ON THE FLOW DYNAMICS AND OUT-OF-PHASE PHENOMENA IN ORBITALLY SHAKEN BIOREACTORS

Transcription

1 14 th European Conference on Mixing Warszawa, September 2012 ON THE FLOW DYNAMICS AND OUT-OF-PHASE PHENOMENA IN ORBITALLY SHAKEN BIOREACTORS W. Weheliye, M. Yianneskis and A. Ducci University College London, Department of Mechanical Engineering, Torrington place, London, WC1E 7JE, UK Abstract. Particle Image Velocimetry, PIV, was employed to study the flow dynamics in a 100 mm diameter cylindrical shaken vessel. Phased-averaged velocity characteristics were determined for different combinations of Froude number, Fr, non-dimensional fluid height, h/d i, and Reynolds number, Re. The experiments revealed two horizontal counter-rotating vortices near the free surface for Δh/h < 0.5 (where Δh is the maximum difference in liquid height, also denoted as wave height, and h the height of liquid in the reactor at rest) that enhanced the mixing process. As Fr was increased either by varying the tray rotational speed, N, or the orbital diameter, d o, these vortices increased in size and extended all the way to the bottom of the cylinder. This condition occurred when the normalised wave height reached a critical value Δh/h = 0.5. For Δh/h > 0.5 the two vortices were gradually displaced towards the vessel wall until the vortices disappeared and a flow transition was observed. This transition elucidated the fluid dynamics associated to the out-of-phase phenomenon, which is characterized by an increasing volume of liquid not moving in-phase with the rotation of the shaker table. A scaling law for in- and out-of-phase conditions was established. Keywords: Shaken bioreactor, flow dynamics, mixing, out-of-phase phenomenon, flow transition. 1. INTRODUCTION In recent years microscale technology has been employed in the early stages of bioprocess development (for example, microbial fermentation, bioconversion and recovery techniques), before the developed process is implemented in a large-scale industrial stirred tank. One such microscale approach relies on the use of microwell plates, where complete mixing is achieved by shaking rather than stirring. Despite the extended use of shaken bioreactors (flasks and microwells), less than 2% of relevant publications on bioreactors have dealt with shaken bioreactors [1]. Moreover larger shaken bioreactors have recently become available in pilot and industrial scale (Sartorius and Khüner AG). This offers a novel scale-up platform, which can help improve process reproducibility and robustness upon scale-up. Consequently, a systematic characterization of bioreactor performance is timely to identify scaling laws and parameters. The current review focuses only on fluid mechanics aspects of shaken bioreactors as they affect mixing and oxygen transfer dynamics. Few articles have dealt with the flow in shaken bioreactors, all involving Computational Fluid Dynamics, CFD [2, 3, 4]. The flows in a 250-ml Erlenmeyer flask and in 24-well and 96-well bioreactors were investigated by [2] and [3], respectively. These studies aimed mainly at determining macro-parameters such as the power consumption, obtained from the integral of the local dissipation rate, the interfacial area, a, and the volumetric mass transfer coefficient, k L a, which are relevant to assess the overall performance of the bioreactors, but assessment of the local flow dynamics and transitions occurring at different operating conditions, and identification of flow scale parameters are lacking. From the dissipation rate distribution it was found that most of the energy is dissipated 509

