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Physics of mixing  "A Methodology and Study of Microplate Mixing Techniques"
Optimization of mixing parameters in lab automation for high & low sample volumes
Mixing efficiency of Bioshake 3000 plate shaker  Authored by: Tanya Knaide, Artel, Inc.
Experimental studies of mixing efficiency in 96 well microplates
Experimental studies of mixing efficiency in standard tubes
Videos for optimization of mixing frequencies
Optimization of temperature control in microplates
Optimization of mixing parameters
Optimization of mixing parameters in lab automation for high & low sample volumes
1. Abstract
In the past the significance of microplate mixing has mainly been ignored as a serious problem, although potentially it could undermine a generation of meaningful data.
We analyzed orbital microplate mixing technologies to get a better understanding of the current requirements for mixing technologies that can be applied to compounds or bioassays in microplates.
This poster reviews some results of studies with BioShake orbital plate shaker, such as where the greatest need for improved mixing of high sample volume in standard tubes against low sample volume in HTS microplates.
It also discusses the influences of construction material, shape and well volume of the sample carrier to the mixing results depending on the physical properties of the liquids.
2. Introduction and Background
Orbital shaking is undoubtedly a simple and non invasive way for mixing of assay components. Simply putting the samples on a shaker table doesn't guarantee that a complete blending is reached after the mixing process.
It is important to choose the most appropriate process parameters in dependency of the sample volume and the geometry of the sample container.
The following section describes the mathematical background of calculating the minimal necessary mixing frequency for exceeding the surface tension of the medium, depending on the filling volume, the shaking diameter and other physical and geometrical parameters.
In Figure 1 the resulting liquid distribution in a well due to the orbital movement of a microplate is shown. If the effect of friction and surface forces is neglected the free surface of the fluid, which is a face of an equal pressure level, forms a rotational paraboloid.
The acting forces to a volume element d_{m} within the free surface are gravity and centrifugal force. In a comoving reference frame the fluid appears to rotate along a stationary wall. Interesting values are the minimal and the maximal height of fluid depended of amplitude d_{0} and mixing frequency n. Further Information about calculating liquid distribution can be found in [2].
The choice of appropriate operating parameters for orbital mixing, especially the mixing frequency n and the amplitude d_{0}, is depending on:
 microplate filling volume V_{F},
 well geometry (diameter D_{W}, height h),
 surface tension of fluid and construction material σ,
 fluid density ρ,
 and kinematic viscosity of the fluid ν.
The most important requirement for an effective mixing process is the formation of a macroscopic flow. As microplate well volumes decrease the impact of surface tension increases because of the low volume/surface ratio of the usually thin and tall well geometry. For this reason it is necessary to generate a high centrifugal acceleration to achieve an intensive macroscopic flow. A large number of commercially available instruments have been developed for use with larger laboratory vessels and they are not designed to generate a centrifugal acceleration which is required for processing small volumes. The labour required for surface enlargement must be delivered by the centrifugal force. The increased centrifugal force exceeds the surface tension at a critical shaking frequency [3]
with the surface tension σ, the well diameter D_{W}, the fill volume V_{F}, the fluid density ρ and the amplitude d0. The value of centrifugal force respectively acceleration depends on the amplitude d_{0} and the mixing frequency n. Against expectation it is crucial to choose the right value of amplitude d_{0}.
3. Test Methods
The minimal necessary value of mixing frequencies has been calculated using the formula shown in the previous section. All sample containers have been mixed using a BioShake orbital plate shaker to find the optimal mixing frequency. The basic requirement to ensure a fast and efficient mixing result is the generation of a vortex which allows to produces a flow of the total sample volume. For observing the movement of the fluid in the samples container during the process at different mixing frequencies a high speed camera system (The Imaging Source®, DFK 21BU04) was used. The knowledge obtained was used for optimization of mixing speed and amplitude. The results of the calculated minimum necessary mixing frequency have been compared to the experimentally determined frequency which leads to a movement of the fluid in the sample containers.
4. Results and Discussion
Figure 2 shows the calculated start of mixing effects in dependence of the orbit, shaking speed, filling volume and geometry of the sample container.
The adjustment of the optimal mixing frequency for microplates or tubes should always be made in dependence on the size of the well or tube and the filling volume. Only in this way optimum results can be achieved with in shortest process time with highest reproducibility.
The calculated data in Figure 2 fit very well to the measured data.
5. Conclusion
The significance of microplate mixing is taking on increasing importance, partly in order to be able to improve bioassays in microplates. If efforts to reduce assay result uncertainty are to be truly comprehensive, then it is absolutely clear that the microplate mixing protocol needs to be included as one of the key variables to be optimized during method development.
It is very important to use appropriate parameters to mix samples in biotechnology. Larger volume should be mixed with a higher orbit and less speed. Smaller volumes require a lower orbit, but a much higher speed. For example a 96 well microplate requires at least 1200 to 2200 rpm on an orbit of 2.0 mm and a 1536 well microplate requires at least 2500 to 5000 rpm on an orbit of 1.2 mm to see mixing effects.
Mixing on the right frequency saves time and money.
References
[1] SIGLOCH, H.: Technische Fluidmechanik. 1. Auflage. Springer Verlag, 2008
[2] BÜCHS, J. ET AL.: Calculating liquid distribution in shake flasks on rotary shakers at waterlike viscosities. In: Biochemical Engineering Journal 34 (2007), S. 200208
[3] HERRMANN, R. ET AL: Characterisation of GasLiquid Mass Transfer Phenomena im Microplates. In: Biotechnology and Bioengineering 81 (2003),. Nr. 2, S. 178186
[4] MITRE, E. ET. AL.: TurboMixing in Microplates. In: Journal of Biomolecular Screening 3 (2007), Nr. 12, S. 361369
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