Continuous Cell Suspension Processing Using Magnetically Stabilized Fluidized Beds
Brenda E. Terranova Genetics Institute, Andover, Massachusetts, 01003 Mark A. Burns* Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136 Received March 24, 7989/Accepted July 25, 1990
The behavior of a cell suspension in a continuous magnetically stabilized fluidized bed (MSFB) was investigated both experimentally and theoretically. The low, constant pressure drop and fluidity of the solids phase in the MSFB allowed a continuous countercurrent separator to be constructed. The magnetic field eliminated all motion of the solids phase (nickel spheres) and produced a device similar to a packed-bed depth filter. Yeast cells were used as the suspended solids and the performance of the MSFB filter was assessed as a function of the bed height, solids velocity, cell concentration, and liquid composition. Removal rates could be adjusted by controlling the cell/support interaction and were found to be as high as 99%. A mathematical model was used to aid in understanding t h i s filtration and was found to agree qualitatively with all experimental observations. Comparison of the model with the data suggests that both celkell binding and cell shadowing are occurring. INTRODUCTION
Processing of cell suspensions is necessary in many commercial biochemical and biomedical processes. In recovering dissolved chemicals from fermentation broths, for example, the cell-laden broth usually undergoes a solid/liquid separation step before solute recovery can begin. This separation step is necessary since most solute recovery processes use column separation techniques (ion exchange, affinity, etc.) that cannot handle suspended solids in the feed. In single-cell protein recovery, the cell is the product and solid/liquid separation devices must adequately dewater the resulting cake. In other applications, such as whole-blood processing or in viable cell harvesting, the viability of the cells is the primary concern and the collection device must be gentle and nondestructive. For each application, there are a wide variety of cell separation techniques that can be used. Sedimentation is a relatively simple technique but can only be used for * To whom all correspondence should be addressed. Biotechnology and Bioengineering, Vol. 37, Pp. 110-120 (1991) 0 1991 John Wiley & Sons, Inc.
large cells or when the cells flocculate (either naturally or by induction). For small, nonflocculating cells, centrifugation or vacuum filtration is typically used and produces a more concentrated cell paste. If viability of the cells is important, membrane filtration in the form of hollow-fiber or spiral-bound cartridges is the method of choice. Membrane units, though, typically have fouling problems even when operated in a cross-flow mode. The device we are studying, the magnetically stabilized fluidized bed (MSFB), is more versatile than the above listed cell-processing techniques. Viable cells can either be collected (for cell recovery applications) or allowed to pass through the column unharmed (for whole-broth processing and recovery of product). The low pressure drop across the column means that high flow rates can be used and the fluidized nature of the bed allows the solids to be added and withdrawn so that continuous filtration is possible. Since the solid support in these continuous systems is constantly removed and treated, the device does not clog or foul. Previous work has shown that the MSFB can be used to recover proteins from an aqueous solution.”’ This work focuses-oninvestigating and characterizing the behavior of cells in stabilized beds. BACKGROUND Magnetically Stabilized Fluidized Beds (MSFBs)
The MSFB is a fluidized bed of magnetically susceptible particles placed in a weak, uniform magnetic field. Although there were studies of magnetic fields applied to fluidized beds and of the resulting stabilization as early as 1960, a large majority of the work in gas fluidized beds was published by Rosensweig, Siegell, and others at Exxon in 1979.3-6Their applications included hydrocarbon ~ e p a r a t i o n ,catalytic ~ c o n ~ e r s i o n ,and ~ molecular sieve a d ~ o r p t i o n .Several ~ ’ ~ groups have also CCC 0006-3592/91/020110-11$0400
investigated the use of the MSFB for removing fine particles from gases.326p7 More recently, we and others have used MSFBs in the area of biochemical separations using liquid as the fluidizing medium.1~''8 There are three properties which make the MSFB ideally suited for biochemical separations. First, the magnetic stabilization of the solids in the bed eliminates all solids mixing. The solid/liquid contacting characteristics of the bed, therefore, are more similar to a packed bed than a fluidized bed. Since the solids are not mixing, the liquid flow through the column approaches plug flow motion and the liquid dispersion seen in the bed is on the order of dispersion seen in a packed bed of similar solid^.