Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation

This project was supported by the National Natural Science Foundation of China (Nos. 41572116, 51576114, ​41630317), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (No. CUG160602) and the Natural Science Foundation of Fujian Province of China (No. 2016J01254). The authors of the figures that used in presented review are also highly appreciated.Peer reviewedPostprin

A continuous time random walk model of transport in variably saturated heterogeneous porous media

We propose a unified physical framework for transport in variably saturated porous media. This approach allows fluid flow and solute migration to be treated as ensemble averages of fluid and solute particles, respectively. We consider the cases of homogeneous and heterogeneous porous materials. Within a fractal mobile-immobile (MIM) continuous time random walk framework, the heterogeneity will be characterized by algebraically decaying particle retention-times. We derive the corresponding (nonlinear) continuum limit partial differential equations and we compare their solutions to Monte Carlo simulation results. The proposed methodology is fairly general and can be used to track fluid and solutes particles trajectories, for a variety of initial and boundary conditions.Comment: 12 pages, 9 figure

Robust spatially resolved pressure measurements using MRI with novel buoyant advection-free preparations of stable microbubbles in polysaccharide gels

MRI of fluids containing lipid coated microbubbles has been shown to be an effective tool for measuring the local fluid pressure. However, the intrinsically buoyant nature of these microbubbles precludes lengthy measurements due to their vertical migration under gravity and pressure-induced coalescence. A novel preparation is presented which is shown to minimize both these effects for at least 25 min. By using a 2% polysaccharide gel base with a small concentration of glycerol and 1,2-distearoyl-sn-glycero-3-phosphocholine coated gas microbubbles, MR measurements are made for pressures between 0.95 and 1.44 bar. The signal drifts due to migration and amalgamation are shown to be minimized for such an experiment whilst yielding very high NMR sensitivities up to 38% signal change per bar

Nonlinear diffusion from Einstein's master equation

We generalize Einstein's master equation for random walk processes by considering that the probability for a particle at position $r$ to make a jump of length $j$ lattice sites, $P_j(r)$ is a functional of the particle distribution function $f(r,t)$. By multiscale expansion, we obtain a generalized advection-diffusion equation. We show that the power law $P_j(r) \propto f(r)^{\alpha - 1}$ (with $\alpha > 1$) follows from the requirement that the generalized equation admits of scaling solutions ($f(r;t) = t^{-\gamma}\phi (r/t^{\gamma})$). The solutions have a $q$-exponential form and are found to be in agreement with the results of Monte-Carlo simulations, so providing a microscopic basis validating the nonlinear diffusion equation. Although its hydrodynamic limit is equivalent to the phenomenological porous media equation, there are extra terms which, in general, cannot be neglected as evidenced by the Monte-Carlo computations.}Comment: 7 pages incl. 3 fig

Fluid transport through porous media: A novel application of kinetic Monte Carlo simulations

With increasing global energy demands, unconventional formations, such as shale rocks, are becoming an important source of natural gas. Current efforts are focused on understanding fluid dynamics to maximise natural gas yields. Although shale gas is playing an increasingly important role in the global energy industry, our knowledge of the fundamentals of fluid transport through multiscale and heterogeneous porous media is incomplete, as both static and dynamic properties of confined fluids differ tremendously from those at the macroscopic scale. Transport models, derived from atomistic studies, are frequently used to bridge this gap. However, capturing and upscaling the interactions between the pore surface and fluids remains challenging. In this thesis, a computationally efficient stochastic approach is implemented to simulate fluid transport through complex porous media. One-, two-, and three-dimensional kinetic Monte Carlo models were developed to predict methane transport in heterogeneous pore networks consisting of hydrated and water-free micro-, meso-, and macropores, representative of shale rock minerals. Molecular dynamics (MD) simulations, experimental imaging and adsorption data, which describe the surface – fluid interaction and the pore network features respectively were utilised to inform the KMC models. The stochastic approach was used to (1) quantify the effect of the pore network characteristics (pore size, chemistry, connectivity, porosity, and anisotropy) on the transport of supercritical methane, (2) estimate the permeability of an Eagle Ford shale sample and evaluate the effect of proppants on permeability, and (3) to upscale atomistic insights and predict fluid diffusivity through different size pores. The results obtained were consistent with the analytical solutions of the diffusion equation, experimental data, and MD simulations, respectively, demonstrating the effectiveness of the stochastic approach. In addition, the applicability of less computationally intensive deterministic approaches was examined using multiple case studies; recommendations are provided on the optimal conditions under which each method can be used