Fluid dynamics of flow fields in a disposable 600-mL orbitally shaken bioreactor

Accepted Manuscript Title: Fluid dynamics of flow fields in a disposable 600-mL orbitally shaken bioreactor Authors: Likuan Zhu, Dominique T. Monteil, Yukui Wang, Boyan Song, David L. Hacker, Maria J. Wurm, Xiaobin Li, Zhenlong Wang, Florian M. Wurm PII: DOI: Reference:

S1369-703X(17)30307-8 https://doi.org/10.1016/j.bej.2017.10.019 BEJ 6813

To appear in:

Biochemical Engineering Journal

Received date: Revised date: Accepted date:

2-2-2017 28-8-2017 31-10-2017

Please cite this article as: Likuan Zhu, Dominique T.Monteil, Yukui Wang, Boyan Song, David L.Hacker, Maria J.Wurm, Xiaobin Li, Zhenlong Wang, Florian M.Wurm, Fluid dynamics of flow fields in a disposable 600-mL orbitally shaken bioreactor, Biochemical Engineering Journal https://doi.org/10.1016/j.bej.2017.10.019 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Fluid dynamics of flow fields in a disposable 600-mL orbitally shaken bioreactor Likuan Zhu1,2, Dominique T. Monteil2, Yukui Wang1, Boyan Song1, David L. Hacker2,3, Maria J. Wurm4, Xiaobin Li5,*, Zhenlong Wang1,*, and Florian M. Wurm2,*,+ 1

School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, P.R. China 2

Laboratory of Cellular Biotechnology (LBTC), Faculty of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland 3

Protein Expression Core Facility (PECF), Faculty of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland 4

ExcellGene SA, CH-1870, Monthey, Switzerland

5

School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, P.R. China

Present address +

ExcellGene SA, Route de l’Ile-au-Bois 1A, CH-1870 Monthey, Switzerland

*Corresponding authors Xiao-bin Li Email: Telephone:

[email protected] +86 0451 864 03254

Zhen-long Wang Email: [email protected] Telephone: +86 0451 864 13485 Florian M. Wurm Email: [email protected] Telephone +41 24 471 9660 1

Graphical abstract

Highlights 

Fluid dynamics in the OSR600 were studied by a CFD method.



The CFD model was validated by liquid wave imaging of the OSR600.



The energy dissipation rate was calculated for different operating conditions.



The effects of operating condition on kLa and shear stress were investigated.



The highest shear stress was at the lower conical part of the vessel wall.

Abstract Orbitally shaken bioreactors (OSRs) are commonly used for the cultivation of mammalian cells in suspension. Here we conducted a three-dimensional computational fluid dynamics (CFD) simulation to characterize the fluid field in the disposable 600-mL orbitally shaken bioreactor (OSR600), basically a cylindrical vessel with a conical bottom and a ventilated cap. The CFD models established for the OSR600 were validated by visual comparison of the liquid flow pattern in an experimentally agitated OSR600. In the model, both shear stress and energy dissipation rate (Φ) were calculated to evaluate the hydrodynamic stress environment for cell cultivation. The highest values of shear stress and Φ were localized along the lower part of the conical vessel wall. The effect of filling volume and shaking speed on kLa, Φ and shear stress were also analyzed. An increase of the percentage of the liquid affected by 2

higher shear stress and Φ was observed at filling volumes of 300 mL and 400 mL compared to lower filling volumes. This may be due to the twisted curvature at the base of the liquid wave under these conditions. In conclusion, the CFD model provided a means to characterize the fluid dynamics of the OSR600 under various operating conditions to help identify those most suitable for cell cultivation.

Key words: Orbitally shaken bioreactor; computational fluid dynamics; shear stress; energy dissipation rate; oxygen transfer rate; mammalian cells

1. Introduction The suitability of cylindrical orbitally shaken bioreactors (OSRs) for suspension cultivation of mammalian, insect, and plant cells applied for recombinant protein production has recently been investigated [1-10]. OSRs are now commercially available for culture volumes of up to 200 L, with disposable 50-mL and 600-mL orbitally shaken tubes (OSR50 and OSR600) being available for culture volumes of 5-10 mL and 100-500 mL, respectively [11-15]. These are shaped similar to centrifuge tubes with a conical bottom of 50 and 500 mL volume, respectively, but they have each ventilated caps with a filter membrane for sterility and gas transfer.

