Phenomenological Model of Nonlinear Dynamics and Deterministic Chaotic Gas Migration in Bentonite: Experimental Evidence and Diagnostic Parameters

Understanding gas migration in compacted clay materials, e.g., bentonite and claystone, is important for the design and performance assessment of an engineered barrier system of a radioactive waste repository system, as well as many practical applications. Existing field and laboratory data on gas migration processes in low-permeability clay materials demonstrate the complexity of flow and transport processes, including various types of instabilities, caused by nonlinear dynamics of coupled processes of liquid–gas exchange, dilation, fracturing, fracture healing, etc., which cannot be described by classical models of fluid dynamics in porous media. We here show that the complexity of gas migration processes can be explained using a phenomenological concept of nonlinear dynamics and deterministic chaos theory. To do so, we analyzed gas pressure and gas influx (i.e., input) and outflux (i.e., output), recorded during the gas injection experiment in the compact Mx80-D bentonite sample, and calculated a set of the diagnostic parameters of nonlinear dynamics and chaos, such a global embedding dimension, a correlation dimension, an information dimension, and a spectrum of Lyapunov exponents, as well as plotted 2D and 3D pseudo-phase-space strange attractors, based on the univariate influx and outflux time series data. These results indicate the presence of phenomena of low-dimensional deterministic chaotic behavior of gas migration in bentonite. In particular, during the onset of gas influx in the bentonite core, before the breakthrough, the development of gas flow pathways is characterized by the process of chaotic gas diffusion. After the breakthrough, with inlet-to-outlet movement of gas, the prevailing process is chaotic advection. During the final phase of the experiment, with no influx to the sample, the relaxation pattern of gas outflux is resumed back to a process of chaotic diffusion. The types of data analysis and a proposed phenomenological model can be used to establish the basic principles of experimental data-gathering, modeling predictions, and a research design.

A Novel High-Throughput Chaotic Advection Microreactor for the Preparation of Uniform BaSO4 Nanoparticles

Owing to high mixing efficiency, microreactors are used to synthesize uniform BaSO4 nanoparticles, but application in industrial scale is limited due to poor throughput. In this work, a high-throughput passive four-stage asymmetric oscillating feedback microreactor using chaotic mixing mechanism was developed to prepare BaSO4 nanoparticles of high size uniformity. Three-dimensional unsteady simulations showed that chaotic mixing could be induced by three unique secondary flows (i.e., vortex, recirculation, and oscillation), and the fluid oscillation mechanism was examined in detail. Simulations and Villermaux-Dushman experiments indicate that almost complete mixing in molecular level could be achieved when total volumetric flow rate Qtotal was larger than 10 mL/min, and the prepared BaSO4 nanoparticles were with narrow particle size distribution (PSD). Through the adjustment of Qtotal and reactant concentrations, it is easy to control the average size. An average size of 26 nm with narrow PSD could be achieved at Qtotal = 160 mL/min.

Numerical study of mixing index in offset inlets 3-D T mixer with bend shape mixing channel

The objective of this paper is the computational analysis on the mixing index of simple T shape mixer, offset inlets T shape mixer, and offset inlets T mixer with bend shape mixing channel by CFD simulation. Computational fluid dynamics software package solves conservation of mass equation, conservation of momentum equation, and conservation of energy equation. In the case of offset inlets T shape mixer, as the aspect ratio (height to width ratio) of mixing channel increased so mixing quality also increased and offset inlets T mixer with bend shape is a combination of increased aspect ratio as well as chaotic advection mechanisms, so it provides advanced mixing index than offset inlets T shape mixer and simple T shape mixer. Pressure fall in offset inlets T shape mixer is excess than simple T shape mixer but narrowly degraded than offset inlets T mixer with bend shape. Chaotic advection rooted microchannel generates secondary flow because of which motives a high-pressure drop in the microchannel.

Fouling Mitigation via Chaotic Advection in a Flat Membrane Module with a Patterned Surface

Fouling mitigation using chaotic advection caused by herringbone-shaped grooves in a flat membrane module is numerically investigated. The feed flow is laminar with the Reynolds number (Re) ranging from 50 to 500. In addition, we assume a constant permeate flux on the membrane surface. Typical flow characteristics include two counter-rotating flows and downwelling flows, which are highly influenced by the groove depth at each Re. Poincaré sections are plotted to represent the dynamical systems of the flows and to analyze mixing. The flow systems become globally chaotic as the groove depth increases above a threshold value. Fouling mitigation via chaotic advection is demonstrated using the dimensionless average concentration (c¯w*) on the membrane and its growth rate. When the flow system is chaotic, the growth rate of c¯w* drops significantly compared to that predicted from the film theory, demonstrating that chaotic advection is an attractive hydrodynamic technique that mitigates membrane fouling. At each Re, there exists an optimal groove depth minimizing c¯w* and the growth rate of c¯w*. Under the optimum groove geometry, foulants near the membrane are transported back to the bulk flow via the downwelling flows, distributed uniformly in the entire channel via chaotic advection.

A stretchable micromixer with enhanced performance for intermediate Reynolds numbers

Chemical reactions in microscale require good mixing at a relatively low flowrate. However, mixing in microscale faces the major challenge of stable laminar flow associated with the low Reynolds number, the relative ratio between inertial force and viscous force. For low Reynolds numbers of less than unity, mixing occurs due to molecular diffusion. For high Reynolds number of more than several tens, chaotic advection enhances mixing. However, in the intermediate regime, mixing is not efficient. This paper reports a stretchable micromixer with dynamically tuneable channel dimensions. Periodically stretching the device changes the channel geometry and the curvature induced secondary Dean flows. The dynamically evolving secondary and main flows in the mixing channel result in chaotic advection and enhance mixing. The concept was demonstrated in a stretchable micromixer with a serpentine channel. We evaluated the performance of this stretchable micromixer both experimentally and numerically. At the intermediate range of Reynolds numbers from 4 to 17, the periodically stretched micromixer showed a better mixing efficiency than the non-stretched counterpart. Therefore, our stretchable micromixer is a potential candidate for applications where precious reagents need to be mixed at relatively low flow rate conditions.

A stretchable micrometer with enhanced performance for intermediate Reynolds numbers

Chemical reactions in microscale require good mixing at a relatively low flowrate. However, mixing in microscale faces the major challenge of stable laminar flow associated with the low Reynolds number, the relative ratio between inertial force and viscous force. For low Reynolds numbers of less than unity, mixing occurs due to molecular diffusion. For high Reynolds number of more than several tens, chaotic advection enhances mixing. However, in the intermediate regime, mixing is not efficient. This paper reports a stretchable micromixer with dynamically tuneable channel dimensions. Periodically stretching the device changes the channel geometry and the curvature induced secondary Dean flows. The dynamically evolving secondary and main flows in the mixing channel result in chaotic advection and enhance mixing. The concept was demonstrated in a stretchable micromixer with a serpentine channel. We evaluated the performance of this stretchable micromixer both experimentally and numerically. At the intermediate range of Reynolds numbers from 4 to 17, the periodically stretched micromixer showed a better mixing efficiency than the non-stretched counterpart. Therefore, our stretchable micromixer is a potential candidate for applications where precious reagents need to be mixed at relatively low flow rate conditions.