^*'^ The solids dispersion is identical to that found in a packed bed (zero). This low degree of dispersion for both phases allows many theoretical stages to be contained in a single column as opposed to a normal, single-stage fluidized bed. Second, since the bed is fluidized, the pressure drop through the column remains constant regardless of flow rate and is equal to the bed weight divided by the cross-sectional area.' The uniform magnetic field exerts no net force on the bed and, therefore, does not alter the required operating pressure. The constant pressure drop in this system is in sharp contrast to other typical biochemical separations performed in packed columns. The small particles and/or compressible gels used tend to limit the flow rate of liquid through gel-packed columns to a linear velocity of -1 cm/min." MSFBs of small particles (25-50 pm) can easily handle velocities of 100 cm/min or greater at relatively low field strengths (50 G requiring less than 10 W power/L magnetic field).12 Third and last, the solids still have fluid-like characteristics and can be easily removed from the column. If a port is opened in the bottom of the bed, the solids The unique feature of will flow through the this transport is that since the magnetic field eliminates solids mixing, the motion of the solids down through the bed is plug flow. Thus, with liquid flowing up and solids flowing down, a true countercurrent solids/liquid contractor can be formed. While these properties have been exploited in initial investigations involving continuous protein separations,'922sno work has been done on the behavior of whole cells in continuous MSFBs. Understanding the behavior of cells in continuous stabilized beds is important since these devices can be used as whole-broth processors. Since the structure of the solids phase in MSFBs is similar to that of packed beds, collection of cells can be obtained in the bed. The mechanism of collection is similar to that in depth filters, although due to the unique, fluid-like behavior of the solids phase, the operation is somewhat different. Depth Filtration
Deep-bed filtration is a separation technique used mainly for the treatment of water and wastewater. Liq-
uid to be filtered is passed down through a packed bed of granular material and suspended particles present in the fluid are retained in the bed. Collection of particles in this type of filter will be spread throughout the length of the unit. This is in sharp contrast to filters that use a barrier in which the collection occurs at the surface of this barrier or in the cake that forms above it. The depth filter is usually operated batch-wise and can be cleaned by merely reversing the flow of fluid in the device to form a fluidized bed. The description of suspended particle collection in a bed of spheres is complex. The complexities arise mainly from the fact that ordinary models of transport to a sphere in a flowing fluid, such as that proposed by Levich,13 are no longer applicable when the particle to When the be collected exceeds about 1 pm in particles exceed this limit, as they usually do with cells, other mechanisms of transport to the surface of the support must be considered. These other mechanisms have been largely addressed in the literature on depth filtration rnechanism~.'~-'~ There are five possible methods of transport in a deep-bed filter. These are inertial impaction, sedimentation, interception, brownian diffusion, and straining." As alluded to above, brownian diffusion is only important when the particle size is less than 1 pm in diameter. Tien also points out that inertial impaction is typically negligible in liquid systems and that straining is only important when the collected particle diameter is at least 20% of the diameter of the support." Thus, the most likely filtration mechanisms in MSFBs for yeast cells (-7 pm diameter) and other similarly sized particles are sedimentation and interception. Rajagopalan and Tien have proposed a model using trajectory calculations to describe the performance of deep-bed filters.16In their method, the particles are assumed to move along streamlines around the support. The particles that are on streamlines which come close to the support can intercept the support surface and become attached. Others never intercept the support surface and are, therefore, not retained. Wang et al. have extended this model to account for collection onto partially filled support particles." Their model also uses the trajectory approach to predict collection, but once one particle has been collected, the fate of the next particle can be affected. That next particle may be traveling on a streamline that would have it intercept the support surface in the same place as the first particle, but the presence of the first particle on the collector surface prevents interception. Depending on the specific trajectory of the second particle, it could be forced to go around the first particle and not be collected. This shadowing of the support surface by collected particles implies that total coverage of the support's surface by the particles may never be achieved. We can use this information on depth filtration to analyze our MSFB filter. The experimental runs we performed are compared to a mathematical model developed on the above principles.
