The free surface of a liquid sample in a microplate well, under orbital shaking conditions, is taking a parabolic shape if viscosity, surface and interfacial tensions are neglected.
Available literature is presenting an analytical solution method for calculation liquid distribution in conical flasks and other large bioreactor systems without consideration of the surface tension as viscosity is the predominant factor within the examined dimensions [1,2]. Furthermore several methods of Computational Fluid Dynamics (CFD) like the Volume of Fluid (VOF) method are well established for calculation of sloshing problems [4,5]. Because of the complex preprocessing that is necessary these methods are not applicable for users without this specialized knowledge.
Based on the insight, that the surface tension is the key factor to determine the surface shape of the liquid in microplates and similar small scale vessels, we modified the governing equations presented by Lubarda  for calculating liquid distribution in a uniformly rotating cylinder in the presence of surface tension in a way so that they are now applicable to the problem of liquid distribution in orbitally shaken microplate wells. The modified equations consider three possible cases of liquid distribution which are illustrated in figure 4. In figure 1 the impact of this modification is shown. The figure displays the differences in the liquid distribution, when calculated with and without consideration of surface tension, in a 384 microplate well. The simulation results are validated against experimental data. It becomes obvious that already at low mixing frequencies the deviation of the maximum resulting liquid height is significant and the results of the experimental data is in correlation with the presented simulation.
The aim of the presented work is to develop a software that allows an end-user the examination and selection of appropriate and reliable technical parameters by entering a few known input values.