Internal Processes Of Sand And Other Porous Media
This dissertation discusses internal processes of porous media from multiple perspectives. In chapter 2, "Statistical Mechanics of Unsaturated Porous Media," we derive a statistical mechanical model of fluid retention characteristics in porous media in terms of known surface energies and void geometry within the permeable solid based on the Ising model from magnetism. In the limit of vanishing inertial and viscous forces, the theory predicts the fuid retention curve that relates saturation of the porous matrix to applied capillary pressure. We show how the fluid retention curve can be calculated from the statistical distribution of two dimensionless parameters measuring, respectively, the areas of link cross-section and wetted cavity surface with respect to cavity volume. The theory attributes hysteresis of the retention curve to collective first-order phase transitions in the network of cavities. Furthermore, we illustrate predictions with a porous domain consisting of a random packing of spheres, and reproduce the behavior of Haines jumps, which we associate with phase transitions. Chapters 3 and 4 features experimental studies of a particular type of particulate porous media - sand and explores the internal processes of sand dunes and their surface ripples. Chapter 3, "Temperature and Humidity within a Mobile Barchan Sand Dune," (co-authored with A. Valance, A. Ould el-Moctar, A. G. Hay and R. Richer), attempts at answering a practical question of potential importance to dune stabilization, whether temperature and moisture deep within relatively fast moving hyperarid mobile dunes present a suitable habitat for microbes. We contrast deep thermal records obtained from implanted probes with measurements of diurnal variations of the temperature profile just below the surface, and show that temperature within fast moving dunes is predictable, as long as dune advection is properly considered. Observations and analyses also suggest that small quantities of rain falling on the leeward face escape evaporation and endure within the dune until resurfacing upwind. At depths below 10 cm, we show that moisture, rather than temperature, determines the viability of microbes. Toward elucidating how a wavy porous sand bed perturbs a turbulent flow above its surface, in Chapter 4, "Pore Pressure in a Wind-swept Rippled Bed," (co-authored with R. A. Musa, S. Takarrouht, and M. E. Berberich), we record and model pressure within a permeable material resembling the region just below desert ripples. We discovered that, unlike flows on impermeable waves, the porous rippled bed diffuses the depression upstream, reduces surface pressure gradients, and gives rise to a slip velocity, thus affecting the turbulent boundary layer. Pressure gradients within the porous material also generate body forces rising with wind speed squared and ripple aspect ratio, partially counteracting gravity around crests, thereby facilitating the onset of erosion. Although these three essays differ in method and focus, they are all address the internal processes of porous media.
statistical mechanics; porous media; transport processes
Stroock,Abraham Duncan; Desjardins,Olivier
Ph. D., Mechanical Engineering
Doctor of Philosophy
dissertation or thesis