Oxygen transport and consumption by suspended cells in microgravity ...

ARTICLE Oxygen Transport and Consumption by Suspended Cells in Microgravity: A Multiphase Analysis Ohwon Kwon,1 Surendra B. Devarakonda,1 John M. Sankovic,3 Rupak K. Banerjee1,2 1

Department of Mechanical Engineering, University of Cincinnati, Cincinnati, Ohio; telephone: 513-556-2124; fax: 513-556-3390; e-mail: [email protected] 2 Department of Biomedical Engineering, University of Cincinnati, Cincinnati, Ohio 3 Microgravity Science Division, NASA Glenn Research Center, Cleveland, Ohio Received 5 February 2007; revision received 17 May 2007; accepted 4 June 2007 Published online 5 July 2007 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/bit.21542

ABSTRACT: A rotating bioreactor for the cell/tissue culture should be operated to obtain sufficient nutrient transfer and avoid damage to the culture materials. Thus, the objective of the present study is to determine the appropriate suspension conditions for the bead/cell distribution and evaluate oxygen transport in the rotating wall vessel (RWV) bioreactor. A numerical analysis of the RWV bioreactor is conducted by incorporating the Eulerian–Eulerian multiphase and oxygen transport equations. The bead size and rotating speed are the control variables in the calculations. The present results show that the rotating speed for appropriate suspensions needs to be increased as the size of the bead/cell increases: 10 rpm for 200 mm; 12 rpm for 300 mm; 14 rpm for 400 mm; 18 rpm for 600 mm. As the rotating speed and the bead size increase from 10 rpm/200 mm to 18 rpm/600 mm, the mean oxygen concentration in the 80% midzone of the vessel is increased by
85% after 1-h rotation due to the high convective flow for 18 rpm/600 mm case as compared to 10 rpm/200 mm case. The present results may serve as criteria to set the operating parameters for a RWV bioreactor, such as the size of beads and the rotating speed, according to the growth of cell aggregates. In addition, it might provide a design parameter for an advanced suspension bioreactor for 3-D engineered cell and tissue cultures. Biotechnol. Bioeng. 2008;99: 99–107. ß 2007 Wiley Periodicals, Inc. KEYWORDS: rotating wall vessel; cell suspension; oxygen transport; oxygen consumption; Eulerian multiphase

Introduction The conventional cell culture dishes/flasks and stirred fermentors for in vitro cellular investigations have disadvantages that include hypoxic conditions and necrotic damage in the center of cell aggregates and the loss of specific

differentiation features (Hammond and Hammond, 2001; Unsworth and Lelkes, 1998). These problems are related to inadequate nutrient supply, insufficient area for generating three-dimensional (3-D) macroscopic tissue equivalents, high turbulence and shear stress. In order to overcome these limitations of conventional culture methods, optimized suspension bioreactors have been developed for many applications (Martin and Vermette, 2005). The rotating wall vessel (RWV) bioreactor developed by NASA/JSC is one of the noble suspension-type reactors. The RWV bioreactor that is designed originally for simulating microgravity conditions on earth provides an adequate oxygen supply and mass transfer (Schwarz et al., 1992). In addition, it has characteristics of solid-body rotation and reduced shear force on the cells which are cultured on the surface of microcarrier beads of similar density with the culture medium (Nickerson et al., 2003). The microcarrier bead is added to the vessel to promote cell attachments on its surface, especially in the case of anchorage-dependent cell lines. Various kinds of cells and tissues have been cultured using the RWV bioreactor not only to investigate the microgravity effects on the cell physiology, but also to exploit the vessel to generate engineered tissue equivalents (Duray et al., 1997; Freed and Vunjak-Novakovic, 1997; Jessup et al., 1993). The unique fluid mechanics and mass transfer in the RWV bioreactor have been studied by many researchers (e.g., Gao et al., 1997a,b; Hammond and Hammond, 2001; Tsao et al., 1994). The gravitational force that causes the sedimentation of cell aggregates in the vessel is on average vectorless because of the hydrodynamic forces that are created by rotation, including centrifugal, Coriolis, and shear forces. The maximum shear stress experienced by a microcarrier is as low as 0.07 dyne/cm2 in the RWV, as compared to 5 dyne/cm2 in a typical stirred vessel (Tsao

Correspondence to: R.K. Banerjee Contract grant sponsor: NASA Glenn Research Center Contract grant number: NASA-GSN-6234

ß 2007 Wiley Periodicals, Inc.

