Biotechnol. Prog. 1992, 8, 11-18

11

Cell Death in the Thin Films of Bursting Bubbles Robert S. Cherry*and Carl T. Hullet Center for Biochemical Engineering, Duke University, Durham, North Carolina 27706

A sparged gas bubble floating at the liquid interface has a liquid film which drains and thins until the film spontaneously ruptures at a point. This causes rapid retraction of the film, forming a rim of collected fluid. This rim moves at a constant velocity of about 3 m/s and any cells in the bubble film are rapidly accelerated to this velocity in the moving rim. Half of the surface energy originally in the thin film is converted t o kinetic energy of the rim, while the rest is dissipated in this rim. The rate of energy dissipation per mass of rim fluid is approximately 9000 m2/s3,which corresponds to a Kolmogorov eddy size of 3.2 pm in fully developed turbulence or a shear stress of 95 N/m2 in laminar flow. Either of these limiting cases presents an environment in which rapid cell death would be expected. Experiments with3f-9 insect cells suggest that the cell concentration in these thin films is 0.6 times the bulk liquid concentration and that about 20%of these cells are killed when the film ruptures. An equation based on this mechanism accurately predicts the death rate.

Introduction Sparging of a bioreactor to increase the oxygen transfer rate is commonly used in the culture of bacteria and yeast cells but is detrimental to many animal and insect cell lines even at mild conditions (Radlett et al., 1972;Tramper et al., 1986; Gardner et al., 1990). Recent experiments have suggested that the harsh effects of sparging are only present a t the top of the bioreactor, where a bubble reaches the air-liquid interface (Handa-Corrigan et al., 1989; Tramper et al., 1988; Kunas and Papoutsakis, 1990a,b). These reports suggest that cell death does not result from interaction of the cella with the flow field around the bubble or with the rising bubble itself. No detailed mechanism has yet been proposed as to how bubble behavior at the surface causes cell death, although numerous speculations have appeared. The primary objectives of this paper are to show that a quantitative analysis of the interactions of cells with bubble films at the liquid surface can be used to model the death of cells in a sparged bioreactor and to describe a mechanism by which bursting bubbles might damage suspension cells in sparged bioreactors. A gas bubble in a sparged system rises to the air-liquid interface, deforming the surface. A thin liquid film containing suspended cells forms between the quasihemispherical bubble and the interface (Figure la). This film thins by gravity and capillary forces until it reaches a certain critical thickness and spontaneously ruptures (Figure lb). Although this thickness is about 0.5 pm for 0.1-1 cm diameter films in surfactant systems (Vrij and Overbeek, 19671, we assume here that the film ruptures when it thins to about the diameter of a cell (12-15 pm) or, more specifically, when the thin layer of liquid covering a cell in a thinning film is about 0.1-0.5 pm thick. The lack of colors in bioreactor bubbles indicates that their thickness is at least 1.5 pm, several times the wavelength of light. After rupture, a rim of collected fluid and cells accumulates as surface tension retracts the film (Figure IC). This rim continues to grow in size (Figure Id) until it

* Corresponding author. Also affiliated with the Department of Mechanical Engineering and Materials Science, Duke University. Present address: Molecular Biosystems, Inc., San Diego, CA. f

8756-7938/92/3008-0011$03.00/0

LOLiquid

b

Figure 1. Details of a bursting bubble: (a) bubble at the surface, (b) spontaneous rupture, (c) retraction of film, and (d) growth of rim as film retracts further.

reaches and blends with the bulk fluid. It may not remain toroidal but may break into droplets by the unstable propagation of capillary waves (MacIntyre, 1972; Pandit and Davidson, 19901, in which case the remaining film reforms the growing rim. Cells essentially stationary in the thin film at the time of rupture are rapidly accelerated to the high velocity of the retracting rim. The intense hydrodynamicforces associated with this acceleration and the flow inside the rim are of sufficient magnitude to cause cell death. On the basis of this assumed mechanism,the first-order death rate constant k based on the entire reactor contents can be written as

k = [(fractional death in a film)(cell density in film) X (film volume/ bubble)(bubbles/ time)]/ [(cell density in fluid)(total liquid volume)] =

This equation predicts that cell death is proportional to the gas flow rate and inversely proportional to the biore-

