Determination of a scale-up factor from mixing time studies in orbitally shaken bioreactors

Efficient mixing in bioreactors is essential in order to avoid concentration gradients which can be harmful for mammalian cells. To study mixing and its scalability in orbitally shaken cylindrical bioreactors, we measured mixing times in containers with nominal volumes from 2 to 1500 L with a colorimetric method using two pH indicators. Four operating parameters were tested: the liquid height, the shaking diameter, the agitation rate, and the inner diameter of the container. The mixing time decreased as the agitation rate increased until a minimal value was reached. As the shaking diameter was reduced, a higher agitation rate was needed to reach the minimal mixing time. The liquid height did not have a significant effect on the mixing time, but for a constant volume, an increase of the inner diameter slightly reduced the mixing time. The fastest mixed zones were close to the wall of the container while the zone in the center of the bulk liquid was the last to achieve homogeneity. Our study showed that the free-surface shape correlated with the mixing regime and that by keeping the inner-to-shaking diameter ratio as well as the Froude number (Fr) constant, the free-surface shapes and the mixing regimes of a 1500-L bioreactor could be mimicked in a 30-L bioreactor. We concluded that the mixing in orbitally shaken cylindrical bioreactors ensures homogeneity for mammalian cell cultures at scales up to 1500 L and that the inner-to-shaking diameter is a suitable scale-up factor for mixing.