% (w/w) sucrose solution containing 0.02% (w/v) Alkawet-N surfactant, (Lonza Inc., Long Beach, CA). The carrier liquid density was determined to be 1.090 ± 0.001 g/mL, and its viscosity was 0.0185 P. For gravitational SPLITT cell 3 experiments with micron-size particles, a binary mixture of latex beads was suspended in 18.0% (w/w) sucrose solution containing 0.02% (w/v) Alkawet-N. The density of this carrier liquid was 1.075 ± 0.001 g/mL, and it had a viscosity of 0.0161 P. Latex Particles and Their Suspensions. Uniform submicron size latex beads were obtained from Seradyn Diagnostics (Indianapolis, IN) as 10% by weight suspensions. These were polystyrene (PS) beads with a particle diameter of 0.822 ± 0.008 μm and density of 1.050 g/mL and poly(methyl methacrylate) (PMMA) beads with a mean particle diameter of 0.586 μm and density of 1.210 g/mL. The standard deviation in the PMMA particle diameter was not available, but they had a narrow distribution. These two types of particles can be easily distinguished by their sizes in electron micrographs. A typical mixture of the two classes of colloidal particles was obtained by adding 100 to 300 μL of 10% weight suspension of each latex bead to 1000 mL of sucrose solution. The volume of each concentrated latex suspension to be added to the sucrose solution was varied to obtain the desired composition of particles (typically, close to 50:50 number fractions) in the mixture. E


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Industrial & Engineering Chemistry Research all reported experiments are listed in the Supporting Information.

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RESULTS AND DISCUSSION The volumetric flow rate ΔV̇ 2 traversed by a class 2 particle is determined from the channel dimensions, applied field strength, and sedimentation coefficient, as shown by eqs 1−3. The corresponding volumetric flow rate ΔV̇ 1 traversed by class 1 particles is similarly calculated. Their relationship with V̇ , V̇ a, and V̇ b determines the quality of the binary separation and the degree of cross contamination, if any. According to theoretical predictions, for centrifugal SPLITT systems, the class 1 particles which accumulate at the inner wall of the channel and exit outlet a will not be contaminated with class 2 particles if V̇ a is less than ΔV̇ 2. Similarly, the class 2 particles will exit as a pure product from outlet b if V̇ b is less than ΔV̇ 1. The sedimentation coefficients for the 0.822 μm PS and 0.586 μm PMMA particles in the 21.6% sucrose solution were calculated to be 8.12 × 10−10 and 12.4 × 10−10 s, respectively, and those of the 13.48 μm PS and 4.04 μm PMMA particles in the 18.0% sucrose solution to be 15.7 × 10−8 and 7.60 × 10−8 s, respectively. The calculated values of ΔV̇ 1 and ΔV̇ 2 for the submicron particles at the two different field strengths used for SPLITT cells 1 and 2 are provided in Table 1. The corresponding values for the 13.48 μm PS and 4.04 μm PMMA particles separated using gravitational SPLITT cell 3 are also listed in Table 1.

Figure 4. Scanning electron micrographs showing the effect of V̇ b/V̇ on the quality of fractionated products. Experimental conditions: SPLITT cell 1 with a field of 42.8g and inlet volumetric flow rate V̇ = 0.85 mL/min. Composition of the feed mixture: 48% of 0.586 μm PMMA and 52% of 0.822 μm PS by number.

Table 1. Values of Traversed Flow Rates ΔV̇ for PS and PMMA Nanoparticles in 21.6% Sucrose Solution and Centrifugal SPLITT Cells 1 and 2 and for PS and PMMA Microparticles in 18.0% Sucrose Solution and Gravitational SPLITT Cell 3, together with the Maximum Flow Rates V̇ max for which Complete Separation Is Theoretically Possible in Each Case SPLITT cell

field (g)

1

42.8

1

61.6

2

42.8

2

61.6

3

1.0

latex beads

ΔV̇ (mL/min)

V̇ max (mL/min)

0.822 μm PS 0.586 μm PMMA 0.822 μm PS 0.586 μm PMMA 0.822 μm PS 0.586 μm PMMA 0.822 μm PS 0.586 μm PMMA 13.48 μm PS 4.04 μm PMMA