0 1992 American Chemical Society and American InstRute of Chemical Engineers

Biotechnol. Prog., 1992, Vol. 8, No. 1

12

actor volume, results that have been confirmed numerous times (Tramper et al., 1988; Handa-Corrigan et al., 1989; van der Pol et al., 1990; Jobses et al., 1991). Equation 1 also predicts an increased cell death rate with a decrease in bubble radius r. Small bubbles have a larger ratio of surface area to volume and hence generate more thin liquid film for the same gas flow rate. Smaller bubbles have been found to be more harmful to cells (Handa et al., 1987; Wu et al., 1990). The work reported here measures values for \k and cb/ Cf and attempts to describe h in a bursting bubble containing a cell suspension. We use these values in a quantitative evaluation of the forces on a cell in bursting bubble and show that the hydrodynamic conditions in the thin liquid film of a bubble are quite sufficient to cause cell death. We close with a discussion of several alternative explanations of cell death in bubbles, estimating the forces on a cell in each case.

Materials and Methods Cell Line. Experiments on sparging and foam fractionation used Spodoptera frugiperda (Sf-9) insect cells cultured in spinner flasks with Ex-Cell 400 medium (JRH Biosciences). Ex-Cell 400is a proprietary serum-free, lowprotein medium which contains 0.1 wt % Pluronic F-68 surfactant. The thin film experiments used TC-100 medium (Sigma), which does not contain Pluronic F-68, with 5% fetal bovine serum. Sf-9 cells for this work were grown at 27 "C under a normal atmosphere. All experiments were conducted at ambient conditions less than 30 min after the cells were removed from the 27 "C incubator. Cells used in each experiment were in exponential growth at a cell density of about 1.5 X lo6 cells/mL. Sparging Experiments. Cell sparging experiments were run by bubbling compressed gas through a 5.75-in. Pasteur pipet (Scientific Products) into 5 or 10 mL of the medium-cell mixture in a 2.6-cm diameter plastic beaker large enough to prevent foam overflow. The medium used in this work was Ex-Cell 400. The bubbles generated by this system ranged in size from 0.5 to 1.0 cm in diameter. Gas flow rates were controlled in the range 50-135 mL/ min with an adjustable rotameter. Viable and total cell numbers were determined using trypan blue exclusion and a hemacytometer. Foam Fractionation Experiments. To measure cell density in the foam layer, foam fractionation experiments were carried out in a 25-mL disposable pipet (Fisher). The pipet contained approximately 10mL of solution and was held tip up at a 4 5 O angle. Gas was fed into the lower end of the pipet a t a constant flow rate. Foam rose through the tube and was collected as it exited the tip; it did not rupture and drain back into the bulk solution while in the pipet. The foam collapsed to liquid in the collection vessel and was collected in fractions. Samples were taken from this collapsed liquid phase, stained with trypan blue, and counted in a hemacytometer. Before each run the pipet was wetted with a medium-cell mixture to ensure that cells did not stick to the walls of the pipet as they rose with the foam. Thin Film Experiments. Thin liquid films of cell suspension in medium were formed in a 2-cm diameter copper wire loop (wirediameter 260pm), similar to a child's bubble-blowing toy. Consistent films were obtained by dipping the end of a glass microscope slide into the suspension and drawing the loop across the end of the slide to form the film. The loop of liquid was held at a 4 5 O angle inside a vial of Dulbecco's phosphate-buffered saline (PBS),just above the liquid surface, until the film

1

lo

0

Em

.-5 e

0

10

20

30

Time (minutes)

Figure 2. Death of cells in spargingexperiments. Liquid volume 5 mL. Open symbols: sparge rate 50 mL/min, death rate k = 0.00036 0.00051 s-l. Closed symbols: sparge rate 135mL/min, k = 0.00117 0.00074 s-l.

* *

spontaneously burst. Typically this took 0.5-3 s. The loop was then dipped into the PBS to transfer any liquid drops remaining on it. For control experiments the unburst films were dipped directly into the PBS to transfer the cells. Once dipped, the loop could not be withdrawn without creating another film, although the cell concentration in it should be much lower than in the original film. This problem was addressed by partially withdrawing the loop vertically and blowing on the small amount of exposed film until it burst; the rest of the loop could then be removed cleanly. This procedure was repeated 25 times to put a large number of cells into the PBS and to average out loop-to-loopvariations in initial film thickness, thickness at bursting, etc. The cells in the two containers of PBS, one containing cells exposed to a thin film only and the other containing cells exposed to spontaneously ruptured thin film, were counted using a Particle Data cell counter. The ratio of these numbers is the fractional recovery.