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et al., 1994). The microcarrier dynamics and migration in simulated microgravity conditions have been studied numerically and experimentally by several groups of researchers, who found that decreasing the density difference between the microcarrier and the culture medium can reduce the maximum shear stress and increase the particle suspension time (Gao et al., 1997a,b; Lappa, 2003; Pollack et al., 2000). In addition, RWV mass transport has been investigated by considering cells as the oxygenconsumption sink. Gao et al. (1998) studied mass transfer in the RWV associated with multiple microcarrier of larger size, but bead–bead interactions and actual cell distributions had not been included in their calculations. Begley and Kleis (2002) also studied mass transport in the RWV assuming uniform cell distribution. The previous studies have not included oxygen distribution and consumption by cells within the vessel in relation to the bead location. It is difficult to decide the operating conditions of the bioreactor for the optimal suspension of cells through trial and error due to the dimensions of the cells and beads and the high costs of materials (Martin et al., 2004). Therefore, the optimal flow conditions of the bioreactor need to be parametrically determined by calculations. This study analyzes the fluid and mass transfer in the RWV bioreactor, utilizing the multiphase comprising of culture medium, bead/cell particles and oxygen species while considering the positions and numbers of cells. The objective of the present study is to simulate the RWV bioreactor to investigate the appropriate suspension conditions for bead/cell distribution and evaluate oxygen transport, while calculating varying particle sizes and rotating speeds. The results from the present study can serve as criteria for identifying operating parameters, such as the size of microcarriers and rotating speed, as observed by the growth of cell aggregates. In addition, the result can be used to design an advanced bioreactor for 3-D engineered cell and tissue cultures.

Methods Geometry The RWV bioreactor consists of two concentric cylinders which rotate in the same direction and at the same speed. The geometry and dimensions for this study are taken from the slow turning lateral vessel (Synthecon, Inc., Houston, TX). The outer cylinder has a diameter of 5.7 cm and the inner cylinder has a diameter of 2 cm with a hydrophobic membrane (Fig. 1). The space between the two cylinders is filled with a culture medium. In order to promote cell growth, especially for anchorage-dependent cell lines, the microcarrier beads (Cytodex-3) are seeded with the cells. Governing Equations The computational volume in the RWV bioreactor contains four different materials of interest: culture medium,

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Figure 1.

Schematic illustration of rotating wall vessel (RWV ).

microcarrier beads, cells, and oxygen. Cells are attached to the surface of microcarrier beads (the term ‘‘beads’’ is used, hereafter, to represent beads and cells attached to the bead surface). A user-defined scalar (UDS) is included to calculate the coupled oxygen transport, including both the oxygen supply from diffusion through the inner membrane and the consumption of oxygen by the beads. The Eulerian two-phase (medium and beads) model solves momentum equations for each of the phases. The continuity equation for the model is: @ ðai ri Þ þ rðai ri~ vi Þ ¼ 0 @t

(1)

P where ai is the volume fraction of each phase: 2i¼1 ai ¼ 1, ri is the density of each phase. The medium has a density of 1,020 kg/m3 (rm) and a viscosity of 0.001 kg/(m  s). The density of the beads (rb) is 1,040 kg/m3, slightly higher than the medium. The conservation of momentum for the medium phase is: @ ðam rm~ vm Þ þ rðam rm~ vm~ vm Þ @t vb  ~ vm Þ ¼ am rp þ rtm þ am rm~ g þ Kbm ð~

(2)

and the conservation for the beads phase is: @ ðab rb~ vb Þ þ rðab rb~ vb~ vb Þ @t vm  ~ vb Þ (3) ¼ ab rp  rpb þ rt b þ ab rb~ g þ Kmb ð~ where Kbm(¼Kmb) is the interphase momentum exchange coefficient which is related to the drag function, based on the relative velocity between the medium and the beads phase

Biotechnology and Bioengineering, Vol. 99, No. 1, January 1, 2008 DOI 10.1002/bit

