Modeling of mixing in 96-well microplates observed with fluorescence indicators

Mixing in 96-well microplates was studied using soluble pH indicators and a fluorescence pH sensor. Small amounts of alkali were added with the aid of a multichannel pipet, a piston pump, and a piezoelectric actuator. Mixing patterns were observed visually using a video camera. Addition of drops each of about 1 nL with the piezoelectric actuator resulted in umbrella and double-disklike shapes. Convective mixing was mainly observed in the upper part of the well, whereas the lower part was only mixed quickly when using the multichannel pipet and the piston pump with an addition volume of 5 microL or larger. Estimated mixing times were between a few seconds and several minutes. Mixing by liquid dispensing was much more effective than by shaking. A mixing model consisting of 21 elements could describe mixing dynamics observed by the dissolved fluorescence dye and by the optical immobilized pH sensor. This model can be applied for designing pH control in microplates or for design of kinetic experiments with liquid addition.