Modelling surface aeration rates in shaken microtitre plates using dimensionless groups

The volumetric oxygen transfer coefficient (k(L)a) in shaken microplate microbial cultivations has been modelled using dimensionless groups. The k(L)a correlation was derived from experimental measurements of air-liquid specific surface area and k(L)a values for three microwell geometries operated over a range of shaking frequencies and diameters. The air-liquid surface area was determined from the rate of evaporation and also from high-speed video photography. k(L)a values were calculated from the mass transfer limited growth rate of a strict aerobe, Bacillus subtilis, and were also directly measured using the dynamic gassing out technique. For both surface area and k(L)a measurements there was good agreement between each of the two methods used. The overall correlation for k(L)a values comprised two separate correlations based on different dimensionless groups. The first described the increase in specific air-liquid surface area (a(f)/a(i)) as a function of Froude (Fr) and Bond (Bo) numbers and is represented as: a(f)/a(i) = c(1)Fr(c2) Bo(c3) where c(1) is a geometry-dependent constant, c(2) ranged from 0.51 to 0.86 and c(3) ranged from 0.03 to 0.18. As expected, when the diameter of a microwell decreases, the significance of surface forces increases and the importance of inertial forces decrease. The second correlation related the Sherwood (Sh) number in terms of Reynolds (Re) and Schmidt (Sc) number and is represented as Sh = 0.19 Re(0.68) Sc(0.36). This correlation was independent of microwell geometry. By combining the two correlations it was possible to predict k(L)a values over a wide range of operating conditions. These models provide a rigorous engineering basis for more reproducible and rational selection of operating conditions for microplate scale cell cultivation. (c) 2005 Elsevier Ltd. All rights reserved.