(Gidaspow et al., 1992). 3 ab am rm j~ vm j 2:65 vb  ~ Kbm ¼ CD am 4 db Kbm ¼ 150

ðam > 0:8Þ

ab ð1  am Þmm ab rm j~ vm j vb  ~ þ 1:75 db am db2

(4)

(5)

ðam  0:8Þ where the drag coefficient, CD, is: CD ¼

24 ½1 þ 0:15ðam Reb Þ0:687  am Reb

(6)

600 mm and the v increases from 10 to 20 rpm. The maximum packing limit of the beads is set at 0.6. No-slip boundary conditions are applied at both the inner and the outer walls. The cell culture vessel rotates continually on an axis, which is horizontal to the ground; thus, the gravitational vectors are randomized over the surface of the cells. Also, the fluid shear stress is minimized through synchronous solid-body rotation of the vessel that results in the combination of hydrodynamic forces such as shear, centrifugal and Coriolis forces. Therefore, the rotating speed should be adjusted to balance the gravitational sedimentation of the cells on the beads. The speed needs to be increased based on the growth of the cell aggregates.

and the relative Reynolds number, Reb, is: Finite Volume Method r j~ vm jdb vb  ~ Reb ¼ m mm

(7)

in the Eq. (3), pb is the solid phase pressure that is made up of the kinetic theories of granular flow and particle–particle interactions. To calculate oxygen transport in the vessel, a UDS equation is solved, using the volume fraction and the velocity of the beads phase as calculated by the momentum equations. Since oxygen consumption occurs only in the beads phase, the UDS equation is: @ab rb f þ rðab rb~ vb f  ab GrfÞ ¼ Sb @t

(8)

where f is the scalar for the oxygen mass fraction, Sb represents the oxygen consumption of 5  1017 molo/ (cell  s) (Griffiths, 1986) in the cells for the beads phase, and G, set at 3  106 kgo/(m  s), is the diffusion coefficient of oxygen.

Initial Conditions It is assumed that the vessel is initially divided into two zones: sedimented bead zone (
7% volume out of the vessel) and bead-free zone; the volume fractions of each zone are 0.58 and 0.01, respectively (Fig. 1). Thus, the average volume fraction of the beads in the vessel is around 0.05, if suspended homogeneously. At the oxygenator membrane, the saturation value for oxygen that is dissolved in the medium is set to 8 ppm (i.e., 8 mgo/l) and the medium is considered, at first, to contain 4 ppm (i.e., 4 mgo/L).

Boundary Conditions In order to investigate the mixing of the medium and beads and the oxygen mass transport quantities, the vessel’s rotating speed (v) and the beads’ size (db) are set as parameters in the calculations. The db varies from 200 to

The numerical solutions for the discrete governing equations are based on control volume methods (FLUENT 6.2, Fluent, Inc., Lebanon, NH). The segregated solver is set for Eulerian multiphase calculations. Pressure–velocity coupling is achieved by the SIMPLE algorithm. The second-order upwind discretization scheme is adapted for momentum and UDS equations, and the QUICK scheme for the volume fraction of phases. The computational mesh is generated using a four node quadrilateral element with a total number of
20,000 elements. Mesh independency is checked by increasing the number of elements by 20% from the previous mesh and compared for results. The mesh with the increased number of elements shows less than a 1% difference in velocity and UDS scalar values.

Validation To validate the current numerical methods, an analysis is conducted using the conditions of a reference experiment by Rao et al. (2002), who used the nuclear magnetic resonance (NMR) imaging to noninvasively observe the solid concentration of suspensions. The experimental conditions for this reference experiment are different from the one explained in Figure 1 and in the ‘‘Methods’’ Section: initial and boundary conditions. The inner wall rotates at a constant speed of 55 rpm while the outer wall remains fixed for a reference experiment. The particles are lighter than fluid by
5%; thus, they are initially located at the top of the vessel. Figure 2 shows a comparison of NMR images and numerical predictions of particle distribution from our current computational results after 45, 135, and 225 revolutions of the vessel. As the vessel begins to rotate, the packed zone thins out at a slower rate due to inertia effects. Later, the mixing occurs close to the outer wall because of shear-induced migration (Rao et al., 2002). From the qualitative perspective, NMR images from Rao et al. (2002) and our numerical results for beads distribution agreed well.