Experimental Results Cell Death by Sparging. The growth and natural death rate of these cells is negligible over the short duration of these experiments, so changes in cell counts were caused only by the experimental conditions. Preliminary experiments showed that the starting cell density and the type of sparged gas ( 0 2 , N2, or air) do not affect the results of sparging experiments. Figure 2 confirms that a greater flow rate produces more cell death in the system. The death rate It is roughly proportional to the flow rate, although the wide confidence limits do not allow a firm conclusion with these data. Figure 3 shows the protective effects of the surfactant Pluronic F-68 in this system. When 0.2 ?G Pluronic is added to the system, fewer cells are killed compared to a control. This effect has also been reported by many others including Kilburn and Webb (1968), Mizrahi (19751, Handa et al. (19871, Murhammer and Goochee (1988, 19901, and Goldblum et al. (1990). Foam Fractionation. Assuming no cells die in the bulk liquid phase during sparging, the ratio of cell concentration in the foam (actually, in the liquid portion of the foam phase) to that in the bulk liquid can be estimated from a differential cell balance on a sample of sparged liquid as it is sparged to form a foam phase: CW = aCb dV

(2)

13

Biotechnol. Prog., 1992, Vol. 8, NO. 1

lo

I

0

10 20 30 40 Time (minutes)

50

Figure 3. Pluronic F-68 protects cells from sparging damage. Liquid volume = 10mL, air flow = 135mL/min. Closed symbols: control run, k = 0.00031 f 0.00012 s-l. Open symbols: 0.2 w t % Pluronic F-68, k = 0.00017 & 0.00011 8-l.

1 :

0

.

I

100

.

1

200

.

I

300

. ’ . 400

I

500

. ” 600

Time (seconds)

Figure 4. Fractionation of cells into foam. Three runs are shown. Cb,O and Cb,f refer to initial and final concentration of cells in the bulk liquid.

Substitution of N = CbV leads to the solution (3)

Thus a can be found using only the cell concentrations of the bulk liquid phase as increasing amounts of that phase are changed to foam by sparging. Figure 4 shows the results of such experiments. The points on the left and right side of the graph are the bulk fluid cell concentrations before and after the run. The pointsinside the graph are the cell concentrations in the foam overflow. Substituting measured values for the original and final liquid cell concentrations and volumes into eq 3 yields an average a of 0.6 for the three runs. This value may be biased high due to the impossibility of collecting the foam the instant before it ruptures. The foams collected are still “immature” and will drain more cells and liquid before spontaneously rupturing. Because the films continue to drain after the foam is collected but before the foam bubbles burst, the collected fluid used for cell counts does not contain a representative sample of cells from the foam layer only. On the other hand, it is more similar to the foam than the remaining bulk liquid is. This result that insect cells are not enriched in a foam layer was unexpected, as bacteria cells are known to be concentrated in the drops ejected by bursting bubbles (Blanchard and Syzdek, 1970, 1972; Quinn et al., 1975). However, two independent aspects of the data support this conclusion. First, the trend of the bulk cell concentration is upward with time in each run, which could happen only if the cells were preferentially retained in the bulk phase. The same is true in the foam fraction. This is completely analogous to the behavior of the less volatile materials in a batch distillation. Second, in all six instances where the bulk liquid and foam cell densities were measured at the same time, the bulk phase concentration was higher. This may be either because cells do not partition into the foam layer (in accord with the present theory) or simply because cells are lysed and disappear when the foam ruptures in the collection vessel. Cell lysis would cause a difference between Cfand cb but would not change their values with time. Equation 3 would apply with a = 1,but the data do not show that. Simple loss of cells in aerosol droplets during foam collapse would not affect the cell concentration in the remaining fluid. Cells i n Bursting Thin Films. The experiments with the wire loop provided an estimate of the fraction P of cells killed in a bursting film. In addition, they showed that cell death resulted from the bursting of the film and