0.269 0.410 0.387 0.590 0.362 0.552 0.521 0.795 0.493 0.239

0.679

fixed sample flow rate and field strength the purity of the fractionated products varied with V̇ b/V̇ . A cursory observation suggests that, as V̇ b/V̇ is increased, purity of the PS fraction obtained from the outlet a improves. On the other hand, the purity of the PMMA fraction from the outlet b becomes worse as V̇ b/V̇ is increased. Predicted number fraction plots for the separations of the mixture of 0.822 μm PS and 0.586 μm PMMA particles suspended in 21.6% (w/w) sucrose solution are shown in Figure 5. These separations were carried out using the SPLITT cell 1 at a sample flow rate of 0.85 mL/min and two different field strengths of 42.8 and 61.6g. The sample flow rate of 0.85 mL/min is greater than the calculated V̇ max of 0.68 mL/min at 42.8g. Therefore, there is no outlet flow rate ratio for which complete separation of the particles is predicted, as can be seen by examination of Figure 5a. The predicted number fraction f 2(b) of PMMA particles in outlet stream b is equal to 1.0, indicating pure PMMA product, for V̇ b/V̇ ≤ ΔV̇ 1/V̇ = 0.32. At this limiting V̇ b/V̇ , the predicted f 2(a) > 0 indicating incomplete removal of PMMA particles from the PS particles exiting at outlet a. The PS particle fraction at outlet a is predicted to be free of contamination only for V̇ b/V̇ > 1 − ΔV̇ 2/V̇ = 0.52. At a field strength of 61.6g, however, V̇ max > V̇ and there is a range of V̇ b/V̇ (between 0.31 and 0.46) for which complete separation is theoretically possible. Experimental data points, derived from particle counting as previously described, for the separation at a field of 42.8g are in an excellent agreement with the theoretical curves as shown in Figure 5a. Experimental data points together with the predicted curves for the separations carried out with a field of 61.6g are shown in Figure 5b. The agreement of data points with the theoretical curves is not quite as good as shown in Figure 5a

0.977 0.914 1.32 0.732

For any given flow rate regime, the predicted fractional retrievals for the class 1 and class 2 particles at the two outlets are obtained using eqs 4−7. Equations 9 and 11 may be used to calculate predicted number fractions f 2(b) and f 2(a) of class 2 particles in the products collected from b and a outlets, respectively. Separation with SPLITT Cell 1 at 42.8 and 61.6g. Figure 4 provides several scanning electron micrographs taken for products fractionated by SPLITT cell 1 with a centrifugal field of 42.8g and sample flow rate of 0.85 mL/min. The feed mixture contained number fractions 0.48 of 0.586 μm PMMA particles and 0.52 of 0.822 μm PS particles suspended in the 21.6% sucrose solution. These micrographs indicate that for a F


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Figure 5. Separation using SPLITT cell 1 with an outlet flow splitter. Feed mixture consisted of 48% of 0.586 μm PMMA and 52% of 0.822 μm PS by number. Experimental conditions: (a) field = 42.8g and V̇ = 0.85 ± 0.01 mL/min and (b) field = 61.6g and V̇ = 0.85 ± 0.01 mL. Solid circles and squares are experimental data points. Predicted values are shown by short-dashed curves obtained from combination of eqs 9 and 11 together with eqs 4−7. Particle counts and calculated number fractions are listed in the Supporting Information.

Figure 6. Separation using SPLITT cell 2 without an outlet flow splitter. Feed mixture consisted of 48% 0.586 μm PMMA and 52% 0.822 μm PS by number. Experimental conditions: (a) field = 42.8g and V̇ = 0.85 ± 0.01 mL/min and (b) field = 61.6g and V̇ = 0.85 ± 0.01 mL/min. Solid circles and squares are experimental data points. Predicted number fractions correspond to the short-dashed curves. Particle counts and calculated number fractions are listed in the Supporting Information.

but is still quite reasonable. This indicates that there may have been some distortion of the edge of the Teflon splitter at the higher field strength. Any distortion of the edge of the splitter would lead to curvature of the OSP about its ideal position, which would allow some cross-contamination of particle populations emerging from the two outlets. Separation with SPLITT Cell 2 at 42.8 and 61.6g. The calculated ΔV̇ 1 and ΔV̇ 2 are higher for SPLITT cell 2 than for SPLITT cell 1, see Table 1. For ideal OSPs that are exactly planar and parallel to the channel walls, it would therefore be expected that, for some given field strength and sample flow rate, separation using SPLITT cell 2 would be at least as good as with SPLITT cell 1. This was not the case. SPLITT cell 2 does not include a physical flow splitter between the outlets to aid the division of flow. Without a physical splitter, it is extremely unlikely that the OSP would be planar and parallel to the channel walls. A planar OSP would require perfect alignment and symmetry of the channel outlets. The slightest offset of the position of one outlet from the other or the slightest difference in the angles that the outlet tubes make with the channel walls would give rise to asymmetry of fluid flow in the outlet region. This would result in distortion of the OSP with consequent reduction of separation efficiency. The reduced purities of the collected fractions compared to the ideal predicted purities are apparent in Figure 6a,b.

