A largely unexplored type of hydrodynamic instability is examined: long-time algebraic growth. Such growth is possible when the dispersion relation extracted from classical stability analysis indicates neutral stability. A physically motivated class of partial differential equations that describes the response of a system to disturbances is examined. Specifically, the propagation characteristics of the response are examined in the context of spatiotemporal stability theory. Morphological differences are identified between system responses that exhibit algebraic growth and the more typical case of exponential growth. One key attribute of predicted algebraically growing solutions is the prevalence of transient growth in almost all of the response, with the long-time growth occurring asymptotically at precisely one wave speed.

Overutilization of organic-based compounds (e.g., fertilizers) in agricultural settings continues to cause concern due to potential adverse impacts on the health of humans and the environment. Adsorbents, such as activated carbon, are widely used due to their ability to adsorb various contaminants. Limitations in the effectiveness of activated carbon, where high uptake capacities are desired, require the need for alternatives to current state-of-the-art adsorbents. In this work, the adsorption capability of a lightweight, carbon-based aerogel is presented. The aerogel is composed of 0 to 2 wt % mixture of both graphene nanoplatelets (GnP) and single-walled carbon nanotubes (SWCNT). Two organic compounds, 2,4-dichlorophenoxyacetic acid (2,4-D) and 1-pyrenebutyric acid (PBA), served as the contaminants of interest. Results show that the aerogel containing 0.2 wt % SWCNT-GnP achieved an uptake capacity of 0.22 mg of 2,4-D/mg of aerogel and 0.083 mg of PBA/mg of aerogel. Compared to activated carbon, from a kinetic standpoint, the aerogels produced in this work demonstrated 39-fold higher adsorption of 2,4-D and 5-fold higher adsorption of PBA, making them a viable candidate as a next generation adsorbent.