not simple exposure to some interfacial force. The control (0%) data in Figure 5 show that 20 % of the cells in burst films are missing compared to unburst films. The addition of Pluronic alcohol F-68 or F-127 prevents this loss of cells. This disappearance is attributed to cell lysis, since weighing showed less than a 5% loss of liquid during bursting. However, repeated experiments showed a significant variation in the fraction of cells which disappear in this type of experiment, with results ranging from 0 to 40%. The reasons for this are not known but may depend on the exact state of the culture. We have found that these cells subculture well if growing exponentially but rather poorly in late exponential or stationary phase. Culture age may affect the results here by the release into the medium of cellular materials such as proteins which act as surfactants. The time between the film bursting and the cell counting was unmeasured but roughly constant; if lysis of a fatally injured cell can take several minutes to occur, this delay could be important. In addition, drawing uniform films each time is a matter of practice. There was a significant variation in the time it took the burst films to spontaneously break, and the amount of “rainbowing” in each film immediately before it brokeindicative that the thickness of the film was approaching the wavelength of light, 0.4-0.7 pm-varied between about 5 and 30% of the film area. However, combining 25 films in each test should have minimized the consequences of the random variations in the procedures. For the calculations in this paper, @ is estimated a t 0.2. A similar experiment (Tramper et al., 1986) showed that cells are killed in bursting bubbles blown from a pipet. From Figure 5 of that paper, one can estimate that approximately 8% of the cells died with each bursting. While this value is lower than the current P value of 20 % , it is similar in magnitude. In an alternative way of measuring cell death during bubble bursting, a total cell balance can be performed on the data in Figure 4. The product of the bulk phase cell concentrations and liquid volumes gives the total cell numbers in the vial at the start and end of the experiment. The difference should appear in the foam,in the absence of cell lysis. Integrating each curve in Figure 4 over time and multiplying by the rate at which the foam was generated gives the number of cells appearing in the foam. Since the foam is collected before it ruptures and drains back into the bulk liquid, all cell death has occurred in one

14

0 Q,

V.V

0% 0.1 O/O 0.2% Pluronic F-68

0% 0.2% 0.4% Pluronic F-127

Figure5. Addition of Pluronicalcoholsprotects cells from death in bursting loops.

pass or one film bursting. In these three runs an average of 15%of the cells are unaccounted for and hence must have lysed when the foam burst in the collection vessel.

Discussion of Experimental Results Are There Cells in Bubble Films? A key assumption of this work is that there are cells in the thin film of a bubble. To view them in a geometrysimilar to a real bubble in a sparged system, a small bubble of culture medium was suspended on the tip of the pipet. Cells in the spherical bubble were observed through an extremely long working distance microscope (Cherry, 1991) to collect a t the pool of liquid a t the bottom of the bubble (Figure 6). They can be seen throughout the bubble but their concentration decreases higher up the bubble, perhaps because the bubble film is thinner there. This pattern matches, at least qualitatively, the distribution of liquid in the bubble. There was no evidence of downward draining of the cells with time. In fact, large streams of cells moved erratically around the bubble, possibly driven by disturbances triggered by air drafts. In other visualization work, cell-containing bubbles were blown from a pipet and floated in a small vial backlit by a high-speed strobe. Numerous photographs were taken of a near silhouette of the bubble. They showed no evidence that the spherical film is dimpled or distorted by the presence of the cells, although rivulets of draining fluid could readily be discerned in the images. Because the light reflected from the surface of the bubble, the photographs could not show cells in the film. These results suggest either that the film is at least as thick as the diameter of the insect cells or that there are no cells in the film. However, cells in the films of bubbles have been videotaped (Bavarian et al., 1991;Chalmers and Bavarian, 1991), and the foam fractionation experiments show that cells do exist at some significant concentration in the foam. Even though there are cells in the film, their concentration is less than in the bulk fluid. This difference is caused by the exclusion of cells from the fluid within one cell radius of the air-liquid interface. This is best illustrated by considering the concentration of infinitesimal cell centers, not of finite-sized whole cells. In the bulk liquid the concentration of these points equals the bulk cell concentration. Near an inpenetrable interface the center point cannot approach closer than one cell radius, so the concentration of cell centers is zero near the wall. In a bioreactor this 7.5 pm thick exclusion zone is negligible, but in a bubble film of 15-100 pm thickness it can greatly affect the apparent cell density. For instance, a 40-pm film would have two 7.5-pm layers from which cells were excluded, making the apparent film cell density 25/40of the bulk cell density. More realistically, a bubble