2 at the bioreactor wall, while a power law relationship was found between the power consumption and interfacial area of a 250-ml Erlenmeyer flask [2]. The space-averaged velocity flow fields obtained for various combinations of shaker rotational speed, N, and fluid viscosity, ν, by [4] showed that for large Re the space-averaged flow field in a vertical plane through the axis is dominated by two large counter rotating vortices present on either side of the axis. When Re is decreased or a greater viscosity is considered, the vortices decrease in size and are pushed towards the centre of the cylinder, while two smaller vortices rotating in the opposite direction with respect to the previous two emanate from the cylinder walls. Flow visualization in Erlenmeyer flasks carried out by [5] identified the so called out-of-phase phenomenon that occurs at high N, and is characterized by an amount of liquid not following the movement of the shaking table, thus reducing the volumetric power consumption, mixing and the gas/liquid mass transfer. A non-dimensional phase number, Ph, was defined which is a function of the ratio between the orbital diameter and the flask maximum diameter, d o /d max, Re, and Fr: when Ph>1.26 and Fr>0.4 the flow is in-phase", while out-of-phase" conditions occur for Ph<1.26 and Fr<0.4. The motivation for the present study is to enhance understanding of the phenomena involved in orbitally shaken bioreactors and throw light on the magnitude and distribution of mixing, interfacial area, energy dissipation and volumetric power consumption, in order to help improve their design and operation. The filling volume, V f, shaking frequency, N, and orbital diameter, d o, which strongly affect the transport phenomena in shaken bioreactors, are considered in an attempt to understand both fundamental and engineering aspects of the flow and identify scaling laws to establish the occurrence of the out-of phase phenomenon in a cylindrical reactor with a flat bottom. 2. MATERIALS AND METHODS 2D PIV was employed to characterize the flow in the bioreactor. The PIV system comprised a diode laser of 532 nm wavelength, a cylindrical lens, a mirror and an intensified camera which were rigidly mounted to the tray of the shaker table. A timing box and a magnetic encoder allowed to synchronize the image acquisition and to obtain phase-averaged velocity as well as ensemble-averaged velocity data. The purpose-built rig comprised a glass cylinder with a transparent bottom placed in a square acrylic trough. Measurements on horizontal and vertical planes were obtained using the PIV set-ups shown in figures 1 and, respectively. Figure 1. PIV systems used to measure the velocities on a vertical and a horizontal plane. The cylinder inner diameter, d i, height, H, and wall thickness, t, were 100 mm, 250 mm and 5 mm, respectively. The flow was seeded with neutrally buoyant 50 µm rhodamine particles and an orange filter with cut-off wavelength of 570 nm was mounted on the 45 mm camera lens. The working fluid was water with kinematic viscosity ν=10-6 m 2 s. An in-house image processing routine was developed to detect the profile of the free surface on the laser plane on each PIV image. A Khüner AG lab shaker LS-X was used. The filling volume and shaker rotational speed were varied in the ranges V f = ml and N= rpm, respectively. The 510

3 PIV experiments were obtained for d o =25 mm, while the inclination of the free surface was determined by image analysis for d o =15-50 mm. In the rest of the article a cylindrical coordinate system, r, θ, z is employed with the origin positioned at the cylinder axis on the bioreactor base. The origin of the angular coordinate, φ, of the position of the tray/cylinder along its clockwise orbit corresponds to the point furthest to the left when the system is viewed from the top. 3. RESULTS AND DISCUSSION 3.1 Flow characterization for in phase condition In this section data are first presented for a reference operating configuration with h/d i =0.3 (V f =235 ml) and N= 90 rpm, while subsequently different h and N are considered. The 2D phase-resolved velocity fields and the contour plots of the tangential component of the vorticity, ω θ, are shown in figures 2 (a-c) for three phase angles, while the ensembleaveraged vector and vorticity fields are shown in figure 2 (d). The sketches above the plots indicate the angular position of the cylinder (blue circle) along its orbit (dotted circle). (c) Figure 2. Phase-resolved vectors and contours of the tangential component of the vorticity,! ", for five different phase angles (h/d i =0.3, N=90 rpm): φ=0 o ; φ=40 o ; (c) φ=90 o ; (d) Ensemble-averaged velocity vectors and vorticity contours. In figure 2 two counter-rotating vortices are observed close to the cylinder walls. The intensity of the two structures is similar with absolute vorticity levels in the range! " (# N) = 0!1. Figure 2 shows the flow when the tray reaches furthest to the left, φ=0 o, and the fluid experiences the maximum centrifugal acceleration. The free surface assumes its maximum inclination, and the two vortices are completely separated with no fluid exchanged between the two. Further along the cylinder orbit, figures 2 (b-c), the free 511 (d)

