Table 2.

Formulae for modelling hydrodynamic effects on animal cells grown on microcarriers and cell aggregates in suspension cultures.

parameter	formula	explanations	significance, remark	reference
Reynolds number	Re = (NDi2)/ν	N = impeller rotation rate Di = impeller diameter ν = kinematic viscosity Re = dimensionless quantity that is used to help predict similar flow patterns in different fluid flow situations	Re > 10 000—turbulent regime turbulence distribution throughout the reactor depends on impeller and vessel geometry	[29,30]
Kolmogorov eddy length	L = (ν3/ɛ)¼	ɛ = power dissipation per unit mass (or specific energy dissipation rate) ɛ = NpDi5N3/Vd, where Np = dimensionless power number Vd = dissipation volume	the eddy size decreases as the agitation speed increases. Kolmogorov eddies with sizes similar to approximately 70% of the carrier/aggregate diameter are detrimental for the adherent cells	[31]
maximum mean aggregate size	Dmax = Cɛανβ	parameters C, α and β can be estimated from experiments (e.g. [32])	the equation permits the estimation of the maximal aggregate/clump size dependent on kinematic viscosity and viscous energy dissipation	[33]
maximum shear stress	τmax = 5.33ρ(ɛν)½	ρ = density	suspended single cells are damaged at high agitation rates; the formula provides estimation of the maximum shear stress which a cell experiences in suspension	[34]