Figure 6. Photomicrograph of a hanging bubble showing cells and cell clumps (dark spots) in the bubble film. A ridge of draining liquid is visible in the top left corner. Accumulated liquid forms a dark pool at the bottom. The central dark ring is an artifact of the illumination. Image width is 6.5 mm.

film will have different thicknesses at different positions, so the apparent film cell density will represent the average over the entire bubble. The thinnest film at the top of the bubble may be nearly void of cells, while the film near the perimeter would have almost the bulk concentration of cells. One requirement for obtaining this reduced cell concentration is that the cells must have a higher drainage rate from the bubbles than the liquid. This is achieved if the flow profile in the film is parabolicor a similar shape, with the maximum velocity along the center line of the film and lower liquid velocities near the film surface where there are no cells. Zero velocity at the film surface, a noslip condition, can be obtained if surfactants are present because their relatively slow equilibration with the dissolved surfactant pool inhibits surface flow as the surfactant molecules are compressed toward the edge of the bubble (Prins and van't Riet, 1987). Proteins, from either the medium, added serum, or cell lysis, or added surfactants and antifoams may be acting in this way. Prediction of Cell Death Rate. Applying eq 1 to a typical set of conditions for this work gives

= (0.2)(0.6)

(0.3 cm)(5 cm3)

= 0.00081 s-' (4) The values for \k and for cf/cbwere obtained in independent experiments reported here. The average value of cell diameter, measured using a particle analyzer, was used for the thickness h. This computed value for the death rate, derived from a presumed mechanism and using only independently obtained constants, agrees with the measured death rate better than is justified by the quality of the \k and cf/cbdata. Five runs a t this condition had an averagedeath rate k of O.OOO82 s-lwith a 95?6 confidence interval of f0.00071 s-*. In a bubble column with an average bubble diameter of 6 mm, Tramper et al. (1988) report a "killing volume" of 0.004 m3 of liquid/m3of sparged gas in which all cells are killed. Assuming the bubbles are hemisphericalboth while rising and while floating on the surface, the thickness of the killing volume is approximately 5 pm. This estimate

B b t e d " . Rug...1992, Vol. 8, No. 1

15

counted energy retained as kinetic energy in circulation of the rim fluid. Assume that the rim diameter at some instant during the bubble burst is, say, 50 pm, and ignore for simplicity any symmetry requirement for two counterrotating vortices of noncircular cross section. Then, a cylindrical rim with the appropriate amount of stored kinetic energy rotates around its central axis at 6800 revolutions/s and has a surface centrifugal force of 9200g. These extreme results make it unlikely the unaccounted energy is retained in some form of rotational energy. Assuming this excess surface energy is indeed dissipated at a rate equaling its input to the rim, the rate of dissipation per mass of fluid can be written as

bulk liquid Figure 7. Details of the rim of fluid in a bursting bubble.

of h is in accord with this work since their calculation explicitly assumed, in the terminology of this paper, that \k = 1. If less than 100% of the cells in the "killing volume" die, its calculated thickness increases correspondingly. Although Pluronic alcohols reduce the cell death rate, the work reported here does not identify how the postulated death mechanism is affected. There was not an apparent change in bubble size r. This leaves \k, Cf, and h as the factors which surfactants might affect. Surfactants and antifoams affect bubble stability by altering the critical thickness h a t which they spontaneously burst. Surfactants might also change the partitioning of cells to the air-liquid interface, affecting Cf.However, neither of these alone explains the protective effect of Pluronic in viscometer experiments. \k( might have been affected through changes in surface tension, by the turbulence structure inside the rim, or by biochemical changes in the cells themselves. Further work is necessary to resolve this important issue.