Although computational fluid dynamics (CFD) is a standard approach to the modeling of hydrodynamics in stirred-tank bioreactors (STRs) [16-24], CFD tools have only recently been used to model hydrodynamics in OSRs [25, 26]. By using experimental approaches and dimensionless analysis, a scale- and volume-independent volumetric mass transfer coefficient (kLa) correlation was described in OSRs with volumes from 2 L up to 200 L [27]. We have recently used CFD tools to model the hydrodynamics in the OSR50 [28]. In this work, the interaction of the gas and liquid phases was studied, and the gas transfer 3

rate was analyzed with different filling volumes and shaking speeds. It was found that the observed high kLa of the OSR50 appeared to be a favorable factor to support the now observed very high cell densities when using today’s rich media formulations [28]. For the OSR600, the volumetric power consumption, kLa, and mixing time have been determined [29], but the fluid field in this vessel has not yet been modeled with CFD tools.

The aim of this study was therefore to numerically characterize the fluid flow and other bioprocess-associated parameters such as kLa and hydrodynamic stress in these vessels. In order to obtain the computed kLa values, the mass transfer coefficient (kL) and the specific interfacial area (a) were modeled separately, and the calculated kLa values were validated experimentally. The shear stress and energy dissipation rate (Φ) distribution were calculated with different filling volumes and shaking speeds. To our knowledge, this is the first study on characterization of the fluid dynamics in OSR600 containers.

2. Materials and methods

2.1 Measurement of kLa

kLa values were determined using the static gassing-out method in an OSR600 (TPP, Trasadingen, Switzerland) containing ultra-high purity (UHP) deionized water at various filling volumes and agitated at 180 rpm [30]. Nitrogen was sparged into the water until the air saturation of the liquid reached a constant value close to zero. Then air was flushed into the gas phase (headspace) of the OSR600. Each vessel was then orbitally shaken on an ES-X shaker (Kühner AG, Biersfelden, Switzerland) at a shaking diameter of 50 mm. The increase of the dissolved oxygen (DO) concentration in the liquid phase was recorded using a non-invasive optical sensor spot (PreSens GmbH, 4

Regensburg, Germany) during agitation. The kLa was calculated from the following mass balance equation (Eq. 1) [30]:

d CL dt

 kL a(C*  CL )

(1)

where CL [mol.L-1] is the DO concentration in the liquid phase, C* is the DO concentration at saturation [mol.L-1], and t is the time [s].

2.2 Imaging of liquid wave in an agitated OSR600

A high-speed camera (PHANTOM V9.1, Vision Research, New Jersey, USA) was used to capture the moving liquid wave within the OSR600. For each condition, 10 μL Methyl Red (Fisher Scientific, Pittsburgh, PA) was added to the liquid to better visualize the liquid wave shape. The camera was fixed on the shaker platform to keep it static relative to the vessel wall. An external light source (Light star, Dragon Image, Sydney, Australia) was applied for illumination. The image resolution was 1200×1024 [DPI×DPI], and the frame rate was 800 fps. To validate the CFD model, the values of liquid height on the vessel wall were measured from the recorded video. For the measurement of liquid height, all the recorded frames in one revolution were sequentially imported into the Matlab software. In each frame, one height value of the liquid wave on a chosen vertical line located at the vessel wall was detected by a critical red-green-blue (RGB) value in the Matlab code. The circumferential angle for a specific liquid height was determined by Eq. 2:



 S -1  N  360 f

(2)

60

where the  is the circumferential angle (°), S represents the sequence number of the frame, f is the frame rate (fps), and N is the shaking speed (rpm).

2.3 CFD models 5

In order to track the moving interface between gas and liquid phases, a volume of fluid (VOF) model was employed for numerical simulation [31]. Briefly, the VOF model is proposed by solving the transportation of the phase void fraction between two phases. The equation for the phase void fraction is defined in Eq. 3：   u   0 t

(3)

where α=1 indicates a computational volume that is completely full of liquid, α=0 indicates a volume with no liquid, 0<α<1 defines the gas-liquid interface, and u represents the linear velocity vector [m.s-1].

The governing equations for fluid flow, including the continuity (Eq. 4) and momentum equations (Eq. 5), are shown below:   ( u)  0 t  ( u)  ( uu)  p  ( )+ g+F t

(4) (5)

where p is the pressure (Pa),  is the stress tensor (Pa), and  g [N.m-3] and F [N.m-3] are the gravitational body force and external body forces,

respectively. The density (ρ) is defined in Eq. 6:

    l  (1   ) g

(6)

where the subscripts g and l represent the gas and liquid phases, respectively. To analyze the shearing environment in the fluid flow field of the OSR600, the shear stress  was divided into a three-dimensional shear stress factor in Eq. 7:

  ( xy2 + yz2 + zx2 )1/ 2

(7)

where  xy ,  yz ,  zx are the three components of the three-dimensional shear stress. These three components can be calculated from Eqs. 8-10 as follows:

 xy   (

ux u y + ) y x

(8)

6

 yz   (  zx   (

u y z

+

uz ) y

(9)

uz ux + ) x z

(10)

where μ [kg.m-1.s-1] is the viscosity of the fluid in the bioreactor as defined in Eq.11:

    l  (1   )g

(11)

Eqs. 8-10 were modeled by a user-defined function in the CFD software.