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MATERIALS
Yeast cells (Saccharomyces cerevisiae, Type 11) were purchased from Sigma Chemical Company. Polystyrene/2.5% divinylbenzene particles were obtained from Seradyne and had a mean diameter of 5 pm. Water was distilled using a Barnstead still while deionized water was produced by running the distilled water through a Barnstead four-module Nanopure water purification system. The magnetically susceptible support, 100-150 pm diameter nickel ipheres (AESAR/ Johnson Mathey), was used with no surface treatment. All other chemicals were reagent grade and were obtained from commercial sources. METHODS Particle Suspensions
Yeast cells were suspended in the desired liquid and stirred for at least 2 h or until no clumps could be observed by the naked eye. For some experiments yeast cells were grown from the Sigma supply in a growth medium consisting of 5 g/L (NH)zS04,2 g/L KHzP04, 0.5 g/L MgS04, 0.2 g/L NaCl, 0.2 g/L proteose peptone, 0.2 g/L yeast extract, and 5 g/L glucose. Experiments with latex particles used deionized distilled water and all other runs used distilled water as the solvent. Column Construction
A diagram of the continuous MSFB is given in Figure 1. The experimental apparatus consisted of a 2-cm-i.d. glass column with a removable polypropylene liquid distributor (Porex Technologies Corp.). The solids were removed through a 1.5-mm-diameter plastic tube inserted
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1
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Distilled
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through the liquid distributor. The removal rate was controlled by a pinch valve automatically operated by an infrared emitter-detector pair placed on the side of the column. The magnetically susceptible support was added at a constant rate by controlling the flow rate of water to a glass tube 3.5 cm diameter x 25 cm with a drawn tip (0.3 cm diameter). The tube was completely filled with support and solvent at all times. The fluidizing liquid containing the suspended solids was injected below the liquid distributor. At the top of the column, the clarified liquid was removed and pumped through a flow-through spectrophotometer cell (610 nm) for on-line analysis of cell concentration. The magnetic field was produced by passing DC current through a pair of modified Helmholtz coils (13.5 cm diameter x 2.5 cm thick with centers spaced 9 cm apart). A field strength of 56 G (power consumption of 17 W) was used throughout this work. Typical Continuous Filtration Experiment
The column was assembled and flushed with cell-free liquid, the magnetic field was applied, and the flow of solids was started. When the level of solids reached the set point and the controller took over height control, the feed liquid was switched to the desired cell suspension, and data collection was started on the spectrophotometer (610 nm). The run was then allowed to proceed until the output cell concentration reached a steadystate value (usually 3 to 8 min depending on the solids velocity). Once steady state had been reached, the liquid feed was switched back to cell-free liquid and the magnetic field was turned off. The remaining solids were then drained from the column and the system was rinsed. The support was cleaned as stated below before reuse. The standard operating conditions used in most runs are reported in Table I. Actual run conditions are different from the standard conditions only when specifically stated. The “4 salt” solution used in some runs consisted of the four salts in the yeast growth medium stated above at the same concentrations. For runs with broth, the yeast growth medium was used as listed above, except that it contained only 0.5 g/L of glucose.
Magnetic Coils
Particle Suspension
Solids Collection Beaker
Figure 1. Magnetically stabilized fluidized bed (MSFB) apparatus used for continuous particle filtration.
112
Table I. Standard operating conditions. Parameter
Standard Value
Column height Magnetic field strength Magnetic field orientation Liquid velocity Support Filtrate concentration Suspending liquid Salt composition PH
3 cm 56 G vertical 34 cm/min 100-150 Fm Ni spheres 0.03% dry weight distilled water none 6.5
These conditions were used in all runs, unless otherwise noted.
BIOTECHNOLOGY AND BIOENGINEERING, VOL. 37,JANUARY 1991
Batch Filtration Experiment
EXPERIMENTAL RESULTS AND DISCUSSION
For batch filtration experiments, the column was prepared and filled in the same manner as the continuous runs. Once the desired amount of support was introduced into the column, the solids flow was eliminated and the liquid feed was switched to the desired particle suspension. The breakthrough of this step input was then monitored as a function of time.
Support Cleaning
Between experiments, collected cells were rinsed from the support using a 4M NaCl solution. About 100 mL of nickel was placed in a 500-mL Erlenmeyer flask and 200 mL of the salt solution was added. The flask was covered and allowed to stir at approximately 200 rpm overnight. The next day, the salt solution was decanted and replaced. This rinsing procedure was continued until the liquid above the nickel was clear (approximately 3 days). The support was then placed in a column and rinsed with at least 20 column volumes of distilled water to remove the salt solution.
Pulse Analysis
To determine the number of theoretical stages in the column, a pulse analysis technique was used." A 2-s pulse of BSA was fed into the column and the output concentration (absorbance at 280) was measured as a function of time. The level of liquid above the column was lowered to 2 mm to prevent additional tracer dispersion. The number of stages was then calculated using the equation Stages = 5.54(t,/tW)'
Bed Behavior
The behavior of cells in a continuous MSFB filter is similar to that observed for cell debris.20If there is an attraction between the magnetically susceptible support and the suspended solids, then filtration will occur. The amount of particles collected can be varied by varying this interaction. In our system, the positively charged nickel and the negatively charged cells created an attractive electrostatic interaction. As described in Methods and shown in Figure 1, the experimental runs were performed by simultaneously feeding a cell suspension to the bottom and 100-150 pm nickel spheres to the top of an MSFB column. The cells adsorbed on the surface of the support and were carried down through the column and removed at the bottom of the bed. The liquid exited at the top of the column and was analyzed for cell concentration by absorbance measurements. The percentage of cells removed from the inlet stream was then calculated. Figure 2 shows the percentage of cells removed during continuous filtration runs at different solids velocities and bed heights. Because the cells adhere to the surface of the support, increasing the solids flow rate (or increasing rate of addition of fresh adsorptive sites) increases the fraction of cells collected. In addition, increasing the residence time of the liquid in the column (increasing the bed height) increases the fraction of cells collected. The behavior of the MSFB filter in these two cases is expected and is common to all countercurrent contactors. From Figure 2, it is apparent that increasing the solids velocity improves filtration more than increasing the bed height. This result can be understood in light of
(1)
where t, is the time for the peak maximum to emerge and t, is the width of the peak at half its maximum value.
