Particle energy partitioning and transverse diffusion during rarefied travel on an experimental hillslope

Rarefied particle motions on rough hillslope surfaces are controlled by the balance between gravitational heating of particles due to conversion of potential to kinetic energy and frictional cooling of the particles due to collisions with the surface. Here we elaborate on how particle energy is partitioned between kinetic, rotational, and frictional forms during downslope travel using measurements of particle travel distances on a laboratory-scale hillslope, supplemented with high-speed imaging of drop–impact–rebound experiments. The drop–impact–rebound experiments indicate that particle shape has a dominant role in energy conversion during impact with a surface. Relative to spherical and natural rounded particles, angular particles give greater variability in rebound behavior, resulting in more effective conversion of translational to rotational energy. The effects of particle shape on energy conversion are especially pronounced on a sloping sand-roughened surface. Angular particles travel shorter distances downslope than rounded particles, though travel distance data for both groups are well fit by generalized Pareto distributions. Moreover, particle–surface collisions during downslope motion lead to a transverse random-walk behavior and transverse particle diffusion. Transverse spreading increases with surface slope as there is more available energy to be partitioned into the downslope or transverse directions during collision due to increased gravitational heating. Rounded particles exhibit greater transverse diffusion than angular particles, as less energy is lost during collision with the surface. Because the experimental surface is relatively smooth, this random-walk behavior represents a top-down control on the randomization of particle trajectories due to particle shape, which is in contrast to a bottom-up control on randomization of particle trajectories associated with motions over rough surfaces. Importantly, transverse particle diffusion during downslope motion may contribute to a cross-slope particle flux and likely contributes to topographic smoothing of irregular hillslope surfaces such as scree slopes.

Template Instrumentation for "Accurate Constant via Transient Incomplete Separation" (ACTIS)

<p>ACTIS is a new method for finding the equilibrium dissociation constant <i>K</i>_d of a protein–small molecule complex based on transient incomplete separation of the complex from the unbound small molecule in a capillary. This separation is caused by differential transverse diffusion of the complex and the small molecule in a pressure-driven flow. The advection-diffusion processes underlying ACTIS can be described by a system of partial differential equations allowing for a virtual ACTIS instrument to be built and ACTIS to be studied in silico. The previous in-silico studies show that large variations in the fluidic system geometry do not affect the accuracy of <i>K</i>_d determination, thus, proving that ACTIS is conceptually accurate. The conceptual accuracy does not preclude, however, instrumental inaccuracy caused by run-to-run signal drifts. Here we report on assembling a physical ACTIS instrument with a fluidic system that mimics the virtual one and proving the absence of signal drifts. Furthermore, we confirmed method ruggedness by assembling a second ACTIS instrument and comparing the results of experiments performed with both instruments in parallel. Despite some differences between the instruments and, accordingly, significant differences in their respective separagrams, we found that the <i>K</i>_d values determined for identical samples with these instruments were equal. Conclusively, the fluidic system presented here can serve as a template for reliable ACTIS instrumentation.</p>

Template Instrumentation for "Accurate Constant via Transient Incomplete Separation" (ACTIS)

<p>ACTIS is a new method for finding the equilibrium dissociation constant <i>K</i>_d of a protein–small molecule complex based on transient incomplete separation of the complex from the unbound small molecule in a capillary. This separation is caused by differential transverse diffusion of the complex and the small molecule in a pressure-driven flow. The advection-diffusion processes underlying ACTIS can be described by a system of partial differential equations allowing for a virtual ACTIS instrument to be built and ACTIS to be studied in silico. The previous in-silico studies show that large variations in the fluidic system geometry do not affect the accuracy of <i>K</i>_d determination, thus, proving that ACTIS is conceptually accurate. The conceptual accuracy does not preclude, however, instrumental inaccuracy caused by run-to-run signal drifts. Here we report on assembling a physical ACTIS instrument with a fluidic system that mimics the virtual one and proving the absence of signal drifts. Furthermore, we confirmed method ruggedness by assembling a second ACTIS instrument and comparing the results of experiments performed with both instruments in parallel. Despite some differences between the instruments and, accordingly, significant differences in their respective separagrams, we found that the <i>K</i>_d values determined for identical samples with these instruments were equal. Conclusively, the fluidic system presented here can serve as a template for reliable ACTIS instrumentation.</p>

Generalized Darcy’s Law in Filtration Theory

We study the hydrodynamics of flow in a porous medium modeling the grain filling in filters. Using the lattice approximation, we derive the structure of the current in porous media and obtain the transverse diffusion coefficient D which proves to be proportional to the diameter d of the grains as constituents of the medium. We consider the axially-symmetric stationary flow in a cylindrical filter and show that the vertical velocity takes its maximal value at the wall, this effect being known as the “near-wall” one. We analyze the solution to the Euler equation with the modified Darcy force, which depends not only on the velocity but also on the gradient of the pressure included in the Darcy coefficient. Finally, within the scope of the perturbation method, we derive the main filtration equation and discuss the influence of modifying the Darcy’s law on the efficiency of the filtration process.