Thermofluidic Transport in Evaporating Droplets: Measurement and Application
Microscale environments provide significant resolution and distortion challenges with respect to measurement techniques; however, with improvements to existing techniques, it is possible to gather relevant data to better understand the thermal and fluidic mechanisms at such small scales in evaporating droplets.
Infrared thermography provides several unique challenges at small scales. A primary issue is that the low native resolution of traditional infrared cameras significantly hamper the collection of details of microscale features. Furthermore, surfaces exhibiting vastly different emissivities, results in inaccurate temperature measurements that can only be corrected with irradiance-based emissivity maps of the surface; however, due to the resolution limitations of infrared thermography, these emissivity maps can also display significant errors. These issues are overcome through the use of multi-frame super-resolution. The enhanced resolution allows for better capture of microscale features, therefore, enhancing the emissivity map. A quantitative error analysis of the system is conducted to quantify the feature size resolution improvement as well as the smoothing effect of super-resolution reconstruction. Furthermore, a sensitivity analysis is conducted to quantify the impact of registration uncertainty on the accuracy of the reconstruction. Finally, the improved emissivity map from super-resolution is demonstrated to show the increased accuracy over low-resolution mapping.
When applied to water droplets, particularly on nonwetting surfaces, infrared thermography is confounded by the presence of nonuniform reflectivities due to the spherical curvature of the liquid-air interface. Thus, when measuring the temperature along the vertical axis of a water droplet, it is necessary to correct the reflection. Using a controlled background environment, in conjunction with the Fresnel equations, it is possible to correct the reflective effects on the interface and calculate the actual temperature profile. This allows for a better understanding of the governing mechanisms that determine the thermal transport within the droplet. While thermal conduction is the primary transport mechanism along the vertical axis of the droplet, it is determined that the temperature drop is partially dampened by the convective transport from the ambient air to the liquid interface. From this understanding revealed by the measurements, the vapor-diffusion-based model for evaporation was enhanced to better predict evaporation rates.
Further exploration into the mechanisms behind droplet evaporation on nonwetting surfaces requires accurate knowledge of the internal flow behavior. In addition, the influence of the working fluid can have a significant impact on the governing mechanisms driving the flow and the magnitude of the flowrate. While water droplet evaporation has been shown to be governed by buoyancy-driven convection on nonwetting substrates, similar studies on organic liquid droplets are lacking. Particle image velocimetry is effective at generating a velocity flow field, but droplets introduce distortion due to the refraction from the spherical interface of the droplet. As such, velocity correction using a ray-tracing approach was conducted to correct the velocity magnitudes and direction. With the velocity measurements, the flow was determined to be surface-tension-driven and showed speeds that are an order of magnitude higher than those seen in buoyancy-driven flow in water droplets. This resulted in the discovery that advection plays a significant role in the transport within the droplet. As such, the vapor-diffusion-governed evaporation model was adjusted to show a dramatic improvement at predicting the temperature gradient along the vertical axis of the droplet.
Armed with the knowledge of flow behavior inside droplets, it is expected that droplets with aqueous solutions should exhibit buoyancy-driven convection. The final part of this work, therefore, leverages this phenomenon to enhance mixing during reactions. Colorimetry is a technique that is widely utilized to measure the concentration of a desired sample within some liquid; the sample reacts with a reagent dye the color change is measured, usually through absorbance measurements. In particular, the Bradford assay is used to measure protein concentration by reacting the protein to a CoomassieTM Brilliant Blue G-250. The absorbance of the dye increases, most significantly at the 590 nm wavelength, allowing for precise quantitation of the amount of protein in the solution. A droplet-based reaction chamber with buoyancy-enhanced mixing has the potential to speed up the measurement process by removing the need for a separate pre-mixing step. Furthermore, the reduced volume makes the process more efficient in terms of reactant usage. Experimental results of premixed solutions of protein sample and reagent dye show that the absorbance measurement through a droplet tracks strongly with the protein concentration. When the protein sample and dye reagent are mixed in situ, the complex interaction between the reactants, the mixing, and the adsorption of protein onto the substrate creates a unique temporal evolution in the measured absorbance of the droplet. The characteristic peaks and valleys of this evolution track strongly with concentration and provide the framework for measurement of concentration in a droplet-based system.
This thesis extends knowledge about droplet thermal and fluidic behavior through enhanced measurement techniques. This knowledge is then leveraged in a novel application to create a simple, buoyancy-driven colorimetric reaction setup. Overall, this study contributes to the field of miniaturized, efficient reaction and measurement devices.