2.4 Calculation of kLa

The kLa is derived from the mass transfer coefficient (kL [m.h-1]) and the specific interfacial area (a [m-1]). The value of the latter was defined in Eq. 12: a

A interfacial area  VL filling volume

(12)

where the value of A was predicted by the VOF model. Based on Higbie’s penetration theory and surface renewal model [32, 33], kL was calculated by Eq. 13.

 14 k L  K  DL  ( ) 

(13)

where ε [m2.s-3] is the turbulent energy dissipation rate, υ represents the kinematic viscosity of the liquid phase (1×10-6 m2.s-1), DL is the diffusion coefficient of gas in the liquid (1.97×10-9 m2.s-1), and K is the model constant (0.4).

2.5 Orbital shaking movement

Agitation of the OSR600 by orbital shaking can be divided into two separate 7

movements. One is the angular velocity of the circular translational movement with the shaking radius around the center of the shaker and the other is the rotation with respect to the center of the OSR600 [34]. This movement results in a centrifugal force applied to the liquid in the container. Thus, a centrifugal force was incorporated into the Navier-Stokes equation as a source term to realize the orbital shaking movement as described by Eqs. 14 and 15: Fx  ω2 R S  cos(ω  t )

(14)

Fy  ω2 R S  sin(ω  t )

(15)

where RS [m] is the shaking radius, Fx [m.s-2] and Fy [m.s-2] are the centrifugal force components in the x and y directions, respectively, t is the time [s], and ω [rad.s-1] is the rotation speed.

2.6 Simulation conditions

The simulations were carried out using the commercial CFD package FLUENT in ANSYS 15.0 (ANSYS Inc., Canonsburg, PA, USA). The k-ω-SST turbulence model was used to enclose the governing equations of the fluid motion [35]. The pressure-implicit with splitting of operators (PISO) method was adopted to solve the velocity and pressure, which was suitable for transient simulation. The no-slip condition was used at the wall boundaries of the fluid domain. Air and water were chosen as the gas and liquid phases in the bioreactor. The time step was set as 0.0001 s which proved suitable for a fast and stable simulation in the OSR600. A convergence criterion of ～1×10-4 was used for simulation. The vessel geometry was discretized by structured grids (hexahedron) using the Trelis CFD meshing software (Trelis 15, Csimsoft, American Fork, UT). All the simulations were executed on a 64G RAM 16 processor (Dell, Round Rock, TX, USA).

3. Results 8

3.1. Fluid flow pattern

The computed maximum liquid height as a function of time was employed to test the grid independence using a filling volume of 100 mL and an agitation speed of 180 rpm. Due to the effects of gravity and centrifugal forces, the shape of the liquid wave geometry remained unchanged after a short acceleration period of a few seconds for all the grid numbers tested (Fig. 1). As a consequence, the liquid height distribution on the container wall could be determined at a fixed vertical line from a series of frames during one simulated revolution of the OSR600. The grid number of 2.0×105 was found to be sufficient for a stable solution and was therefore used for all further simulations in this work. The stable shape of the liquid wave was considered favorable to predict the oxygen transfer rate (OTR) of the OSR600. A similar phenomenon has also been found for the fluid flow pattern in a non-baffled Erlenmeyer-like flask [36].

The fluid flow pattern of the OSR600 was simulated at various filling volumes (100 – 500 mL) at a shaking speed of 180 rpm. The liquid shapes were slightly different as there was a noticeable impact of the lower conical part of the container at filling volumes of 100 and 200 mL in comparison to the other filling volumes (Fig. 2, top panels). Under the same conditions as for the simulations, the liquid wave in the OSR600 was captured by a high-speed camera fixed on the shaker. For each filling volume, the liquid wave shape was similar to the simulated conditions (Fig. 2, bottom panels). The major difference was that the curved surface of the liquid wave observed under experimental conditions was not as smooth as predicted by the simulations. The difference between the recorded and simulated conditions was decreased when using a higher-order turbulence model with a penalty of longer computing times (data not shown). For filling volumes of 300 and 400 mL, bubbles were observed in both 9

simulated and experimental conditions (Fig. 2C, D). The bubble size in the simulations was smaller than under experimental conditions. This may have been due to the VOF model’s inability to simulate bubble interactions such as bubble coalescence. The smallest diameter of bubbles the VOF model could resolve was about 1.1 mm for the grid number of 2.0×105. The fluid flow pattern was also simulated at different shaking speeds (140 – 220 rpm) at a constant filling volume of 100 mL. The liquid wave became steeper and the liquid height increased as the shaking speed increased (Fig. 3). The distribution of liquid heights (highest point of the wave) on the wall of the vessel was compared between the measured and simulated conditions at different filling volumes and at a constant shaking speed. As shown in Fig. 4, the modeled data reflected very well the recorded data (less than 10% difference) and thus verified the validity of the CFD model.

