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We consider a slowly condensing droplet levitating near the surface of an evaporating layer, and develop a mathematical model to describe diffusion, heat transfer and fluid flow in the system. The method of separation of variables in bipolar coordinates is used to obtain the series expansions for temperature, vapour concentration and the Stokes stream function. This framework allows us to determine temperature profiles and condensation rates at the surface of the droplet, and to calculate the upward force that allows the droplet to levitate. Somewhat counter-intuitively, condensation is found to be the strongest near the bottom of the droplet, which faces the hot liquid layer. The experimentally observed deviations from the classical law predicting the square of the radius to grow linearly in time are explained by the model. A spatially non-uniform phase change rate results in a contribution to the force not considered in previous studies, and comparable to droplet weight and the upward force calculated from the Stokes drag law. The levitation conditions are formulated accordingly, resulting in the prediction of levitation height as a function of droplet size without any fitting parameters. A simple criterion is formulated to define the parameter ranges in which levitation is possible. The results are in good agreement with the experimental data except that the model tends to slightly underpredict the levitation height. 

Evaluation of Gastrointestinal Stromal Tumors (GIST) during initial clinical staging, surgical intervention, and postoperative management can be challenging. Current imaging modalities ( e.g. , PET and CT scans) lack sensitivity and specificity. Therefore, advanced clinical imaging modalities that can provide clinically relevant images with high resolution would improve diagnosis. KIT is a tyrosine kinase receptor overexpressed on GIST. Here, the application of a specific DNA aptamer targeting KIT, decorated onto a fluorescently labeled porous silicon nanoparticle (pSiNP), is used for the in vitro & in vivo imaging of GIST. This nanoparticle platform provides high-fidelity GIST imaging with minimal cellular toxicity. An in vitro analysis shows greater than 15-fold specific KIT protein targeting compared to the free KIT aptamer, while in vivo analyses of GIST-burdened mice that had been injected intravenously (IV) with aptamer-conjugated pSiNPs show extensive nanoparticle-to-tumor signal co-localization (>90% co-localization) compared to control particles. This provides an effective platform for which aptamer-conjugated pSiNP constructs can be used for the imaging of KIT-expressing cancers or for the targeted delivery of therapeutics.