Onset of convective instability in an inclined porous medium

The diffusion of a solute from a concentrated source into a horizontal, stationary, fluid-saturated porous medium can lead to a convective motion when a gravitationally unstable density stratification evolves. In an inclined porous medium, the convective flow becomes intricate as it originates from a combination of diffusion and lateral flow, which is dominant near the source of the solute. Here, we investigate the role of inclination on the onset of convective instability by linear stability analyses of Darcy's law and mass conservation for the flow and the concentration field. We find that the onset time increases with the angle of inclination ($\theta$) until it reaches a cut-off angle beyond which the system remains stable. The cut-off angle increases with the Rayleigh number, $Ra$. The evolving wavenumber at the onset exhibits a lateral velocity that depends non-monotonically on $\theta$ and linearly on $Ra$. Instabilities are observed in gravitationally stable configurations ($\theta \geq 90^{\circ}$) solely due to the non-uniform base flow generating a velocity shear commonly associated with Kelvin-Helmholtz instability. These results quantify the role of medium tilt on convective instabilities, which is of great importance to geological CO$_2$ sequestration.Comment: 18 pages, 7 figure

Onset of transient convection in a porous medium with an embedded low-permeability layer

Deep saline aquifers used for CO2 sequestration are commonly made of sedimentary formations consisting of several layers of distinguishable permeability. In this work, the effect of a non-monotonic, vertically varying permeability profile on the onset of convective instability is studied theoretically using linear stability analyses. The onset time depends on the interaction between the permeability profile and the location of the concentration perturbation peak beyond which the concentration of CO2 decays. A thin low-permeability layer can either accelerate or delay the onset time of the convective instability depending on the nature of the permeability variation – whether the permeability transition is smooth or layered, the Rayleigh number (Ra), and the location of the permeability change (a^) relative to the perturbation peak (a^c*), which scales as a^c*≈14Ra−1 for homogeneous systems. However, the low permeable layer has no effect on the onset time when it is near the lower boundary of a medium with sufficiently large Ra (a^c*≪a^). This nontrivial dependence highlights the implication of ignoring geological features of a small spatial extent, indicating the importance of a detailed characterization of CO2 storage sites.</p

Regular and complex singularities of the generalized thin film equation in two dimensions

We use a generalized version of the equation of motion for a thin film of liquid on a solid, horizontal substrate as a model system to study the formation of singularities in space dimensions greater than one. Varying both the exponent controlling long-ranged forces, as well as the exponent of the nonlinear mobility, we predict the structure of the singularity as the film thickness goes to zero. The spatial structure of rupture may be either 'pointlike' (approaching axisymmetry) or 'quasi-one-dimensional', in which case a one-dimensional singularity is unfolded into two or higher space dimensions. The scaling of the profile with time may be either strictly self-similar (the 'regular' case) or discretely self-similar and perhaps chaotic (the 'irregular' case). We calculate the phase boundaries between these regimes, and confirm our results by detailed comparisons with time-dependent simulations of the nonlinear thin film equation in two space dimensions.</p

A tunable high-pass filter for simple and inexpensive size-segregation of sub-10-nm nanoparticles

Recent advanced in the fields of nanotechnology and atmospheric sciences underline the increasing need for sizing sub-10-nm aerosol particles in a simple yet efficient way. In this article, we develop, experimentally test and model the performance of a High-Pass Electrical Mobility Filter (HP-EMF) that can be used for sizing nanoparticles suspended in gaseous media. Experimental measurements of the penetration of nanoparticles having diameters down to ca 1nm through the HP-EMF are compared with predictions by an analytic, a semi-empirical and a numerical model. The results show that the HPEMF effectively filters nanoparticles below a threshold diameter with an extremely high level of sizing performance, while it is easier to use compared to existing nanoparticle sizing techniques through design simplifications. What is more, the HP-EMF is an inexpensive and compact tool, making it an enabling technology for a variety of applications ranging from nanomaterial synthesis to distributed monitoring of atmospheric nanoparticles.ChemE/Materials for Energy Conversion & Storag