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Figure 2. Comparison of NMR images (A; Rao et al., 2002) and present computational predictions (B) of beads distribution after 45, 135, and 225 revolutions of the vessel. [Color figure can be seen in the online version of this article, available at www.interscience.wiley.com.]

Results and Discussion The combinations of rotating speed (v) and beads size (db) for simulating micro-g conditions are selected such that the beads are located away from the vessel wall region thus avoiding bead–wall interaction. A balance of forces surrounding a particle such as gravity, centrifugal, and Coriolis forces results in solid-body rotation. Consequently, a higher concentration of beads in the midzone of the vessel is critical to simulate the micro-g environment. The midzone is defined as the 80% area of the vessel that is away from the inner and outer vessel walls (Fig. 3).

Figure 3.

Criteria for optimized suspension conditions to simulate micro-g: (1) balance of forces surrounding a particle which results in solid-body rotation and (2) well distribution of particles within 80% midzone.

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Figure 4 shows the contours of the mean volume fraction of beads for the 60-min rotation of the vessel. The calculation parameters vary from 10 to 20 rpm for the v and 200 –600 mm for the db as explained earlier. For the db of the 200 mm cases (Fig. 4A–C), Figure 4A (case 1) reveals the better distribution of beads. It indicates that 10 rpm is appropriate for suitable suspension of 200 mm diameter beads. A mean volume fraction of 0.045–0.063 is distributed over most of the inner region of the vessel and only a small portion of the zone near the outer wall contains a very high fraction of beads that can cause cell damage due to the bead– wall interaction. The mean volume fraction of beads within the 80% of the midzone is 6% higher for 10 rpm as compared with 14 rpm: 0.051 for 10 rpm (case 1), versus 0.049 for 12 rpm (case 2) and 0.048 for 14 rpm (case 3). Case 1 shows 6% higher concentration of beads as compared to case 3. The region with a low fraction of beads near the inner wall continues to increase as the v increases from 10 to 14 rpm. At the same time, a high fraction of beads near the outer wall is observed with a wider band. For the db of the 300 mm cases, the region with a high bead fraction of 0.058–0.077 is found at the bottom of the vessel which indicates sedimentation of the beads at 10 rpm (Fig. 4D, case 4). It implies that gravity force is not balanced by hydrodynamic forces. For 12 rpm case (Fig. 4E, case 5), the region with the significant bead fraction of 0.05–0.09 is distributed more uniformly along the circumferential and radial directions as compared with the case of 10 rpm (case 4). This effect is due the increased velocity for 12 rpm case. At the higher speed of 14 rpm (Fig. 4F, case 6), a high bead fraction of 0.057–0.084 is located in the region near the outer wall, which may lead to cell damage. In addition, the mean volume fraction of the beads in the 80% midzone is 5.0% for the 12 rpm (case 5), while it decreases to 4.8% for the 14 rpm (case 6). Thus, the v of 12 rpm (case 5) is more appropriate for the db of 300 mm than 10 or 14 rpm cases. For the db of the 400 mm cases (Fig. 4G–I), at the lower v of 10 and 12 rpm (cases 7 and 8, respectively), a large area with a high fraction occupies the bottom side of the vessel. It indicates a predominant influence of gravitational force causing settling of beads. As the beads become larger, the speed needs to be increased to prevent the sedimentation of the beads at the bottom of the vessel and thus, minimize the net hydrodynamic force on the beads leading to improved solid-body rotation. It is shown that 14 rpm (case 9) is needed to create weightless effect in the RWV bioreactor at a db of 400 mm (Fig. 4I). A significant bead fraction of 0.05– 0.1 covers about half of the vessel for the 14 rpm case. Regarding the larger clumps of the beads, Figure 4(J–L) shows the contours of the mean volume fraction of beads for db of 600 mm. The contours show cases of v varying from 16 to 20 rpm for db of 600 mm because the range from 10 to 14 rpm that was used for the smaller db [Fig. 4(A–I)] is too slow to avoid sedimentation of the beads at the bottom of the vessel. In the case of 16 rpm (Fig. 4J, case 10), the region with a high bead fraction of 0.1 is found at the bottom of the vessel, which indicates sedimentation of the beads. It implies

Biotechnology and Bioengineering, Vol. 99, No. 1, January 1, 2008 DOI 10.1002/bit

Figure 4.