Cell Viability
Cell viability was studied using a colony counting technique. One milliliter of each liquid sample to be tested was diluted 1:loO with sterile distilled water. This dilution was carried out 3 times to produce samples of lo-', low4,and dilution. Two 1-mL samples were taken from each dilution and placed into empty petri dishes. Enough medium (24 g/L potato dextrose broth and 20 g/L agar) was added to cover the bottom of the dish. The plates were allowed to cool, wrapped around the edges with Parafilm, and stored inverted at 20°C. After 3 days, they were removed from the incubator and counted. The number of colonies were compared with the expected number based on the original cell concentration, the dilution, and the assumption of 10070 viability.
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Support velocity (cmfmin) Figure 2. Effect of column height and solids velocity on continuous cell filtration. Increasing the bed height and solids velocity increases the efficiency of the filter. The feed cell concentration was 0.15% dry weight.
TERRANOVA AND BURNS: CONTINUOUS CELL SUSPENSION PROCESSING
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the fact that particle capture is not diffusion controlled, in this case, because the cells are greater than 1 pm in ~ i z e . ' ~Doubling ,'~ the bed height doubles the residence time, while doubling the support velocity doubles the introduction of new sites to the system. During the increased residence time (in the case of a doubled column height), the cells are collecting onto a more saturated support surface. Since the rate of adhesion depends on surface coverage, adhesion will be slower in the doubled height case. In the doubled support velocity case, the cells are collecting onto a relatively vacant surface. This dependence of the rate of adsorption on the surface coverage can also be shown by changing the concentration of suspended cells. Figure 3 shows this dependence using a 5-cm column and feed concentrations of 0.03 and 0.15% dry weight cells. Increasing the concentration of cells in solution decreased the column efficiency, but this decrease was easily offset by increasing the solids flow rate. For example, to obtain the same filtration efficiency, the solids must be flowing 5 times faster for the 0.15 wt % feed than for the 0.03 wt % feed. Unlike batch MSFB operation in which increased cell concentration can lead to bed instabilities,21 the continuous MSFB remains stable because the cells are quickly removed from the bottom of the column. The magnetic field strength was not found to affect the filtration efficiency of the bed but did affect the bed's stability. As is typical for MSFB operation, higher field strengths result in more stable beds. Stability of the bed is necessary to obtain the high collection efficiencies observed because the rapid solids mixing seen in unstable (normal) fluidized beds results in low adsorption in the bed due to inefficient contact between the liquid and the solids phase and to support-support collisions. Figure 4 shows a continuous run that ini-
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Figure 4. Effect of magnetic field on continuous cell filtration. Fraction of cells filtered is plotted versus dimensionless time (T = liquid residence time in column). The data shows how the magnetic field improves cell filtration. A magnetic field of 56 G was applied at a dimensionless time of approximately 38. The support velocity was 5.1 cm/min.
tially had no applied magnetic field (unstable bed). Stabilizing the bed after a dimensionless time of 38 greatly increased the filtration efficiency. CelVSupport Interaction
The filtration efficiency may be changed not only by varying the flow rate and bed height but also by varying the interaction between the cells and the magnetically susceptible support material. The cells, with a net negative charge, are attracted to the positively charged surface of the nickel spheres. Altering the charge on either of these particles or changing the composition of the suspending solutions will affect the cell/support interaction. Increasing the ionic strength of the solution, for example, should decrease the electrostatic interactions and decrease the efficiency of filtration. This decrease in filtration as the ionic strength of the solution is increased is shown in Figure 5. The ionic interaction was affected by suspending the cells in a salt solution ((NH4)S04,KH2P04, MgS04, and NaCl) instead of distilled water. The salt solution contained the salts in a typical yeast fermentation broth. As expected, the presence of the salt decreases the collection of the cells by shielding the negatively charged cells from the positively charged support. In addition to this salt solution, a fermentation broth was used that contained the above four salts, yeast extract, proteose peptone, and glucose. The filtration from broth was less than that obtained with the salt solution due to the presence of the excess protein (estimated at about 1 mg/mL) and glucose. These results are in agreement with those of Bar and co-workers, who demonstrated that yeast ex-
BIOTECHNOLOGY AND BIOENGINEERING, VOL. 37.JANUARY 1991
1
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Support velocity (cdrnin) Figure 5. Effect of liquid composition on continuous cell filtration. The filtration efficiency of the column is reduced in the presence of salts and broth. This reduction is due to a decrease in the electrostatic interactions between the cells and the support when the liquid contains ions, sugars, and proteins.