3.2 Fluid velocity vector

The velocity of the fluid in a bioreactor is basic information of a flow field and also a fundamental variable for calculating the fluid shear stress. At a shaking speed of 180 rpm and a filling volume of 100 mL, the local fluid velocity field in a vertical section (meridional plane) and two horizontal sections of the OSR600 was evaluated (Fig. 5A). For the vertical section D1, the highest fluid velocity was located at the wave front near the vessel wall, while the region with the lowest fluid velocity was observed near the vessel center (Fig. 5B). At the conical part of the container, a very significant gradient in fluid velocity was found, and the liquid motion appeared more disordered than in other regions, probably indicating a better mixing in this region than in the upper part of the vessel (Fig. 5B). By comparison, the liquid velocity was more uniform within the horizontal sections D2 and D3 (Fig. 5C). A single vortex was observed within D2, and the local fluid velocity was found to be quite low in the vortex center (Fig. 5C). It should be noted that the vortex center was not located at 10

the geometrical center of D2. Rather, it was closer to the liquid wave front (Fig. 5C). Within section D3, the highest fluid velocity (0.86 m s-1) was found to be just behind the wave front (Fig. 5C) and proved to be very close in value to the theoretical maximum speed of 0.80 m s-1 calculated by Eq. 16:

vt max  2 RS N

(16)

where N is the shaking speed [s-1]. The difference between the two values (<8%) may be due to turbulence within the high-speed fluid region. In support of this interpretation, it is known that in STRs the turbulence behind the impeller results in a fluid velocity about 40% higher than at the impeller tip [37].

3.3 Local shear stress distribution at a filling volume of 100 mL

All cultivated animal cells are sensitive to shear stress, and this is an important consideration when cultivating them as single cells in suspension [38, 39]. Information about the shear stress distribution within a bioreactor is therefore a helpful parameter when optimizing and scaling up operations. Based on the CFD simulations described above, the highest shear forces were expected near the wall of the vessel. To further investigate shear forces, the local shear stress was determined at a filling volume of 100 mL and an agitation speed of 180 rpm. The shear stress located on the gas-liquid interface was shown to be close to zero (Fig. 6A). By focusing on three cross-sections located at different heights from the bottom of the vessel [7 mm (A1), 27 mm (A2), and 47 mm (A3)], we observed that the shear stress near the vessel wall was higher than in any other part of the liquid. The maximum level of shear stress was located along the wall at the lower conical part of the vessel (A1), and its value decreased with increasing height within the vessel (Fig. 6A).

3.4 Local energy dissipation rate distribution at a filling volume of 100 mL

11

Shear stress is one of two types of fundamental hydrodynamic stress. The second type is referred to as normal stress which is oriented perpendicular to the fluid velocity. Like shear stress, normal stress also contributes to cell damage [40]. Both shear stress and normal stress can be quantified by the energy dissipation rate (Φ), which is the irreversible conversion of mechanical energy to heat and is defined in Eq. 17 [41]:

    normal 2

2

   shear 

2

 

2 xx

  yy2   zz2  2

 

2 xy

  zx2   yz2 



(17)

where τxx, τyy and τzz are components of normal stress, which are defined by Eq. 18 - 20:

 xx  2

 yy  2  zz  2

ux x

(18)

u y

(19)

y uz z

(20)

The distribution of Φ was determined at a filling volume of 100 mL and a shaking speed of 180 rpm. Similar to the shear stress distribution, the maximum value of Φ (0.293 m2·s-3) was located along the vessel wall at the lower conical zone (Fig. 6B). In addition, the magnitude of Φ decreased as the height increased as observed for the shear stress distribution (Fig. 6B).

3.5 Effect of operating conditions on shear stress

The shear stress was calculated at different filling volumes and shaking speeds. In all cases studied, more than 80% of the total liquid volume was exposed to a low shear stress environment (0-0.1 Pa) (Fig. 7A, B). As the filling volume increased at the shaking speed of 180 rpm, the liquid volume with low shear stress (0-0.1 Pa) also increased, while the liquid volume with a medium level of shear stress (0.1-0.4 Pa) decreased (Fig. 7A). The percentage of the 12

liquid volume with high shear stress (0.4-1.0 Pa) increased when the filling volume increased from 100 - 200 mL to 300 – 400 mL (Fig. 7A). However, when the filling volume reached 500 mL, there was only a very small liquid volume exposed to high shear stress (＜0.2%) (Fig. 7A). As the shaking speed increased, the liquid volume exposed to low shear stress decreased at a constant filling volume of 100 mL (Fig. 7B). However, the percentage of liquid volume with medium (0.1-0.4 Pa) and high (0.4-1.0 Pa) levels of shear stress increased (Fig. 7B).