Contours of mean volume fraction of beads after 60-min rotation. [Color figure can be seen in the online version of this article, available at www.interscience.

wiley.com.]

that gravity force is not balanced by hydrodynamic forces. For 18 rpm case (Fig. 4K, case 11), the region with the significant bead fraction of 0.04–0.08 is distributed more uniformly along the circumferential and radial directions compared with 16 rpm shown in case 10. At the higher speed of 20 rpm (Fig. 4L, case 12), a high fraction of 0.08–0.12 is located in the region near the outer wall, which may lead to cell damage due to wall shear stress. The region with a low fraction of beads near the inner wall increases as the v increases from 18 to 20 rpm. In addition, the mean volume

fraction of the beads in the 80% midzone is 5.3% for the 18 rpm (case 11), while it decreases to 4.7% for the 20 rpm (case 12). Thus, the v of 18 rpm (case 11) is more appropriate for db of 600 mm than 16 or 20 rpm cases. The mean volume fraction of beads along the y-axis of the vessel is shown in Figure 5 as a function of rotating time: 3, 10, 30, and 60 min. Considering the bead fraction contours (Fig. 4), four combinations of rotating speed and beads diameter (v/db): 10 rpm/200 mm (case 1), 12 rpm/300 mm (case 5), 14 rpm/400 mm (case 9), and 18 rpm/600 mm

Kwon et al.: Multiphase Analysis of Oxygen Transport in Micro-g Biotechnology and Bioengineering. DOI 10.1002/bit

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Figure 5.

Mean volume fraction of beads along the y-axis of the vessel.

(case 11) have been chosen as appropriate operating conditions. For these cases, beads did not sediment and were distributed away from the vessel walls, thus maintaining a near solid-body rotation. As time of rotation increases from 3 to 60 min, the initial concentration of bead at the bottom of the vessel (arrow 1 in Fig. 5) reduces and distributes radially toward the midzone of the vessel. This result indicates that there is a balance between the gravityinduced sedimentation forces and rotation-induced forces such as centrifugal and Coriolis forces that are acting on the beads. As the db and v increase, the outer zone of the vessel has increased volume fraction of beads after 60-min rotation. The bead fraction increases from
0.05 for 10 rpm/200 mm (case 1) to
0.08 for 14 rpm/400 mm (case 9) and
0.07 for 18 rpm/600 mm (case 11) at y ¼ 2.7 cm of the vessel (arrow 2 in Fig. 5). This is attributed to the migration of beads toward the outer wall caused by an increased centrifugal force that is higher than the required force needed to offset the gravitational pull. Figure 6 represents the contours of oxygen concentration within the vessel after 60-min rotations for the rotating speed and beads diameter (v/db) combinations: 10 rpm/ 200 mm (case 1), 12 rpm/300 mm (case 5), 14 rpm/400 mm (case 9), and 18 rpm/600 mm (case 11). All the contours are scaled with same maxima and minima of oxygen

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concentration. Oxygen diffuses from the inner oxygenator, composed of a gas permeable membrane, and is consumed by cells attached to the surfaces of beads. After the 60-min rotation, for all the cases, there is adequate diffusion of oxygen from the inner membrane to the fluid medium. As the db and v increase, the minimum oxygen concentration increases from 3.8 ppm (case 1) to 7.2 ppm (case 11) because of the higher convective flux of oxygen along the radial direction. The oxygen concentration along the y-axis of the vessel is plotted in Figure 7. It shows that, in general, oxygen diffuses continually from the inner oxygenator in the radial direction of the vessel (arrow 1 in Fig. 7). Also, as time of rotation increases for the cases 1, 5, and 9, the minimum oxygen concentration decreases in the outer periphery of the vessel due to the consumption of oxygen by cells. The decrease in oxygen concentration is reduced from
5% for 10 rpm/ 200 mm (case 1) to
2% for 14 rpm/400 mm (case 9) at y ¼ 2.7 cm of the vessel (arrow 2 in Fig. 7). The oxygen concentration for the case 11, however, is increased by
60% as time increases from 3 to 60 min. This is attributed to higher convection flux as the db and v increase from 10 rpm/200 mm to 18 rpm/600 mm as also seen in Figure 6. To summarize the combinations of rotating speed and beads diameter, Table I displays the comparisons of bead

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Figure 6. Contours of oxygen concentration within the vessel after 60-min rotation. [Color figure can be seen in the online version of this article, available at www.interscience.wiley.com.]

