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Understanding the recovery of gas from reservoirs featuring pervasive nanopores is essential for effective shale gas extraction. Classical theories cannot accurately predict such gas recovery and many experimental observations are not well understood. Here we report molecular simulations of the recovery of gas from single nanopores, explicitly taking into account molecular gas-wall interactions. We show that, in very narrow pores, the strong gas-wall interactions are essential in determining the gas recovery behavior both quantitatively and qualitatively. These interactions cause the total diffusion coefficients of the gas molecules in nanopores to be smaller than those predicted by kinetic theories, hence slowing down the rate of gas recovery. These interactions also lead to significant adsorption of gas molecules on the pore walls. Because of the desorption of these gas molecules during gas recovery, the gas recovery from the nanopore does not exhibit the usual diffusive scaling law (i.e., the accumulative recovery scales as $R sim t^{1/2}$ but follows a super-diffusive scaling law $R sim t^n$ ($n>0.5$), which is similar to that observed in some field experiments. For the system studied here, the super-diffusive gas recovery scaling law can be captured well by continuum models in which the gas adsorption and desorption from pore walls are taken into account using the Langmuir model.
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Vortices play an unique role in heat and momentum transports in astro- and geo-physics, and it is also the origin of the Earths dynamo. A question existing for a long time is whether the movement of vortices can be predicted or understood based on their historical data. Here we use both the experiments and numerical simulations to demonstrate some generic features of vortex motion and distribution. It can be found that the vortex movement can be described on the framework of Brownian particles where they move ballistically for the time shorter than some critical timescales, and then move diffusively. Traditionally, the inertia of vortex has often been neglected when one accounts for their motion, our results imply that vortices actually have inertial-induced memory such that their short term movement can be predicted. Extending to astro- and geo-physics, the critical timescales of transition are in the order of minutes for vortices in atmosphere and ocean, in which this inertial effect may often be neglected compared to other steering sources. However, the timescales for vortices are considerably larger which range from days to a year. It infers the new concept that not only the external sources alone, for example the solar wind, but also the internal source, which is the vortex inertia, can contribute to the short term Earths magnetic field variation.
The aim of this note is to examine the efficacy of a recently developed approach to the recovery of nonlinear water waves from pressure measurements at the seabed, by applying it to the celebrated extreme Stokes wave.
Using molecular dynamics, we study the nucleation and stability of bulk nanobubble clusters. We study the formation, growth, and final size of bulk nanobubbles. We find that, as long as the bubble-bubble interspacing is small enough, bulk nanobubbles are stable against dissolution. Simple diffusion calculations provide an excellent match with the simulation results, giving insight into the reason for the stability: nanobubbles in a cluster of bulk nanobubbles protect each other from diffusion by a shielding effect.
Ultrasound is known to enhance surface bubble growth and removal in catalytic and microfluidic applications, yet the contributions of rectified diffusion and microstreaming phenomena towards mass transfer remain unclear. We quantify the effect of ultrasound on the diffusive growth of a single spherical CO$_2$ bubble growing on a substrate in supersaturated water. The time dependent bubble size, shape, oscillation amplitude and microstreaming flow field are resolved. We show and explain how ultrasound can enhance the diffusive growth of surface bubbles by up to two orders of magnitude during volumetric resonance. The proximity of the wall forces the bubble to oscillate non-spherically, thereby generating vigorous streaming during resonance that results in convection-dominated growth.
Diffusion is the macroscopic manifestation of disordered molecular motion. Mathematically, diffusion equations are partial differential equations describing the fluid-like large-scale dynamics of parcels of molecules. Spatially inhomogeneous systems affect in a position-dependent way the average motion of molecules; thus, diffusion equations have to reflect somehow this fact within their structure. It is known since long that in this case an ambiguity arises: there are several ways of writing down diffusion equations containing space dependence within their parameters. These ways are all potentially valid but not equivalent, meaning that the different diffusion equations yield different solutions for the same data. The ambiguity can only be resolved at the microscopic level: a model for the stochastic dynamics of the individual molecules must be provided, and a well-defined diffusion equation then arises as the long-wavelength limit of this dynamics. In this work we introduce and employ the integro-differential Master Equation (ME) as a tool for describing the microscopic dynamics. We show that is possible to provide a parameterized version of the ME, in terms of a single numerical parameter (alpha), such that the different expressions for the diffusive fluxes are recovered at different values of alpha. This work aims to fill a gap in the literature, where the ME was shown to deliver just one diffusive limit. In the second part of the paper some numerical computer models are introduced, both to support analytical considerations, and to extend the scope of the ME to more sophisticated scenarios, beyond the simplest alpha-parameterization.
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