tract and glucose had a negative impact on cell adsorption onto a support due to a charge shielding effect." It is also important to note that to simplify the experiments, all of the cells used, unless otherwise noted, were cells resuspended from freeze-dried samples and not from growing cultures. The performance of the two types of cells were qualitatively similar, as shown in Figure 6, but were quantitatively different with grown cells being filtered more effectively than suspended cells. This increase is most likely due to a stronger attraction to the support surface. Each cell line that would be used in the column will have a different affinity for the support but will show the same qualitative trends.
In order to determine the effects of the MSFB on cell viability, a plate counting experiment was done. During continuous cell filtration from broth, samples were taken from the feed beaker, the top of the column, and the solids collection beaker along with a control sample taken from the cell-free feed. These samples were diluted and plated onto a combination of agar and potato dextrose broth to determine the number of viable cells. The results of this study, shown in Table 11, indicate that cell viability is not affected by passage through the column. In all three samples, 81% of the cells were found to be viable. Because the observed cell concentrations in all cultures were less than the calculated values, a low viability strain, rather than damage due to processing, is indicated. These results show that the MSFB can be used for applications where viability is important, such as cell recycle. COMPUTER SIMULATION
In order to better understand the mechanism and principles involved in continuous cell filtration, we developed a mathematical model and correlated it with our experimental results. Our goal in formulating the model was not a detailed prediction of experimental results from first principles but a first attempt at understanding the adhesion process in the bed. Algorithm and Equations
Cell filtration in an MSFB can be described by differential mass balance equations incorporating a specific rate law for the cell adsorption. Accounting for convection of both phases and dispersion in the liquid phase, the equations are
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ac, --- _ V, _ ac, _ at 1 - E az
+ rd
(2)
+ ra - r d
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where D,is the dispersion coefficient, E is the void fraction, C1 and C, are the concentrations of cells in the liquid and solids phases, v! and v, are the superficial and rd are the adsorpliquid and solids velocities, and I-, tion and desorption rates, respectively. Table 11. Plate count results. growncells resuspended cells
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Support velocity (cdmin) Figure 6. Effect nf cell state on continuous cell filtration. Newly grown cells have a surface more favorable for adhesion to the support than resuspended cells, although trends for both are similar.
Sample location
Expected cell concentration
Feed TOP Bottom Control
3.0 X lo6 2.6 X lo6 3.0 x lo6 0
Counted cell concentration 2.44 x
Percentage of expected
lo6
2.11 x 106 2.42 x lo6 0
81 81 81 -
The viability of the input cells (feed) is not affected by passage through the column (top) or adhesion onto the support (bottom).
TERRANOVA AND BURNS: CONTINUOUS CELL SUSPENSION PROCESSING
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We assume that no desorption of cells from the support occurs (rd = 0). This assumption is reasonable for the present system because when the column feed is switched from cells to water at the end of a run, no detectable amount of cells are washed from the column after an hour of rinsing.” The total rate of adsorption of cells is therefore given by r, = ka((i - &)/E)cr(i- 8)’ where k
=
(4)
forward rate constant (cm/s)
a = surface area per volume of solids (cm-‘)
p
= rate exponent 8 = fraction of filled sites, = Cs/C~,max CS,max = binding capacity of the support (mg/mL)
The general form of the rate expression shown above was suggested by Tien and Payatakes for use in analyzing deep-bed fi1trati0n.l~A Langmuir rate equation was suggested for cell adhesion by Bar et al.,” but this form does not fit our data. An equation of the type shown above having an exponent p with a value greater than 1 has traditionally been suitable for cases where the adsorbate requires multiple sites to adsorb. In MSFB filtration, the exponent is needed because the threedimensional cell will block sites for cell adsorption on the downstream side of the support particle. The value of p - 1 indicates the number of such sites blocked. To obtain both unsteady- as well as steady-state solutions easily, the differential equations given above were approximated by difference equations describing a countercurrent distribution operation with a rate process (in this case, cell adhesion) occurring in each stage. Each stage of liquid is allowed to contact the solids phase for a time At set by the liquid flow rate (At = liquid volume in stage/liquid flow rate). During this time, the change in concentration in the liquid is described by the adsorption rate expression -r, = -AC//At = k ~ ( ( 1- E)/.)Cr(l - 0)’