Figure 7.

Oxygen concentration along the y-axis of the vessel.

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Table I.

Comparison of bead fraction and oxygen concentration in the 80% midzone of the vessel after 60-min rotation.

No. Case Case Case Case

1 5 9 11

Bead size (mm)

Rotating speed (rpm)

Mean bead fraction (%)

Oxygen concentration (ppm)

200 300 400 600

10 12 14 18

5.07 4.99 4.62 5.3

4.09 4.07 5.37 7.62

distribution and oxygen concentration in the 80% midzone of the vessel after 60-min rotation. As demonstrated above, in order to maintain appropriate suspension conditions, it is critical that most beads be suspended within the midzone and away from the vessel walls. The combinations of rotating speed and beads diameter (v/db): 10 rpm/200 mm (case 1), 12 rpm/300 mm (case 5), 14 rpm/400 mm (case 9), and 18 rpm/600 mm (case 11) have shown significantly high fraction of beads between 4.6 and 5.3 in the 80% midzone as shown in Figures 4 and 5. As the db and v increase from cases 1 to 9, the mean bead fraction in the 80% midzone decreases by
9%, due to high centrifugal force. The mean oxygen concentration increases by
30% as a result of the higher convection flux for the 14 rpm/400 mm (case 9) as compared to the 10 rpm/200 mm (case 1). For 18 rpm/600 mm (case 11), the oxygen concentration is increased by
85% as compared to case 1.

Conclusions The RWV bioreactor is analyzed utilizing the Eulerian multiphase method having culture medium and beads. In addition, the bead–bead collision is included in the calculation of bead-phase stress in order to consider the influence of the random particle motion in the vessel. Oxygen concentration equation is solved considering the transport and consumption of oxygen in the vessel. The present analysis shows that the v needs to be increased as the db becomes larger with the latter also implying the growth of cell aggregates [10 rpm for 200 mm (case 1); 12 rpm for 300 mm (case 5); 14 rpm for 400 mm (case 9); 18 rpm for 600 mm (case 11)]. As the db and v increase, the outer zone of the vessel has increased volume fraction of beads. The mean oxygen concentration for 18 rpm/600 mm (case 11) also increases due to the increased convective flow as compared to 10 rpm/200 mm (case 1). The current parametric results can be used to minimize costly cell culture experiments for optimizing conditions of cell/bead suspension in the bioreactor (Kwon et al., 2006). In addition, the present results on numerical prediction of the distribution of cell/microcarrier beads and the concentration of biochemical components such as oxygen in the bioreactor may play a significant role in the design of new bioreactors to study optimized suspension cultures of cells and tissues. The limitation of the present study is that the calculation is carried out for 2-D geometry. However, the RWV bioreactor is a 3-D cylinder and hence, there might be alterations in distribution of beads and oxygen transport

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due to the end-effect of the cylindrical vessel. Also, oxygen consumption rate by cells is considered to be a constant in this study but it may depend on the cell proliferation and viability as a function of time. Thus, further research is needed to achieve more realistic estimations of fluid and mass transport in the RWV bioreactor.

Nomenclature CD

drag coefficient

db

diameter of the bead particles (m)

g

gravity acceleration (m/s2)

K

interphase momentum exchange coefficient (kg/m3/s)

p pb

pressure (Pa) bead pressure (Pa)

S

source term (kgo/m3/s)

t ~ v

velocity vector (m/s)

m

viscosity (kg/m/s)

r

density of the phase (kg/m3)

t

stress tensor (Pa)

a G

volume fraction of each phase diffusion coefficient of oxygen (kg/m/s)

f

user-defined scalar

v

rotating speed (rev/min, rpm)

time (s)

Subscripts b

bead phase

i

each phase (bead or medium)

m

medium phase

o

oxygen

This work has been partially supported by NASA Glenn Research Center (NASA-GSN-6234).

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