4 surface oscillates and a radial flow develops with the left vortex pumping fluid towards the right. Although the flow is dominated by this radial motion, the two vortices are still identifiable from the vorticity contours. With increasing φ the left vortex keeps pumping fluid into the right one until the free surface reaches its highest position on the right hand side for φ=180 o (not shown). At this stage a new cycle starts but in this case the radial swing flow has the opposite direction and the vortical cell on the right hand side pumps fluid into the left one. The space averaged velocity field and vorticity contour plots in figure 2 (d) agree qualitatively well with the simulations of [4]. The phase-resolved velocity field and vorticity contour plots for three shaking rotational speeds, N= rpm, are shown in figures 3 (a-c) for h/d i =0.5 at φ=0 o. Similarly to the flow dynamics for h/d i =0.3, two counter rotating vortices can be distinguished. As N is increased (figures 3 a-c), the two vortices start to extend towards the bottom of the cylinder and their intensity increases, with the maximum absolute non-dimensional vorticity more than doubling. For N=110 rpm the two vortices extend over the entire cylinder height (figure 3 c) and completely dominate the flow in the bioreactor. These results are consistent with the findings of [6] who measured the mixing time in a cylindrical shaken bioreactor by means of a colorization technique, and reported that for low N two zones can be distinguished in the reactor: one close to the free surface where mixing is primarily due to convection, and a second close to the bottom of the cylinder where mixing is dominated by diffusion. In figures 3 -(c) a horizontal line drawn by arbitrarily selecting a fixed value of the vorticity (! " (# N) = 0.1) defines the boundary between the convection (A) and the diffusion (B) zones; the latter decrease in size with increasing N. (c) Figure 3. Phase-resolved vector fields and contour plots of the tangential component of the vorticity,! ", for increasing N (h/d i =0.5, φ=0 o ): N=70 rpm; N=90 rpm; (c) N=110 rpm. 3.2 Flow characterization for out-of-phase conditions The out-of-phase phenomenon occurs at high N and is characterized by an amount of fluid, which is not in phase with the movement of the table. While at low N for in-phase conditions the free surface can be approximated by an inclined ellipse whose longer 512

5 (shorter) axis is the straight line at the intersection between the free surface for φ=0 o (φ=90 o ) and the vertical laser plane, for higher N the free surface becomes three dimensional and its intersection with the vertical plane exhibits a wavy profile and a significant change in the flow pattern occurs. This is well illustrated by the vector and vorticity plot of figures 4 for N=130 rpm, h/d i =0.3 and φ=0 o. Figure 4, shows that the flow pattern changes and the vorticity direction near the walls is opposite to the in-phase case. The horizontal plane results (figure 4 b) indicate the formation of a vortex precessing around the cylinder axis. The motion of this vortex exhibits a phase lag cf. the in-phase flow; this effect might be utilized to optimize mixing. Figure 4. Phase-resolved vector fields and contour plots of the tangential and axial component of the vorticity (φ=0 o, h/d i =0.3, N=130 rpm): ω θ,; ω z,. 3.3 Selection of operating conditions for in- and out-of-phase flow The current section aims at deriving a scaling law based on dimensionless parameters that can be used to best design a mixing bioprocess, and select the flow conditions most appropriate to a cell culture. The free surface motion is the main element of the mechanism that determines the flow condition inside the bioreactor, and its maximum inclination, ψ, is directly related to the non-dimensional wave amplitude, Δh/d i (i.e. tan(!) =!h / d i ). Similarly, the free surface inclination is expected to be proportional to the ratio between the centrifugal acceleration, a c =(π N d o ) 2 /(0.5 d o ), determined by the orbital motion and gravity, g. This proportionality is well reflected in figure 5 where the variation of Δh/d i is plotted against Fr 2 =a c /g=(2 π 2 N 2 d o )/g, for different non-dimensional fluid height, h/d i, and nondimensional orbital diameter d o /d i. Figure 5. Variation of Δh/d i with Fr 2 ; Transitional region (shaded grey) from in-phase to out-ofphase conditions in the h/d i, Fr 2 plane, at φ=0 o. From figure 5 it is evident that at a given Fr, for selected combinations of N and d o, the free surface will assume a fixed inclination that is independent of the fluid height, h/d i. The 513

