Fingering instability down the outside of a vertical cylinder

We present an experimental and numerical study examining the dynamics of a gravity-driven contact line of a thin viscous film traveling down the outside of a vertical cylinder of radius R. Experiments on cylinders with radii ranging between 0.159 and 3.81 cm show that the contact line is unstable to a fingering pattern for two fluids with differing viscosities, surface tensions, and wetting properties. The dynamics of the contact line is studied and results are compared to previous studies of inclined plane experiments in order to understand the influence substrate curvature plays on the fingering pattern. A lubrication model is derived for the film height in the limit that ε = H/R≪1, where H is the upstream film thickness, and in terms of a Bond number ρgR3/(γH), and the linear stability of the contact line is analyzed using traveling wave solutions. Curvature controls the capillary ridge height of the traveling wave and the range of unstable wavelength when ε = O(10-1), whereas the shape and stability of the contact line converge to the behavior one observes on a vertical plane when ε ≤ O(10-2). The most unstable wave mode, cutoff wave mode for neutral stability, and maximum growth rate scale as 0.45 where = ρgR2/γ ≥ 1.3, and the contact line is unstable to fingering when ≥ 0.56. Using the experimental data to extrapolate outside the range of validity of the thin film model, we estimate the contact line is stable when <0.56. Agreement is excellent between the model and the experimental data for the wave number (i.e., number of fingers) and wavelength of the fingering pattern that forms along the contact line.

Investigating The Fate Of Positively Charged Nanoparticles In A Soil Environment

The recent increase in the amount of nanoparticles incorporated into commercial products is accompanied by a rising concern of the fate of these nanoparticles. Once released into the environment, it is inevitable that the nanoparticles will come into contact with the soil, introducing them to various routes of environmental contamination. One route that was explored in this research was the interaction between nanoparticles and clay minerals. In order to better define the interactions between clay minerals and positively charged nanoparticles, in situ atomic force microscopy (AFM) was utilized. In situ AFM experiments allowed interactions between clay minerals and positively charged nanoparticles to be observed in real time. The preliminary results demonstrated that in situ AFM was a reliable technique for studying the interactions between clay minerals and positively charged nanoparticles and showed that the nanoparticles affected the swelling (height) of the clay quasi-crystals upon exposure. The preliminary AFM data were complemented by batch study experiments which measured the absorbance of the nanoparticle filtrate after introduction to clay minerals in an effort to better determine the mobility of the positively charged nanoparticles in an environment with significant clay contribution. The results of the batch study indicated that the interactions between clay minerals and positively charged nanoparticles were size dependent and that the interactions of the different size nanoparticles with the clay may be occurring to different degrees. The degree to which the different size nanoparticles were interacting with the clay was further probed using FTIR (Fourier transform infrared) spectroscopy experiments. The results of these experiments showed that interactions between clay minerals and positively charged nanoparticles were size dependent as indicated by a change in the FTIR spectra of the nanoparticles upon introduction to clay.