(5)
solids phases and the amount of cells retained in each stage in the column. Parameter Estimation and Fitting
Although the number of stages in the column could be estimated by tracer dye experiments as described above, the three parameters in the rate expression (p,CS,max, and k f ) were more difficult to estimate and had to be fit. Instead of using data from a cell filtration run to determine the model parameters, a simpler experiment was performed: the adsorption of latex particles in the column. Latex particles 4.3 pm in size were used because their size and charge is similar to that of yeast cells but the latex particles are more uniform and chemically simpler than the cells. Using these particles, we collected batch filtration data using a step input of particles, as described in Methods. The results of this experiment were plotted as dimensionless concentration (C/Co)versus the dimensionless time ( t / ~T, = residence time of liquid in column) and are shown in Figure 7. An excellent fit of this data to our model using parameter values of C,,,, = 29 mg/mL, kf = 0.6, and p = 2.8 is also shown. The values of these parameters that produce the best fit to the data give insight into the mechanisms of particle collection in the bed. The value of the exponent p, 2.8, suggests that the adsorbed particles are shadowing -(p - l), or 1.8, sites behind them. As suspended particles flow over the surface of the support, they are prevented from adsorbing on sites directly behind adsorbed particles. This value of p was also obtained from four continuous cell filtration experiments (data not shown) by plotting the log of the overall cell removal rate versus the log of the estimated fraction of
1.o
..-....”_...-
or for calculation purposes,
-AC, = At ka((1 - E ) / E ) C ~ (0)p ~ = kfCr(1 - 0)’ (6)
0.8
where kf is a lumped dimensionless rate constant. The liquid is then transferred up to the next stage while a fraction of the solids, calculated from a ratio of the two flow rates, are transferred down. The fractional transfer can be performed on either phase with similar results; for our particular experiments, the solids phase was chosen because the solids flow rate was always less than the liquid flow rate. The number of stages used in solving the system of difference equations is dependent on the dispersion present in the MSFB and was determined experimentally. Using a tracer pulse experiment and procedure suggested by Wankat,” the number of stages was found to be 1.6 stages/cm of bed. The output of the model included the final concentrations of cells exiting with the liquid and
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Dimensionless time, t h Figure 7. Model fit of batch latex filtration data. This figure shows that the model with kf = 0.6, C,,,, = 29 mg/mL, and p = 2.8 fits the experimental data very well. The column height was 5 cm and the latex particles had a diameter of 4.3 pm.
BIOTECHNOLOGY AND BIOENGINEERING, VOL. 37,JANUARY 1991
vacant sites (1 - 0) for several solids flow rates. The slope of this line corresponded to p and was equal to 2.8. The fit value of the binding capacity, C,,,,, can be compared to that estimated from first principles by calculating the surface area of one support particle and dividing this quantity by the projected area of one latex particle. The result is then multiplied by a packing factor (0.6) to account for the fact that the latex particles are round and cannot cover up all of the support surface area. After conversion to the desired units, the theoretical value of C , , , , is 50 mg/mL for latex particles. The higher theoretical value of C , , , , than that obtained experimentally (29 mg/mL) could be due to overestimating the tightness of packing of the latex spheres on the surface or to the preferential adsorption of the latex spheres to one side of the nickel support. The lumped parameter kfcontains a number of physical parameters including a forward rate constant for mass transfer. Using the equation for kf [Eq. (6)], we can convert this value of kf = 0.6 into a forward rate constant ( k )of about cm/s, a value typical of mass transfer limited adsorption processes in packed beds. The values of p, kf,and C , , , , obtained from fitting the latex data were then used to predict the batch cell filtration data (Fig. 8). The model describes the data well for dimensionless times less than approximately 30. The larger yeast cells (-7 pm) should have required a higher value for C , , , , (theoretical value is 79 mg/mL), but varying the values of C , , , , or any of the other parameters did not give a substantially better fit to the yeast cell data. Figure 8 clearly shows that the model as formulated could not fit the batch cell data past t/r = 30. The poor
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Dimensionless time, t / ~ Figure 8. Comparison of model with match cell filtration data. The model using the single-rate expression matches the batch cell filtration data but only for f/T < 30. As the surface of the support becomes saturated at later times, cell-cell binding occurs and can be modeled using additional rate expressions (curve labeled “model cell-cell binding”). The column height was 5 cm.