6 linear relationship is more consistent at lower Fr when the flow is in-phase and the free surface inclination is constant across the free surface profile, while at higher Fr, the data are more scattered about the reference line due to the wavy nature of the free surface for out-ofphase conditions. The constant of proportionality, a 0 =1.4, is directly related to the fluid considered (water in this study). Its value is greater than unity because it takes into account the extra inertial forces, besides the centrifugal acceleration of the tray, due to the movement of the fluid inside the cylindrical bioreactor. For an orbital diameter d o /d i =0.25 it was found that transition between in phase and out of phase conditions occurs when Δh/h=0.5 and the toroidal vortex extends to the bottom of the tank. This is also confirmed from figures 2 and 3 (c) for h/d i =0.3 and 0.5, respectively. For Δh/h<0.5 the toroidal vortex will be present in a limited region below the free surface and a diffusion dominated zone appears at the bottom of the tank. A map of in-phase and out-of-phase conditions is shown in Figure 5 in the h/d i, Fr 2 plane. For h/d i <0.5 transition occurs when h/d i =2 a 0 Fr 2, while for h/d i >0.5 it occurs for a o Fr 2 =0.25. In the latter case the toroidal vortex does not reach the bottom for any rotational speed. 4. CONCLUSIONS The present study provides an in-depth analysis of the flow inside a cylindrical shaken bioreactor, and assesses the flow transition occurring when in-phase and out-of-phase conditions are considered. In particular it was found that for in phase condition a single toroidal vortex is present inside the vessel, and its size is dependent on the free surface maximum inclination angle. As this angle increases the toroidal vortex extends towards the bottom of the tank. When out of phase conditions are considered the toroidal vortex disappears and an axial one precessing around the vessel axis develops. A scaling law based on Fr, and the non-dimensional fluid height h/d i was derived to determine the boundary between in-phase and out-of-phase flow. This law provides a foundation for optimization of biochemical process design. 5. REFERENCES [1] J. Büchs "Introduction to advantages and problems of shaken cultures", Biochem. Eng. J., 7, [2] H. Zhang, W. Williams-Dalson, E. Keshavarz-Moore, P. Ayazi-Shamlou, "Computational fluid dynamics (CFD) analysis of mixing and gas liquid mass transfer in shake flasks". Biotechnol. Appl. Biochem., 41, 1 8. [3] H. Zhang, S. Lamping, S. Pickering, G. Lye, P. Shamlou, "Engineering characterisation of a single well from 24-well and 96-well microtitre plates", Biochem. Eng. J., 40, [4] H. Kim, P. Kizito, "Stirring free surface flows due to horizontal circulatory oscillation of partially filled container", Chem. Eng. Commun., 11, [5] J. Büchs, U. Maier, C. Milbradt, B. Zoels, "Power consumption in shaking flasks on rotary shaking machines: II. Nondimensional description of specific power consumption and flow regimes in unbaffled flasks at elevated liquid viscosity", Biotechnol Bioeng., 68, [6] S. Tissot, M. Farhat, D. Hacker, T. Anderlei, M. Kühner, "Determination of a scaleup factor from mixing time studies in orbitally shaken bioreactors. Biochem. Eng. J., 52, [7] X. Zhang, C. Bürki, M. Stettler, D. Sanctis, M. Perrone, M. Discacciati, N. Parolini, M. De Jesus, D. Hacker, A. Quarteroni, F. Wurm, "Efficient oxygen transfer by surface aeration in shaken cylindrical containers for mammalian cell cultivation at volumetric scales up to 1000 l". Biochem. Eng. J., 45,