3.6 Effect of operating conditions on Φ

The value of Φ was calculated at different filling volumes and shaking speeds. Both the average value and maximum values of Φ (Φmean and Φmax, respectively) increased as the filling volume increased from 100 – 200 mL to 300 – 400 mL (Table 1). But lower values of Φmean (0.0037 m2·s-3) and Φmax (0.433 m2·s-3) were observed at a filling volume of 500 mL (Table 1). Moreover, Φmax/Φmean increased from 31.8 to 116 when the filling volume increased from 100 to 500 mL (Table 1). As the shaking speed increased from 140 to 220 rpm, the Φmean and Φmax increased from 0.0075 to 0.0165 m2·s-3 and from 0.239 to 0.411 m2·s-3, respectively (Table 2). However, the value of Φmax/Φmean decreased as the shaking speed increased (Table 2).

3.7 Effect of operating conditions on kLa

The OTR of a bioreactor under fixed operational condition plays an important role in the growth, metabolism and productivity of the recombinant animal cells being cultivated [42]. To investigate the OTR of the OSR600, the kLa was determined at different filling volumes and shaking speeds by using CFD tools to separately calculate the values of kL and a. The former was calculated from a modified form of ε (see Eq. 12) termed ε* [ε* = (ε)0.25]. At a shaking speed of 13

180 rpm, ε* was found to be nearly constant across the range of filling volumes tested (Table 3). Consequently, the kL was also nearly constant as the filling volume increased from 100 mL to 500 mL (Fig. 8A). In contrast, the specific surface area (surface over volume) a, as expected, decreased as the filling volume increased from 100 mL to 500 mL (Fig. 8A). The lowest values for the interfacial area (A) were observed at filling volumes of 100 mL, 200 mL and 500 mL (Table 3). For the two lower volumes, the liquid touched the bottom of the vessel (Fig. 2A), while for the filling volume of 500 mL, the liquid reached the upper section of the cylindrical wall (Fig. 2E). Overall, the calculated kLa decreased as the filling volume increased from 100 to 500 mL at a shaking speed of 180 rpm (Fig. 8A). As the shaking speed increased at a constant filling volume of 100 mL, the values of A and ε* increased (Table 4). As a result, both a and kL increased with the shaking speed (Fig. 8B). As a result, the kLa increased from 47.1 to 110.9 h-1 as the shaking speed increased from 140 to 220 rpm (Fig. 8B).

To verify the results from the CFD model, experimentally determined kLa values were derived by the static gassing-out method. For each filling volume and shaking speed tested, the measured and simulated kLa values differed by <30%, validating the CFD model (Table 5).

4. Discussion

In this report, fundamental fluid dynamic characteristics of the liquid flow field in the OSR600 were investigated by both CFD and video imaging. At a shaking speed of 180 rpm, the fluid flow patterns observed by video imaging at different filling volumes were similar to those calculated from the CFD simulations. The effect of operating conditions on kLa were determined with both CFD simulations and with the static gassing-out method. Similar kLa values were 14

obtained by the two methods. As anticipated, the kLa decreased with filling volume and increased with shaking speed. Based on these results we concluded that the CFD model of the hydrodynamics within the OSR600 is able to provide important information for optimizing bioprocesses in this container.

The Froude number (Fr), the ratio of the centrifugal and gravitational forces on a fluid particle, is the main driving force of the orbital shaking movement in OSRs [43]. The definition of Fr is shown in Eq. 21:

Fr  N 2  r / g

(21)

where N [s-1] is the shaking speed, g [m.s-2] represents the gravitational force, and r [m] denotes the distance between the location of the fluid particle and the axis of the vessel. The maximum value of Fr is thus constant at any given shaking speed, which could be the main reason why the difference among the kL values was less than 25% for the various filling volumes when the agitation speed was set at 180 rpm. It should be mentioned that the higher kL values for the filling volumes of 300 and 400 mL compared to the other conditions tested may be due to bubble burst which can increase the local value of ε significantly [40]. In fact, higher values of ε were observed in the simulations at 300 and 400 mL as compared to the simulations at higher and lower filling volumes (Table 3). According to the theoretical expression of the liquid surface geometry during orbital shaking of the OSR600, the curvature of air-liquid interface is the same for a constant shaking speed at different filling volumes unless the liquid wave touches the part of vessel wall with non-cylindrical geometry [34]. This is likely to have been the reason why the values of A were similar at 300 and 400 mL, but lower at 100, 200 and 500 mL. This may also be the reason why the a values decreased with an increase in filling volume. A similar phenomenon was observed for the simulations of the fluid field in the OSR50 [28]. The emergence of bubbles may have contributed little to the high 15

