## 1 Introduction
During cell culture fermentation at all scales, the power input and hydrodynamics for cylindrical orbitally shaken bioreactor systems can be predicted using this effective, established correlation tool. Mixing efficiency is a key engineering aspect of the bioreactor because it ensures the homogeneity of the culture ferment [19]. An understanding of the characteristics of mixing are therefore necessary to determine any regions of heterogeneity within the bioreactor and gauge resulting concentration gradients that cells may encounter. For the direct method of mixing efficiency determination used the measurement of the mixing time in the bioreactor, which is designated as the time desired to accomplish a certain degree of homogeneity in the liquid [20]. Mixing time measurement methodologies can be distinguished into local and global technologies by the measured volume. The local methods relied on physical measurements (pH, temperature or conductivity) with intrusive probes at specific point. The global approach is not intrusive and depends either on chemically based reactions and/or optical measurement of different mixing regions in the reactor [21; 22; 23]. However, global approaches are usable only in transparent vessels and are less accurate than local methods. Exact mixing time measurement is essential to minimize the concentration gradient that will be harmful to the cell culture in a shaken reactor [24]. Several different methods have been developed for the measurement of mixing time: conductivity or pH method, thermal method, color addition or decolorization methods [25; 26]. [PERSON] et al. [26] utilized the colorimetric method to measure the mixing time. The reported mixing time was the same for both 25- and 50-mm shaken-flask diameter. The dimensionless mixing number remains constant and is independent of the given geometry of the flasks under high Reynolds numbers region. [PERSON] et al. [26] utilized a single indicator system to gauge the mixing time in the Erlenmeyer shaken flasks. [PERSON] et al. [27] used a two pH indicators technique to measure the mixing time in the shaken cylindrical vessels, concluding that the orbital diameter had no symbolic effect on the mixing time in the shaken flask. The fastest diffused mixing area was determined to be in the lower region of the flask. At a low shaking frequency, two different zones could be divided inside the reactor. The first zone is close to the free surface where mixing was increased by convection, and the second zone is in the lower region of the cylinder where mixing was driven by diffusion. [PERSON] et al. [28; 29] compared the orbitally shaken bioreactor and the Erlenmeyer flask with a stirred tank, measuring mixing time and classifying two mixing mechanisms; in-phase and out-of-phase. Mixing time was accurately determined using a dual indicator system (DISMT) to optimize and minimize concentration gradients for harmful cell cultures prevention. For more efficient mixing, the feeding pipe was inserted near the reactor wall and the outside of the vertical structure close to the center of the reactor. [PERSON] et al. [30] indicated the correspondence of the flow transition phenomena at 10-cm inner diameters and 13-cm fluid heights different cylindrical bioreactors. The results also show the feed-pipe position affected the mixing time in the cylindrical reactor. For both systems, it is suggested to insert the pipe near walls with higher shear stress close to the boundary layer of the wall. The highest/lowest sides of the torus are regularly coordinated with the centrifugal acceleration of the shaker table that shifts its direction as phase angle of table increases. The two vortices expand over the whole cylinder height and finally control the flow inside the bioreactor at 110 rpm shaking frequency. [PERSON] and [PERSON] [25] studied the batch mixing of viscous liquids with rotary mixers in 0.24 and 1.8 m diameter vessels. Power input and mixing time were the measured parameters.