m = p(rR2)z

dm = phzU dt Combining and simplifying yields

(9) A value for R is determined by taking the known volume of liquid within the resting hemispherical bubble and converting this to a cylindrical rim volume as the rim accumulates fluid. A hemisphericalbubble 0.3 cm in radius and 15 pm thick contains 0.00085 cm3 of liquid, which generates a rim of 120-pmdiameter just before it hits the. bulk liquid. Using a midpoint value of R = 120/d2 = 85 pm with h = 15 pm gives c = 9 X lo3 m2/s3. In contrast, Culick assumed that the energy dissipation takes place in the thin film in a small region just ahead of where the rim engulfs the thin film, with the length of this region being about 20% of the film thickness. Use of this small dissipation volume leads to an e value 300 times greater than that calculated with eq 9. Forces on the Cells. The current assumption of dissipation in the rim itself is a conservative one and provides a lower limit on the forces to which a cell might be exposed. If this energy dissipation is turbulent, the Kolmogorov eddy size would be

Hydrodynamic Theory of Cell Death Energetics of a Bursting Bubble. To explain how a bursting bubble can kill cells requires an understanding of the events during bursting. Figure 7 is a blowup of Figure Id showing the rim, the thin film, and a cell within the thin film. The rim moves with a constant speed which can be calculated from a momentum balance. This is known as Culick's velocity U (Culick, 1960):

U = (2a/ph)'l2 (5) Assuming a = 0.072 N/m and h = 15pm, the rim velocity is about 3 m/s. This expression for the velocity of the rim has been well confirmed experimentally (Pandit and Davidson, 1990). In fact, disagreement of experimental results with the velocity predicted by an energy balance led to this reformulation of the rim velocity. This rim grows in size as it accumulates liquid and cells. Cells originally in the thin film rapidly accelerate from a stationary stateto Culick's velocity in the rim. Calculating the rim's kinetic energy using Culick's velocity accounts for only half of the total energy (2aA) in the system. Culick attributes the energy loss to inelastic collisions as the moving rim collides with the stagnant film and generates heat. This assumes that the fluid inside the rim has no significant energy content associated with its circulation velocity. The resulting adiabatic temperature rise of 0.004 "C is inconsequential for cell death. The ejection of droplets from the rim does not account for any significant removal of either kinetic or surface energy (Pandit and Davidson, 1990); this process should not be confused with the ejection of a jet drop from the collapsing bubble cavity after the film has retracted into the bulk liquid (MacIntyre, 1972). Neither is the unac-

(7)

= ( v ~ / c ) ' /=~ 3.2 pm (10) Kolmogorov eddy lengths smaller than the diameter of cells show a detrimental effect on cell viability (Kunas and Papoutsakis, 1990a), and hybridoma and myeloma cells lyse after repetitive cycling through a turbulent flow device exposingthem to 3-pm Kolmogorov eddies for 0.240.99 ms at a time (McQueen et al., 1987, 1989). If the energy dissipation is laminar, the corresponding shear stress would be determined by (Schlichting, 1979) 7

.

7 = py = p ( c / ~ ) ' = / ~95 N/m2 (11) Laminar shear stresses as low as 1-2 N/m2 (10-20 dyn/ cm2) have been shown to harm insect cells, although the effect was measured after many minutes of exposure to those low stresses (Tramper et al., 1986; Goldblum et al., 1990). The Reynolds number for the planar film jet entering the rim is about 45 based on the film thickness. This is in the laminar regime, but it is difficult to predict the flow environment inside the rim. However, the turbulent and laminar cases each represent an environment in which rapid cell death would be expected, and indeed, about

Blotechnol. Reg., 1992, Vol. 8, No. 1

16

20% of the cells die in the 2 ms it takes for a bubble to burst. The stresses in eqs 10 and 11 were calculated assuming h = 15 pm, but in fact h varies across the film surface. This may be part of the explanation why only a fraction of the cells in the film lyse when it bursts, since different cells will see different conditions. In an alternative estimation of the conditions in the rim, it is possible to construct a force balance on a cell entering the rim:

a

film

(===yell P,P . ~.

b

-

fi-

cap.

