Modeling of Mixing in 96-Well Microplates Observed with Fluorescence Indicators Svenja Weiss, † Gernot T. John, †,‡ Ingo Klimant, §,| and Elmar Heinzle* ,† Biochemical Engineering Institute, Saarland University, Im Stadtwald, Building 2, D-66123 Saarbruecken, Germany, and Institute of Analytical Chemistry, Chemo- & Biosensors, University of Regensburg, D-93053 Regensburg, Germany 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 μL 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. Introduction Microplates are very popular for a wide area of ap- plications. They are often used as screening tool, e.g., for screening of novel chemical compounds (Burbaum and Sigal, 1997). Toxicity tests, immunoassays, enzymatic assays, and clinical applications are other examples for the use of microplates. Recently, cultivation of micro- organisms in specially designed microplates was de- scribed (Duetz et al., 2000; Girard et al., 2001). The results of kinetic experiments can be influenced by fluid dynamics. Mixing can be defined as the process that decreases the inhomogeneity of a system and is subdivided into micro- and macromixing (Van’t Riet and Tramper, 1991; Moser, 1988). A system is completely mixed if the chance of finding a component at a certain place is equal at each position of the system. Mixing is based on three different mechanisms, convection, disper- sion, and diffusion, and can be characterized by two parameters, the scale and the intensity of mixing. The scale of mixing is the smallest dimension in which inhomogeneity is allowed. Mixing intensity is the residual deviation from the final concentration in percent. Mixing can be characterized by the mixing time at certain scale and the intensity of the mixing. The described methods used for determination of mixing times and the degree of mixing are measurement of pH, conductivity, color, optical density, oxygen, temperature, radioactivity, and fluorescence. Another method for determination of mixing in shaking reactors and shake flasks is based on mea- surement of mixing intensity with a mixmeter by deter- mining the fluid motion as pressure fluctuations (Gerson and Kole, 2001). Flow patterns are observed visually, e.g., by using aluminum powder (Kato et al., 1996). The tracers used have to meet several requirements in order to prevent disturbances of the mixing process and of the system used. The tracer and the system determined should have similar physical properties. If two liquids are mixed, the tracer must have similar viscosity and density. Heat of mixing caused by the addition of the tracer and pulse should be negligible. In contrast to stirring and mixing using gas bubbles, mixing with the aid of shaking is only rarely described in the literature, though it is extensively carried out particularly in flasks and microplates. Reported inves- tigations for mixing using shaking are, e.g., mixing in shaking vessels (e.g., Kato et al., 1996) and in shake- flasks (e.g., Bu ¨ chs et al., 2000a-c; McDaniel and Bailey, 1969; Gerson and Kole, 2001). In microplates, shaking is the preferred method of mixing. Addition of liquid is frequently used, e.g., for starting a reaction, for pH control during reaction, and for control of supply of nutrients for growing cells. Cells and enzymes can be damaged during pH-control processes by local high concentration of alkali or acid caused by insufficient mixing. For such applications knowledge of mixing, i.e., flow pattern and mixing time, is necessary. Despite the significance of mixing in microplates, there has not been published any detailed report about this topic to our knowledge. This is so possibly because of the generally accepted theory that mixing becomes easier when the scale is reduced (Van’t Riet and Tramper, 1991). In this article mixing in microplates was studied to obtain a basis for later establishment of pH control and * To whom correspondence should be addressed. Phone: +49- (0)681-302-2905. Fax: 49-(0)681-302 4572. E-mail: e.heinzle@ mx.uni-saarland.de. † Saarland University. ‡ Present address: PreSens GmbH, D-93053 Regensburg, Ger- many. § University of Regensburg. | Present address: Institute of Analytical Chemistry, Micro- and Radiochemistry, Technical University of Graz, A-8010 Graz, Germany. 821 Biotechnol. Prog. 2002, 18, 821-830 10.1021/bp0200649 CCC: $22.00 © 2002 American Chemical Society and American Institute of Chemical Engineers Published on Web 07/16/2002