Mixing Systems - Disposable Bioprocessing Systems - page 53

4
Mixing Sys tems
The unit operation of mixing is extensively involved in bioprocessing sys-
tems. Some of the keys to mixing operations include mixing to dissolve
components of a buffer, culture media, refolding solution, dispersion of cell
culture in bioreactors, and heating or cooling of liquids.
All mixing operations must be fully validated as part of PAT to ensure
that optimal mixing has been achieved all the time. While the stainless steel
mixing vessels have long been used and the principles behind mixing and
demixing of components with traditional mixing devices have long been
studied, much remains to be understood about achieving homogenous mix-
tures in disposable bags.
In bioprocessing operations, two types of mixing are important: one that
leads to the dissolution of solutes, and the other that provides a homog-
enous environment such as in a bioreactor or a refolding tank. How fast a
mixture of powdered components in a buffer mixture dissolves will depend
to a great degree on the solubility of individual components, the agita-
tion applied, and the temperature and length of mixing. In theory, mixing
involves distributive, dispersive (breaking of aggregates), or diffusive steps.
All of these steps require energy that is provided by the mechanical motion
induced in liquids. A laminar movement of liquid or a turbulent movement
can achieve the mixing, and the Reynolds number (Re) of mixing obtained
can predict this.
In fluid mechanics, the Reynolds number is a dimensionless number that
gives a measure of the ratio of inertial forces to viscous forces and conse-
quently quantifies the relative importance of these two types of forces for
given low conditions. Laminar low occurs at low Reynolds numbers, where
viscous forces are dominant, and is characterized by smooth, constant fluid
motion; while turbulent flow occurs at high Reynolds numbers and is domi-
nated by inertial forces, which tend to produce chaotic eddies, vortices, and
other flow instabilities. In a cylindrical vessel stirred by a central rotating
paddle, turbine, or propeller, the characteristic dimension is the diameter of
the agitator (D). The velocity is ND (where N is the rotational speed (revolu-
tions per second)), μ is the kinematic viscosity, and ρ is the density of fluid.
Then the Reynolds number is
Re = ρ ND 2
53