The plots in Figure 6 indicate that we obtained only enrichment in the concentrations of the desired products relative to the feed mixture of the particles where complete purification was predicted. It is apparent that the separation at 61.6g is quite good for V̇ b/V̇ = 0.25 where a number fraction of 0.98 for PMMA particles was obtained at outlet b and a number fraction of 0.89 for PS particles was obtained at outlet a. Most likely, this is because particle layers at the respective walls become relatively compressed as they approach the outlets, and their boundaries are largely beyond the distorted OSP. It may be concluded that separation can be achieved using a SPLITT channel lacking a physical splitter, but higher fields are required or the throughput must be reduced in order to obtain a separation comparable to those obtained when a flow splitter is used. Separation with Gravitational SPLITT Cell 3. Separations of micron size particles were carried out in SPLITT cell 3 at two inlet flow rates of 0.52 and 0.78 mL/min. As can be seen from Table 1, these flow rates fall below and above the calculated V̇ max of 0.73 mL/min. For this system, number fraction results are compared with theoretical predictions in Figure 7. At the flow rate of 0.52 mL/min, it was predicted that complete separation of PS and PMMA particles would be obtained for V̇ b/V̇ above 0.54. Few PMMA particles eluted with PS from outlet a for V̇ b/V̇ > 0.66 while the purity of PMMA G


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movements of the splitter. Teflon is susceptible to bending if a high enough force is applied and a thinner splitter would be more susceptible. An ideal splitter would be very thin (relative to the channel thickness) and made of hard metallic plate so that it does not bend or distort when the centrifuge is spun at a high speed. The experiments were performed using binary mixtures of monodisperse particles of different size and different density, and the theory was developed for predicting cross-contamination of the separated products in terms of number fractions of the components. This choice was made because of the ease with which the different particles could be distinguished from one another under microscopic examination. However, the theory for predicting conditions for complete binary separation of two monodisperse populations of different density is equally valid for particulate materials that are polydisperse in size. The calculation of ΔV̇ 1 and ΔV̇ 2 must simply be carried out for the particles having the lowest sedimentation coefficients in each population. As for complete separation of binary mixtures of monodisperse components, the sample flow rate V̇ is limited by the flow rate V̇ max = ΔV̇ 1 + ΔV̇ 2, and the outlet flow rate ratio V̇ b/V̇ must be confined to the interval between 1 − ΔV̇ 2/V̇ and ΔV̇ 1/V̇ . When V̇ = V̇ max, the boundaries of this interval are coincident and there is only a single solution for V̇ b/V̇ . However, for complete separation to be obtained at this V̇ b/V̇ , the OSP would have to be perfectly planar and parallel to the channel walls. It is clear that no outlet flow splitter can be perfectly constructed, but the use of an outlet flow splitter is certainly preferable over its omission. The selection of suitable flow conditions can compensate for small imperfections in the flow splitter that result in distortion of the OSP. If the flow rate V̇ is reduced in comparison to V̇ max then the interval for V̇ b/V̇ increases in range. The selection of V̇ b/V̇ close to the middle of the range would allow for some distortion in the OSP while still obtaining complete separation. The lower V̇ allows more time for the particles to migrate beyond the OSP, and its small distortions become irrelevant. By biasing V̇ b/V̇ to one side or the other of the interval, it is also possible to select which of the products is given priority in terms of purity. The SPLITT technique under sink-float mode is expected to be of great advantage in the study of many colloidal, environmental or biological samples where uniformity in terms of both size and density is seldom observed. It may also find applications in the separation and determination of purity of many nanomaterials varying in both size and density. Specifically, centrifugal SPLITT can be extended to much lower particle sizes by improving instrumentation to make use of much higher centrifugal fields. This would necessitate improvements to the rotating seal, the integrity of the channel, and the outlet flow splitter. After a rapid separation based on density, as in this case, the particles can be further characterized using a conventional SPLITT system for separation based on particle size. Techniques such as FFF methods3,12,40 where a high resolution separation is achieved based on particle size would, therefore, provide an accurate particle size distribution complementing the initial SPLITT cell separation. Other techniques such as particle sizing by laser light scattering can also be applied on the SPLITT separated samples.