C

The total force on a cell equals the product of the mass of the cell and its acceleration. This force comprises a static force acting on the cell from the pressure difference between the thin parallel film and the curved rim and a dynamic force from motion of the cell relative to the fluid around it. Multiplying through by dx and expressing mc in terms of the cell volume and density gives mcv dv =

->dP + Fddx

(13)

PC

Integrating this from the conditions of the thin film (v = 0 and P = 0) to the rim conditions of Culick’s velocity and Pcapillary and then solving for the dynamic force term yields

The pressure in this expression is calculated with the formula

In the plane parallel film rl = F2 = so ‘capillary = 0, while in the cylindrical rim rl = R and r2 >> rl SO Pcapillary = a/R. Upon substitution of eq 15and insertion of previous values for the variables, eq 14 has a value of 1 X lo-” kgm2/s2. Approximating the distance Ax over which the cell accelerates by a rim diameter of roughly 100 pm, the average force on the cell is N. This force evenly distributed over the entire area of the cell equals 140 N/ m2. While this itself would be a fatal level of stress, it is only a conservative estimate of the average stress. The peak instantaneous and local forces on the cell could be substantially larger, although their duration would be very short. The total time it takes to accelerate the cell is on the order of the rim diameter divided by its velocity, or about 30 ps. Other Mechanisms of Cell Death. A number of alternative mechanisms for cell death may be associated with bubbles. The formation of liquid jets after the rupture of bubbles, cell interactions with the air-liquid interfaces, and crushing of cells by capillary pressure are all possible cell death mechanisms. The rapid fluid flow around the bubble cavity immediately after bursting causes the formation of a vertical jet and the ejection of a liquid drop (MacIntyre, 1972). The shear stresses in this flow, estimated a t up to 200 N/m2 (Chalmers and Bavarian, 1991), potentially cause cell death. A large fraction of dead cells exists in the ejected drops. This mechanism is plausible for a single bubble bursting at an air-liquid interface but fails to explain cell death in a foam layer where the top bubbles are bursting above a mass of other bubbles rather than liquid. In that situation, no jet would be formed yet cell death still occurs. The dead cells found in the drop may have been killed in the expanding bubble rim.

Figure 8. Deformation of a cell in a thinning film. (a) Fluid caps form when film is slightly thinner than cell; (b) film much thinner than cell;(c)cell flattens in response tounbalanced forces. The thin fluid caps are likely to rupture at stage a, bursting the entire film before the cell deforms much.

T o test whether direct interfacial contact is damaging, a small bubble was blown out of the tip of a 10-pLsyringe and viewed under a microscope. Cells in close contact with the bubble showed no attraction or adherence to the bubble. When the bubble was brought next to cells exceedingly slowly they appeared to avoid the approaching bubble by following the streamline around it. It is hard to imagine how a cell would adhere to a rising gas bubble where the fluid drag forces opposing attachment to the bubble surface would be much larger. The results of Figure 3 also suggestthat there is no particular attraction of insect cells to air-liquid interfaces. Others have reported the same observation (Handa-Corrigan et al., 1989). Cell death may occur from the shearing of cells as they are excluded from the thinning and draining films (HandaCorrigan et al., 1989). Actually, the flow in a thinning film will have an extensional component which may affect cells differently from the more commonly studied shear stress. The presence of a shear component will depend on the assumption of no slip at the gas-liquid interface. In the absence of surfactants there is no reason to assume this, and the flow is purely extensional. The maximum shear stress on a cell in a bubble is estimated by assuming no slip, an arbitrary film thinning rate of 10 pm/s, and a film thickness of one cell diameter, 15pm,a t the perimeter of a 0.3-cm radius bubble. A t the perimeter the mean fluid velocity across the profile is 0.2 cm/s. If the cell moves at this velocity relative to the stationary surface film with a 0.1-pm gap between the cell and the surface (anything smaller being unstable, as discussed next), the shear rate in that gap is 2000 9-l and the local shear stress on the cell is 2 N/m2. While not a trifling amount, neither is this an excessiveshear stress, especially consideringthat the cell is exposed to it for less than 1 s. The extension rate a t the perimeter under those same conditions is much smaller, (l/h)(dh/dt), approximately 0.7 s-l. The extensional stress is correspondingly low and may be ignored. Another possible explanation of cell death in bubbles is that they are crushed by capillary forces if the bubble film becomes thinner than the diameter of a cell, for instance if a cell-containing film thins to something like 0.5 pm before spontaneously rupturing. This situation is depicted in Figure 8. A thin liquid film covers the cells, exerting a capillary pressure estimated by setting r1 = r2 = rcel1 in eq 15. Thus, Pcapillary = 1.9 X lo4 N/m2. This pressure applied on the caps, unopposed in the plane of the film where the capillary pressure is zero, would tend to flatten the cell. This shape change would eventually rupture the cell as its membrane is stretched taut by the increase in cell area at constant volume.