+
fit of the model to the cell data is most likely due to particle/particle (cellhell) adhesion, an event that would probably not occur with the latex particles. The complex nature of the cell surface allows adhesion between cells in solution and cells adsorbed on the surface of the support and increases the amount of cells retained in the bed over that predicted by the model. This particle/particle collection mechanism is similar to that found in cell debris filtration.20 A more complex rate expression that includes this additional collection mechanism can improve the agreement between the theory and the experiments (Fig. 8). While the original rate expression allowed only a monolayer of cells to form on the surface of the support (0 < 0 < 1)’ a combination of rate expressions used for the curve labeled “model + cell-cell binding” allowed a second layer of cells (1 < 6 < 2) to attach to the layer of cells adsorbed on the support’s surface. The rate of adsorption was, at high adsorbed cell concentrations (1 < 0 < 2), proportional to the number of cells available for this cell-cell binding [r = klC1(2- 0)] and, at low adsorbed cell concentrations (0 < 0 < O S ) , a function of cell-support and cell-cell adhesion [r = kzC1(l- O)s + k30].The rater = k2C1(1- 6)s + klC1(2- 0) was used in the transition region (0.5 < 0 < 1). The fit of the model to the data is improved, but higher adsorption than predicted is obtained at high cell loadings, most likely due to additional cell-cell binding (0 > 2). The additional rate expressions, though, do not improve the fit of the model to the data at low values of t/r Because the residence time of the solids in the bed during continuous runs was typically less than 3 min (t/r < 30 in Fig. 8), the model without the cell/cell adhesion rate expressions was used to simulate the continuous runs.
The model was used to predict the behavior of the system for continuous cell filtration from distilled water at two cell concentrations and three different bed heights. The results of these comparisons are shown in Figure 9. In each case, the model predicts the trends observed in cell collection as a function of liquid concentration and solids velocity. The variation in collection efficiency as a function of bed height also agrees and is similar to that shown previously in Figure 2. The fact that the model always predicts better collection than is actually observed is probably due, at least in part, to the differences in running the system in the batch and continuous modes. The model parameters were determined with the system operating in the batch filtration mode. During a continuous run, the bed is subject to the vibrations caused by the solids withdrawal valve and feeder. Also, the solids removal tube inserted in the liquid distributor sometimes allowed by-
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Figure 9. Comparison of model with continuous cell filtration data for 3-cm (a), 5-cm (b), and 7-cm (c) columns. These graphs show the model predictions and the experimental data for cell filtration at two concentrations using three different bed heights. The model in all cases predicts better filtration than is actually observed. Column vibrations were most likely responsible for the deviations.
passing of the feed in the center of the column, resulting in poor feed distribution. A set of runs was done in which these two factors (vibrations and feed bypassing) were minimized. Figure 10 shows the fraction of cells filtered as a function of liquid velocity. The last two data points, drastically below the first three, were due to rapid vibrations caused by the valve and controller in these runs, something that could not be eliminated in our experimental setup. The results of this experiment clearly demonstrate the accuracy of the model. One last comparison of the data with the model's predictions was done using some batch filtration data obtained by Riley.*l Their experiment consisted of a series of batch runs, after which the column was dissected to ascertain the distribution of the collected cells throughout the column. The data in Figure 11 show the cell 118
distribution for three batch runs: a 2-min run at a feed concentration of 0.05% (Fig. lla), a 15-min run at a feed concentration of 0.05% (Fig. llb), and a 10-min run at a feed concentration of 0.01% (Fig. llc). Again, the model predictions compare favorably with the data. While the curves do not lie on top of one another, the trends are very clearly the same, indicating that the model is correctly predicting not only the column output but also the behavior of the individual stages. CONCLUSIONS
The feasibility of continuously filtering cells from solution using an MSFB was demonstrated. The filtration was based on an electrostatic interaction between the positively charged nickel spheres and negatively charged
BIOTECHNOLOGY AND BIOENGINEERING, VOL. 37,JANUARY 1991
loo,
An important step in these feasibility studies was testing the viability of the cells that were retained in the bed and cells that passed through the bed. The former case is important for cell recycle while the latter is important for such applications as toxin removal from a batch fermentation. Cell viability studies clearly demonstrated that for the yeast cells used, there are no harmful effects on the cells due to retention in or passage through the MSFB. The absence of any detrimental effects on the cells from passage through the bed is expected due to the relatively gentle conditions in the bed. The calculated Reynolds number using the support particle diameter is about 0.7, a value that is on the high side of the creeping flow regime (Re < 1) and predicts little turbulence in the system.
0
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Liquid velocity (cdmin)
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Figure 10. Comparison of model with liquid velocity data. The model compares favorably with the data when column vibrations and bypassing are minimized, therefore demonstrating the accuracy of the model. Vibrations in the column at the two highest velocities caused the deviations observed.
yeast cells. In cases where this cell/support interaction was high (in filtration from distilled water), removal rates as high as 99% were observed. In filtration from complex mixtures such as fermentation broths, high recoveries could be obtained by using sufficiently high bed heights and support velocities. A more efficient method of filtering cells from such a mixture, though, would be to use a support that was specifically designed to adsorb cells, such as one containing a high concentration of positively charged surface groups. Decreasing or eliminating the cell/support interaction would allow cells to pass through the system.
