Langmuir (1918) reached the amazing conclusion that the evaporation rate of a droplet is proportional to the droplet radius. As the droplet volume is proportional to the radius cubed the study of small droplets will eventually be hampered by evaporation. Although droplet evaporation has been studied extensively it is not yet completely understood, ttree different situations, most relevant for protein crystallization, can be ranked in complexity:
1. Free droplet in a supporting gas (liquid-gas interface)
2. Sessile or hanging droplets on a supporting solid (liquid-gas-solid interface)
3. Droplet inside a small container (liquid-gas-solid and geometry of container)
tte general evaporation problem is complex and many aspects are of importance; especially the evaporation of sessile droplets with dissolved particles differs fundamentally from pure solvent evaporation, tte factors that influence the evaporation of a fluid are:
- tte droplet volume and shape
- tte temperature of the fluid and surrounding vapor
- tte composition of the fluid
- tte external pressure and the partial vapor pressure
In addition, for a droplet in contact with a solid surface, the surface roughness, composition, temperature and wetting properties as well as the geometry are of importance.
As examples, ingenious experiments have been performed on the evaporation of flying droplets of pure solvents trapped in electric or acoustic fields. In these experiments the presence and influence of a support is eliminated. Beauchamp and coworkers studied the evaporation of charged droplets in the so-called ping-pong configuration (Grimm and Beauchamp 2002; Smith et al. 2002). ttey used droplets generated by electrospray dispensing and controlled the motion of the charged droplets by reversing the electric field direction when the droplets moved outside the observation volume. In the thesis of Eberhardt (1999), the evaporation of levitated droplets trapped in an acoustic field was studied. Both studies confirmed Langmuir s findings and show that the droplet diameter dp as a function of time is given by dp2 (t) = dp2 (0) + Ct, where dv(t) represents the radius at time t and dp(0) the initial radius of a pure liquid droplet, with C (a negative constant) representing the evaporation.
Evaporation of a Binary Mixture of Pure Liquids
Eberhardt (1999) and Sefiane et al. (2003) have studied the evaporation of binary mixtures from free and sessile droplets respectively, ttey both observed the evaporation of the most volatile component first, as expected, but in the presence of a supporting surface there appears an intermediate phase related to the wetting properties of the surface, tte addition of a less volatile component to the droplets will slow down the overall evaporation. Ms observation may allow the reduction of the evaporation of very small droplets of mother liquor too.
Evaporation of a Solvent with a Solute tte evaporation of a solvent with a (nonevaporating) solute proceeds significantly differently from the case discussed before, tte most general case is the evaporation of a solvent with a solute without the presence of a substrate as used in the crystallization in acoustically and/or electrostatically levitated droplets (Chung and Trinh 1998; Santesson et al. 2003; Knezic et al. 2004). In the presence of a surface due to the pinning of the contact line, e.g., the rim of the droplet on the surface, there is a significant flow inside the droplet to supply solvent to the surface of the droplet where the evaporation takes place (as in levitated droplets), tte flow of solvent causes the relative accumulation of solute close to the contact line, tte effect is illustrated by looking at the ring left by a spilled coffee droplet (Deegan et al. 1997). tte solute flow in levitated droplets has been visualized but is difficult to control to improve the crystallization (Chung and Trinh 1998).
In a series of publications the liquid evaporation from silicon microwells showed solute accumulation as a result of contact pinning in very small wells (Hjelt et al. 2000; Young et al. 2003; Rieger et al. 2003). tte accumulation of solute particles and their dynamics has been studied by fluorescence spectroscopy; some characteristic phases in the evaporation process are shown in Fig. 1.5. tte white lines represent the trajectory of the solute during the evaporation, ttese results are relevant for protein crystallogenesis, as they suggest that a concentration gradient builds up during the initial stages of the crystallization experiment.
Practical Approaches to Reduce Evaporation tte aforementioned considerations suggest the following precautions to reduce evaporation, tte most important factor (if not interfering with the crystallization process) is the reduction of the temperature of the droplet (and container). Covering
Fig. 1.5. Contact line pinning in nanovials. In this experiment the trajectories of small fluorescent spheres dissolved in a water-glycerol mixture contained in a nanovial are recorded. The inserts in grey reflect the shape of the meniscus of the evaporating liquid. It is clear that nonevaporation solutes such as the fluorescent beads travel to the liquid boundary and accumulate owing to contact line pinning in nanovials with a radius of 100 |im. (From Rieger et al. 2003)
the droplet with an immiscible liquid with a high boiling point can further reduce the evaporation. Ms approach has been successfully applied in batch crystallization where the droplets are covered with oil. By choosing the appropriate oil-solvent combination, the evaporation can be controlled to a certain extent. Evaporation can be prevented also by controlling the surrounding vapor pressure. During the filling of microarrays the evaporation can hardly be avoided. In our own experiments we use a contact-cooled microarray to prevent evaporation. After dispensing, the array can be covered with oil and sealed with adhesive transparent tape. Cooling the microarray has the additional advantage of reversing the convective flow and thereby reducing the solvent transport form the array (Bodenstaff et al. 2002). For most applications in microbatch crystallization it is also possible to fill the (nano) wells first with oil that has lower density than the volatile component(s) (Chayen et al. 1992; Kuil et al. 2002). Subsequently added components sink to the bottom of the well and are covered with a layer of oil. However, sinking droplets do not always merge and mix if this approach is used. Mayer and Köhler (1997) studied the effect of droplet evaporation in microarrays and reported a linear dependence of the evaporation rate on the opening surface of the container. However, more recently a linear dependence of the evaporation rate on the radius of cylindrical microcompartments was reported and it was concluded that the evaporation is diffusion-limited (Rieger et al. 2003).
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