values of A for filling volumes of 300 and 400 mL, because the volume of bubbles was very limited in these two cases. As a result, the kLa was more dependent on a, which decreased with an increase in filling volume, than kL at a shaking speed of 180 rpm. As the shaking speed increased at the filling volume of 100 mL, the maximum value of Fr increased and more liquid was accelerated into the near wall region (high Fr). Furthermore, at this filling volume, no liquid touched the top conical wall. These factors increased the volumetric percentage of liquid with a high Fr, which might be the reason why both kL and a increased as the shaking speed increased. Thus, the value of kLa increased as the shaking speed increased. These results seemed to indicate that a small filling volume such as 100 mL could be the most favorable for high-density cell cultivation (>5x106 cells/mL) where the oxygen demand is high. In order to supply more oxygen to filling volumes greater than 100 mL, it would be possible to use shaking speeds greater than 180 rpm as suggested by the data in Fig. 8B.

Although the issue of cell damage in bioreactors has been extensively studied, there is still much to understand about how mammalian cells respond to hydrodynamic stress in suspension culture [40, 44]. Much work has been done to determining the critical values of shear stress and Φ, the minimum values that are lethal to cells [45-51]. To evaluate the hydrodynamic stress environment comprehensively, both shear stress and Φ were calculated in the OSR600 at different operating conditions. For the determination of local shear stress, we assumed that the velocities in the gas phase were the same as those in the liquid phase at the gas-liquid interface, according to fluid dynamic principles [52]. Considering that the viscosity in the gas phase was negligible, it followed that the gas phase did not contribute to the shear stress of cells in suspension. Indeed, in our model, the shear stress at the gas-liquid interface was close to zero (Fig. 6A). Moreover, the high shear stress near the vessel wall was due to a large fluid velocity gradient that resulted from the no-slip 16

boundary condition in which the near-wall liquid velocity was assumed to be equal to the shaking speed [53]. The high fluid velocity close to the vessel wall was thought to be a consequence of orbital agitation as the kinetic energy was transferred from the vessel wall to the liquid phase to achieve mixing. The rapid change of the velocity vector observed at the lower conical part of the vessel wall meant that the shear stress increased in this region. Therefore, the conical vessel wall is predicted to be a location with the greatest risk of damage to cells. It is expected that altering the geometry of the lower cone of the OSR600 will reduce the percentage of damaged cells. The angle and height of the lower cone could be optimized to achieve the smallest superficial area of the vessel wall exposed to high shear stress. By doing this, the probability of cell contact with the wall and the duration of the contact would be decreased.

It has been observed that suspended CHO cells experienced a metabolic change and a decrease in productivity when the shear stress was higher than 0.4 Pa [54]. In general, a shear stress below 0.1 Pa is considered mild for CHO cells in suspension [46, 49-50]. Thus, the calculated shear stress in the OSR600 was divided into three ranges to represent low (0-0.1 Pa), medium (0.1-0.4 Pa), and high (0.4-1.0 Pa) shear stress. As the filling volume increased, more liquid was located in regions with low fluid velocity at the vessel’s center. The increased fraction of liquid with low velocity resulted in a decrease in the overall shear stress. However, more of the liquid was locally exposed to high shear stress at filling volumes of 300 and 400 mL. At these two filling volumes, the greater shear stress may be due to the twisted curvature at the bottom margin of the liquid wave where bubbles were observed under both experimental and simulated conditions (Fig. 2 C, D). The slight decrease in the volume fraction exhibiting high shear stress when the filling volume was 400 mL may have been due to an increase in the percentage of liquid having a low fluid velocity. Indeed, the curvature at the 17

liquid wave front at this filling volume was smoother than that at a filling volume of 300 mL (Fig. 2 C, D). The upper inward-slanting neck of the OSR600 (beneath the cap) was found to suppress fluid flow. This may be the main reason why the volume fraction having a high shear stress was limited at a filling volume of 500 mL. Given that the fraction of liquid volume exposed to shear stress in the high range exceeded 1% in 300 mL at the shaking speed of 180 rpm, CHO cell cultivation should be conducted carefully in this condition and surfactants such as Pluronic F-68 may be necessary for a high cell density and viability. As the shaking speed increased, the Fr of the bulk fluid increased, driving more liquid from the center region (low velocity) to the near wall region (high velocity) (Fig. 3). This caused more liquid to be exposed to a high velocity gradient, which may explain why the liquid volume with low shear stress decreased and that with medium and high levels of shear stress increased as shaking speed increased.