Figure 7. Separation using gravitational SPLITT cell 3 with an outlet flow splitter. Feed mixture consisted of 65% 4.04 μm PPMA and 35% 13.48 μm PS by number. Experimental conditions: (a) V̇ = 0.52 ± 0.01 mL/min and (b) V̇ = 0.78 ± 0.01 mL/min. Solid circles and squares are experimental data points. Predicted number fractions correspond to the short-dashed curves. Particle counts and calculated number fractions are listed in the Supporting Information.

particles eluting from outlet b was at around 90%. At the higher flow rate of 0.78 mL/min there is no V̇ b/V̇ for which complete separation is predicted. It was found that PMMA particles eluted as a close to pure product from the outlet b for V̇ b/V̇ up to 0.69, as predicted. The number fractions for PMMA particles eluting from outlet a are also in quite good agreement with the theoretical predictions.

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CONCLUSIONS Good agreement was obtained between experimentally observed number fractions and theoretical predictions for binary separations obtained using both centrifugal and gravitational SPLITT systems that included a physical flow splitter. The observed number fractions diverged significantly from predictions for the centrifugal SPLITT cell that did not include a flow splitter. This suggests that a physical splitter is essential to ensure uniform division of outlet flow streams about an OSP parallel to the channel walls. In this work, the spacers for SPLITT cells 1 and 3 were a laminate material of a Teflon composite with electrodeposited copper foil on each side. The Teflon layer remaining after etching the layers of copper from both sides of the laminate served as the splitter and amounted to 63% of the total thickness of the channel. It is possible that the thickness of the splitter may have contributed to the asymmetry of the dividing flow because the relatively thin spaces to either side are easily influenced by very small H


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V̇ b V̇ max

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b04223. Tables listing PS and PMMA particle counts from electron micrographs and the calculated number fractions as plotted in Figures 5−7. (PDF)

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ΔV̇ 1, ΔV̇ 2 w

volumetric flow rate at outlet b maximum flow rate for which complete separation is theoretically possible volumetric flow rates traversed by class 1 and class 2 particles channel thickness

Greek Symbols

ρ0 density of carrier liquid ρ1, ρ2 densities of class 1 and class 2 particles Δρ1 = ρ1 − ρ0 difference in density between class 1 particle and carrier liquid Δρ2 = ρ2 − ρ0 difference in density between class 2 particle and carrier liquid η viscosity of the carrier liquid

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: 281-7197604. ORCID

Bhajendra N. Barman: 0000-0003-1951-2690 P. Stephen Williams: 0000-0002-5951-2612

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Present Addresses †

Huntsman Advanced Technology Center, 8600 Gosling Road, The Woodlands, TX 77381, United States. ‡ Cambrian Technologies Inc., 1772 Saratoga Avenue, Cleveland, OH 44109, United States.

REFERENCES

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Author Contributions

The manuscript was written through contributions of all authors. All authors, not deceased, have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest. § Deceased.

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GLOSSARY b channel breadth d1, d2 diameters of class 1 and class 2 particles, respectively F1(a), F2(a) fractional retrievals of class 1 and class 2 particles at outlet a F1(b), F2(b) fractional retrievals of class 1 and class 2 particles at outlet b f1(i), f 2(i) number fractions of class 1 and class 2 particles in the feed f1(a), f 2(a) number fractions of class 1 and class 2 particles recovered from outlet a f1(b), f 2(b) number fractions of class 1 and class 2 particles recovered from outlet b G sedimentation field strength L channel length N1(a), N2(a) numbers of class 1 and 2 particles in micrograph from outlet a N1(b), N2(b) numbers of class 1 and 2 particles in micrograph from outlet b Ṅ 1(i), Ṅ 2(i) numbers of class 1 and 2 particles entering channel inlet per unit time Ṅ 1(a), Ṅ 2(a) numbers of class 1 and 2 particles exiting outlet a per unit time Ṅ 1(b), Ṅ 2(b) numbers of class 1 and 2 particles exiting outlet b per unit time s1, s2 sedimentation coefficients for class 1 and class 2 particles u1, u2 field-induced transverse velocities of class 1 and class 2 particles V0 channel volume V̇ total volumetric flow rate (or sample flow rate) V̇ a volumetric flow rate at outlet a I


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Split-Flow Thin (SPLITT) Cell Separations Operating under Sink-Float

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