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Figure 11. Comparison of model with cell distribution data for three different runs: (a) short, high concentration; (b) long, high concentration; and (c) long, low concentration. The model predicts the same trends of cell distribution in the bed as is actually observed. This agreement also lends support to the accuracy of the model. The column height was 5 cm. Note that on all three plots a value of 0.2 g/cm per total grams collected would correspond to even distribution of cells throughout the column.
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In addition to demonstrating the feasibility of the system, we also investigated the mechanisms of filtration in the device. Knowing that the electrostatic interactions between the negatively charged cells and the positively charged support was responsible for the cell filtration, a result that has been observed by other investigators,”-24 we were able to develop a model that reflected the qualitative trends in all the experimental results. This model showed that cells were adsorbing on the surface of the nickel and interfering with the further adsorption of cells by shadowing sites adjacent to these cells. Additions to the model suggested that cell/ cell binding is occurring at high column loadings. The fact that the filtration of latex particles, which do not exhibit strong particle/particle binding in our system, can be accurately modeled without the addition of the particle/particle binding, further supports this theory. In summary, we have shown that a magnetically stabilized bed can be used to process streams containing whole cells. A number of applications of the device can be envisioned, including a filter to recover cells from the output of a continuous fermentor for recycle, a solid/liquid separator to remove the cells from a fermentation broth before downstream processing begins, or a whole-broth contactor that is capable of recovering dissolved chemicals from solution even with whole cells present . The authors acknowledge that this work was performed at the University of Massachusetts (Amherst) in the Chemical Engineering Department. The authors thank the University of Massachusetts, the National Science Foundation (EET8707636 and CBT-8813830), and the Donors of t h e Petroleum Research Fund (administered by the American Chemical Society) for the partial funding of this research and also thank Porex Technologies Corp. for generously supplying porous polymer sheets.
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References 1. M. A. Burns and D. J. Graves, Biotechnol. Prog.. 1(2), 95 (1985). 2. M. A. Burns and D. J. Graves, React. Polym., 6,45 (1987). 3. P. J. Lucchesi, W. H. Hatch, F. X. Mayer, and R. E. Rosensweig, Proc. 10th Petro. Congr. Bucharest, 4, 419 (1979). 4. R.E. Rosensweig, J. H. Siegell, W. K. Lee, and T. Mikus, AIChE Symp. Serz 77(205), 8 (1981). 5. J. H. Siegell and C. A. Coulaloglou, Pow. Tech., 39, 215 (1984). 6. R.V. Albert and C. Tien,AZChE 1, 31(2), 288 (1985). 7. M. Warrior and C. Tien, Chem. Eng. Sci., 41(7), 1711 (1986). 8. C. H. Lochmuller and L. S. Wigman, Sep. Sci. Tech., 22(1), 2111 (1987). 9. M.A. Burns and D. J. Graves, Chem. Eng. Comm., 67, 315 (1988). 10. J. H. Siegell, Powd. Technol., 52, 139 (1987). 11. R. K. Scopes, Protein Purification: Principles and Practices, 2nd ed. (Springer-Verlag, New York, 1982). 12. A.S. Chetty, D. H. Gabis, and M.A. Burns, Puwd. Technol. (to appear). 13. V. G. Levich, Physicochemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1962). 14. R. Rajagopalan and C. Tien, Can. J. Chem. Eng., 55,246 (1977). 15. C. Tien and A. C. Payatakes, AZChE 1,25(5) 737 (1979). 16. R. Rajagopalan and C. Tien, Can J: Chem. Eng., 55,256 (1977). 17. T. S. Wang, M. Beizaie, and C. Tien, AZChE J., 23(6), 879 (1977). 18. C. Tien, C. S. Wang, and D.T. Barot, Science, 196(4292), 983 (1977). 19. P.C. Wankat, Large-Scale Adsorption and Chromatography, Vol. I (CRC Press, Boca Raton, FL, 1986). 20. B. E. Terranova and M. A. Burns, Biotechnol. Prog., 5(3), 98 (1989). 21. D. J. Riley, M. S . Thesis, University of Massachusetts, Amherst, MA (1987). 22. R. Bar, J. L. Gainer, and D. J. Kirwan, Biotechnol. Bioeng., 29, 1045 (1987). 23. N. Mozes, F. Marchal, M. P. Hermesse, J.L. Van Haecht, L. Reuliaux, A. J. Leonard, and P. G. Rouxhet, Biotechnol. Bioeng., 30, 439 (1987). 24. B. Champluvier, B. Kamp, and P. G. Rouxhet, Appl. Microbiol. Biotechnol., 27, 464 (1988).
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