As for the shear stress, the maximum value of Φ was found in the lower conical vessel wall (Fig. 6B). For all the operating conditions analyzed, none of the Φmean and Φmax values were higher than the critical values which can cause damage to CHO cells in suspension, 0.4 m2·s-3 for Φmean and 4.0 m2·s-3 for Φmax [49, 55], demonstrating that the hydrodynamic stress environment to be suitable for CHO cells culture in the OSR600. However, given that the Φmax at a filling volume of 300 mL was 1.25 m2·s-3 and thus was over the critical value of 1.0 m2·s-3 for causing damage to adherent cells [56], the OSR600 should not be used for the cultivation of cells on microcarriers under this condition. Lastly, the ratio of Φmax/Φmean increased with filling volume but decreased with shaking speed, indicating that a more uniform distribution of Φ would be expected in OSR600s at lower filler volume or higher shaking speeds.

The results described here demonstrated that CFD is a valuable tool for evaluating and optimizing cell culture conditions like oxygen supply and 18

hydrodynamic stress in the OSR600 and, by extension, in other OSRs. Moreover, CFD could also be used as a tool to optimize the geometries of OSRs. Overall, the OSR600 was shown to be a suitable vessel for the suspension cultivation of animal cells due to the low hydrodynamic stress and high kLa at the operating conditions tested here.

5. Conclusion

In this study, the flow field in the OSR600 was simulated using a three-dimensional CFD model that was subsequently validated by experiment. The simulated kLa increased with shaking speed but decreased as the filling volume increased. The simulated kLa was found more dependent on a than kL at a constant shaking speed. Moreover, the hydrodynamic stress environment in the OSR600 was proved to be suitable for CHO cell growth in suspension. The highest levels of both shear stress and energy dissipation rate were found near the lower conical vessel wall which was assumed to have a negative effect on cell growth. The investigation of the effect of operating conditions on the hydrodynamic stress suggested that a slightly higher risk for cell damage could be expected in the OSR600 at filling volumes of 300 to 400 mL.

6. Acknowledgments

The authors thank the China Scholarship Council (CSC) (Certification No. 201306120128), the National Natural Science Foundation of China (Certification No. 51506037), and the EPFL for financial support.

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Table 1. The values of energy dissipation rate at different filling volumesa Filling volume VL [mL]

Φmean [m2·s-3]

Φmax/Φmean [-]

Φmax [m2·s-3]

100 200 300 400 500

0.0092 0.0084 0.0135 0.0090 0.0037

31.8 39.5 92.3 109.7 116.0

0.293 0.332 1.250 0.992 0.433

a

The shaking speed was 180 rpm in each case.

Table 2. The values of energy dissipation rate at different shaking speedsa Shaking speed N [rpm]

Φmean [m2·s-3]

Φmax/Φmean [-]

Φmax [m2·s-3]

140

0.0075

31.7

0.239

23

160 180 200 220 a

0.0088 0.0098 0.0113 0.0165

30.11 29.08 25.7 24.9

0.265 0.285 0.326 0.411

The filling volume was 100 mL in each case.

Table 3.

Simulated wave pattern properties at different filling volumesa.

Filling volume VL [mL]

Interface area A [cm2]

TEDRb ε [m2·s-3]

Contribution of TEDR to kLc ε* [m2·s-3]

100 200 300 400 500

78.2 99.6 110.1 107.6 94.5

0.034 0.033 0.051 0.037 0.018

0.043 0.043 0.048 0.044 0.037

a The

shaking speed was 180 rpm in each case. energy dissipation rate (TEDR). c * 0.25 ε =(ε) . b Turbulent

Simulated wave pattern properties at different shaking speedsa. Table 4. Shaking speed N [rpm]

Interface area A [cm2]

TEDRb ε [m2·s-3]

0.015 0.024 0.034 0.051 0.091 a The filling volume was 100 mL in each case. b Turbulent energy dissipation rate (TEDR). c * ε =(ε)0.25. 140 160 180 200 220

66.7 72.6 78.2 89.3 98.2

Contribution of TEDR to kLc ε* [m2·s-3] 0.35 0.39 0.43 0.48 0.55

Table 5. Comparison of simulated and experimental kLa Filling volume VL [mL]

Shaking speed NS [rpm]

Simulated kLa [h-1]

Experimental kLaa [h-1]

Error [%]

100 200 300 400 500 100

180 180 180 180 180 140

67.7 43.7 35.1 22.1 14.0 47.1

62 44.1 27.4 19.4 13.4 42.6

9.2 1.0 28.0 9.2 4.5 13.9

24

100 100 100 a The

160 200 220

57.7 85.7 108.9

51.4 78.5 101.2

12.3 9.2 7.6

measured kLa values were determined by the static gassing-out method.