17

Biotechnol. Prog., 1992, Vol. 8, No. 1

As the liquid film thins to just less than the diameter of the cell, a bulge forms over the cell. This creates a capillary pressure in the liquid in the cap over the cell which causes the liquid to flow out from the cap and the cell to begin to deform. This pressure also centers the cell in the film so it has the same total capillary force on each side. A characteristic time for the cell deformation under this pressure can be estimated by

--k e l l -

2oo kg/(ms) = 0.01 s ('6) 'capillary 1.9 X lo4 kg/(m.s2) The apparent cell viscosity used here is that for a hybridoma line measured by micropipet aspiration (Needham et al., 1991). Assuming the capillary pressure for a spherical liquid cap of the cell's radius, the cell deforms rather rapidly. The corresponding expression for the flow of medium out of the liquid cap is llr 'capillary'

-

C

F F h k m mc N

P R r rl, r2

t

U V u X

(0.001 kg/(ms))(7.5 X lo* m) (1.9 X lo4 kg/(ms2))(1X m)

=

(17) Even at 6 = 0.1 pm, below the spontaneous burst thickness in the absence of a cell, the cap thickness responds 2500 times faster than the cell, and with thicker caps the relative response would be even faster. Of course, P c a p i l h y changes constantly with the actual curvature of the film cap, but this affects both rates equally. The cap of liquid around the cell should thin to the point of spontaneous rupture long before the cell deforms significantly in response to the applied pressure. Meanwhile, the bubble film itself is thinning relative slowly, on the order of seconds based on the time it takes a floating bubble to burst. Rupturing of the cap would initiate rupturing of the entire film at a time when the film was essentially the thickness of the cell diameter. Consequently, the cell would not be extensively deformed by capillary forces. This conclusion is supported by the observation that stable foams created to enhance oxygen mass transfer do not cause death of hybridomas (Ju and Armiger, 1990). Conclusions A bubble rises to the surface and forms a thin film of fluid between the bubble and the interface. Cells are partially excluded from these thin films. The cell density in bubbles such as those was measured to be 0.6 times that in the bulk fluid. Both direct measurements and calculation of the expected death rate of Sf-9 insect cells in bursting bubbles suggest that it is the extremely energetic condition in the expanding rim that causes cell death. This work found that about 20% of the cells in the thin film are lysed instantly by this expanding rim. Agreement of the measured death rate with the theoretical death rate based on this mechanism suggests that the rupture of thin films accounts for most if not all of the cell death within a sparged bioreactor. Equation 1successfullypredicts the first-order cell death rate. The gas flow rate, the bubble size, and the total working volume of the reactor are the easiest parameters to manipulate to minimize the death rate. These parameters, however, affect the mass transfer rate in the bioreactor. Low flow rates, big bubbles, and large volumes all would decrease k but decrease kla as well. An efficient bioreactor would have a large height to diameter ratio to maximize mass transfer for each bubble generated at the sparger. Notation surface area of the bubble, m2 A

z a

cell concentration, cells/m3 flow rate of gas through sparger, m3/s force, N film thickness, m first-order cell death rate constant, s-' mass of fluid in the bubble rim, kg mass of a cell, kg number of cells in the bulk liquid pressure, N/m2 radius of the rim (Figure 7), m radius of a hemispherical surface bubble, m orthogonal radii of curvature, m time, s Culick's velocity of the bubble rim, m/s total volume of bulk liquid phase, m3 velocity, m/s length coordinate, m length of rim in tangential direction, m

cf/c b

thickness of liquid cap over a cell, m c rate of turbulent dissipation of energy per mass of fluid, m2/s3 shear rate, s-l Y Kolmogorov length scale for turbulent eddies, m t) viscosity, kg/ (ms) I.L V kinematic viscosity, m2/s fluid density, kg/m3 P surface tension, N/m d 7 shear stress, N/m2 fraction of cells killed in each thin film when it \k bursts Subscripts avg average b bulk C cell d dynamic f film 0 initial 6

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