Figure legends Figure 1. Analysis of the grid independence for CFD. The simulations were performed in an OSR600 with a filling volume of 100 mL and a shaking speed of 180 rpm. In order to determine the grid number effect on the CFD results, four different grid numbers as indicated in the figure were used for simulation with the same CFD model. The maximum liquid height was exported into a data file at every time-step during the simulation.

25

Figure 2. Comparison of the liquid wave shape between simulated and experimental conditions. The filling volume was varied as indicated, and the shaking speed was kept constant at 180 rpm for the calculated (top panels) and experimental conditions (bottom panels). For the simulated images, the blue color indicates the water phase, the white color indicates the gas phase, and the green color indicates the air-liquid interface. To capture the moving liquid wave, a high-speed camera was fixed on the shaker platform to keep it static relative to the vessel wall. Methyl Red (1.0 M·L-1) was added to the liquid (water).

Figure 3. Simulated liquid waves in the OSR600 at different shaking speeds. Simulations were conducted in the OSR600 with the filling volume of 100 mL at different shaking speeds as indicated. The blue color indicates the water phase, the white color represented the air phase, and the green color represents the air-liquid interface. All simulations were performed until the 26

air-liquid interface shape remained unchanged.

Figure 4. Validation of the CFD model by comparing the liquid height distribution at the vessel wall under experimental and simulated conditions. The shaking speed was kept constant at 180 rpm. In all graphs, the solid black line and green dots represent the liquid height from simulated and measured results, respectively. The circumferential angle (α) is the angle at the vessel wall in cylindrical coordinates as shown in the image in the lower right panel. The height value of the liquid wave on a chosen vertical line located at the vessel wall was detected by a critical RGB value in the Matlab code.

Figure 5. Fluid velocity distribution in the OSR600. The simulation was performed with a filling volume of 100 mL and a shaking speed of 180 rpm. (A) Different locations of the liquid velocity vector distribution are indicated. The liquid velocity vector was determined in a vertical section (D1) and two horizontal sections (D2 and D3). The vertical section was located at the Y-Z plane in the Cartesian coordinate system, and the two horizontal sections were 27

located at heights of 7 mm and 47 mm from the vessel bottom. (B) The liquid velocity distribution in section D1 is shown. In this section vt1 indicates the tangential velocity vector in the Y-Z plane, which is composed of the velocity components in the Y and Z orientations. In order to show the local liquid velocity distribution clearly, a zoom view of the liquid velocity at the vessel bottom is provided. (C) The liquid velocity distribution in sections D2 and D3 is shown. In the horizontal sections D2 and D3, vt 2 denotes the velocity vector formed by the velocity components in the X and Y orientations. The center region of the liquid velocity distribution in section D2 and the liquid velocity distribution of the wave front in section D3 are shown in the zoom images. The color bars at the right of the figure indicate the magnitude of the tangential velocity in (B) and (C).

Figure 6. Local shear stress and energy dissipation rate distribution. (A) The local shear stress distribution at a filling volume of 100 mL and a shaking speed of 180 rpm is shown. (B) The distribution of local energy dissipation rate at a filling volume of 100 mL and a shaking speed of 180 rpm is shown. The magnitude of the shear stress and energy dissipation rate were represented by a color bar at the bottom of each figure. To view the distribution of the shear stress and energy dissipation rate, these two parameters were shown on three horizontal cross-sections at 7 mm (A1), 27 mm (A2), and 47 mm (A3) from the bottom of the vessel. 28

Figure 7. Effect of operating conditions on the shear stress distribution in the OSR600. (A) The results from the analysis of the effect of filling volume on the shear stress distribution are shown. The simulations were performed with different filling volumes as indicated at a shaking speed of 180 rpm. (B) The results from the analysis of the effect of shaking speed on the shear stress distribution are shown. The simulations were performed at different shaking speeds as indicated at a filling volume of 100 mL. The shear stress values were divided into three different ranges, low (0-0.1 Pa), medium (0.1-0.4 Pa), and high (0.4-1.0 Pa). For each simulation, the percentage of the liquid in each shear stress range was calculated.

29

Figure 8. The effect of operating conditions on kLa, kL, and a. (A) Simulations were performed at different filling volumes as indicated at a shaking speed of 180 rpm. (B) Simulations were performed at different shaking speeds at a filling volume of 100 mL. For all trials, the values of kL and a were determined separately using from the simulations. The kLa values were calculated from the kL and a values for each filling volume and shaking speed.

30