Miscible Fluids Research Articles

Experimental and numerical investigation of thermal chaotic mixing in a T-shaped microchannel

In this paper, thermal chaotic mixing characteristics of two miscible fluids in a T-shaped microchannel are investigated experimentally and numerically. In the experiments, fluorescent dye Acid Yellow and Rhodamine B was employed to show the mass mixing behavior and temperature field, respectively. Power input and flow rate were studied to investigate the thermal mixing characteristics in the microchannel. The mixing efficiency increases with increasing power input, while decreases with increasing flow rate. A numerical simulation of conjugate forced convection-conduction heat and mass transfer was employed to investigate the thermal chaotic mixing processes in the T-shaped microchannel. The measured mixing efficiency versus applied voltage and flow rate were compared with numerical simulation results, which showed reasonably agreement.

Folded micro-threads: Role of viscosity and interfacial tension

The shape and evolution of periodically folded threads are experimentally examined in a microfluidic network. The fluidic system is designed for the production and lubricated transport of very uniform folds. To investigate the influence of viscosity and interfacial tension on buckling deformations, multiphase flows are scrutinized using both miscible and immiscible fluid pairs. The parameters used to analyze folding morphologies include thread diameter, arc-length, fold amplitude, and wavelength. When fluids are immiscible, the onset of viscous folding is characterized as a function of the capillary number and the phenomenon of “capillary unfolding” where a corrugated thread straightens along the flow direction is demonstrated. The spatial transition from folding to coiling-like flow behavior of high-viscosity capillary threads is also shown.

Stationary residual layers in buoyant Newtonian displacement flows

We study buoyant displacement flows with two miscible fluids of equal viscosity in ducts that are inclined at angles close to horizontal (β≈90°). As the imposed velocity (V̂0) is increased from zero, we change from an exchange flow dominated regime to a regime in which the front velocity (V̂f) increases linearly with V̂0. During this transition, we observed an interesting phenomenon in which the layer of displaced fluid remained at the top of the pipe (diameter D̂) during the entire duration of the experiment, apparently stationary for times t̂≳103D̂/V̂0 (the stationary residual layer). Our investigation revealed that this flow marks the transition between flows with a back flow, counter to the imposed flow, and those that displace instantaneously. The same phenomena are observed in pipes (experiments) and in plane channels (two-dimensional numerical computations). A lubrication/thin-film model of the flows also shows the transition from back flow to instantaneous displacement. At long times, this model has a stationary residual layer solution of the type observed, which is found at a unique ratio χ of the axial viscous velocity to the imposed velocity. The prediction of the stationary residual layer from the lubrication model is compared with the transition in observed behavior in our pipe flow experiments and our 2D numerical displacements in the channel. Reasonable agreement is found for the pipe and excellent agreement for the channel. Physically, in either geometry at transition, the upper layer of the fluid is in a countercurrent motion with zero net volumetric flux; the velocity at the interface is positive, but the velocity of the interface is zero. This results from a delicate balance between buoyancy forces against the mean flow and viscous forces in the direction of the mean flow.

Lubrication of Highly Viscous Core-Annular Flows in Microfluidic Chambers

We investigate the lubrication transition of high-viscosity fluid threads flowing in sheaths of less viscous fluids, i.e., viscous core-annular flows, in microchannels. Focus is given on the flow behavior of threads as they traverse a quasi-two-dimensional diverging-converging slit microfluidic chamber. The role of the viscosity contrast is examined for both miscible and immiscible fluids, and, for the later case, both partially wetting and nonwetting threads are considered. The conditions for lubrication are established in relation to flow rates of injection, interfacial properties, viscosities, and phenomena such as viscous buckling, wetting, breakup, and coalescence.

Mathematical Modeling of Powder‐Snow Avalanche Flows

Powder‐snow avalanches are violent natural disasters which represent a major risk for infrastructures and populations in mountain regions. In this study we present a novel model for the simulation of avalanches in the aerosol regime. The second scope of this study is to get more insight into the interaction process between an avalanche and a rigid obstacle. An incompressible model of two miscible fluids can be successfully employed in this type of problems. We allow for mass diffusion between two phases according to the Fick's law. The governing equations are discretized with a contemporary fully implicit finite volume scheme. The solver is able to deal with arbitrary density ratios. Several numerical results are presented. Volume fraction, velocity, and pressure fields are presented and discussed. Finally, we point out how this methodology can be used for practical problems.

A new approach to Bäcklund transformations for longitudinal dispersion of miscible fluid flow through porous media in oil reservoir during secondary recovery process

In this paper a theoretical model has developed for the dispersion problem in porous media in which the flow is one dimensional and the average flow is unsteady. The Solution of the dispersion problem is presented by means of a new approach to B?cklund transformations of nonlinear partial differential equations.

Establishing and maintaining the integrity of wells used for sequestration of CO2

There is a tendency for the CCS industry to believe that everything is already known about CO2 injection wells, based upon the experience of miscible fluid injection for the purposes of tertiary oil recovery, combined with the general experience of gas re-injection and gas production internationally. In fact, analysis of the technical issues identifies that CO2 injection wells for sequestration may be more challenging in a number of ways, both in the fluids and pressures they must handle and the long term duration for which full well integrity will be required. Well integrity means the achievement of fluid containment and pressure containment within the well throughout its whole life cycle. The technical challenges of CO2 injection wells are highly dependent on the individual well design parameters, principally the formation being injected into (saline aquifer versus depleted gas formation) and the quality (impurity levels) found in the CO2 source gas. These factors will impact the potential corrosion and other material degradation challenges which may threaten the well components including injection tubing, injection casing, cement and packer materials. The long term integrity of these components is critical to the injection phase of the life and the suspension and abandonment phases (depending upon the strategy selected for well abandonment). A key part of the acceptance of CO2 sequestration as a safe and reliable greenhouse gas control mechanism will be the proof that the well is truly leak-free. This integrity management element requires a comprehensive monitoring and pro-active warning system which highlights developing integrity issues before they become acute. Key well parameters requiring daily monitoring and intermittent testing will be identified in line with industry international standards and regulations. Acceptance criteria for well test results will be defined in the context of a CO2 injection well. The oil and gas industry is only now commencing with comprehensive well integrity management systems and the CCS industry can make good use of the experience which is being established and software products such as the Intetech Well Integrity Toolkit (iWIT) which are proven to cover the comprehensive challenge that carbon dioxide injection wells represent.

Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids

A second-moment closure model is proposed for describing turbulence quantities in flows where large density fluctuations can arise due to mixing between different density fluids, in addition to compressibility or temperature effects. The turbulence closures used in this study are an extension of those proposed by Besnard et al., which include closures for the turbulence mass flux and density-specific-volume covariance. Current engineering models developed to capture these extended effects due to density variations are scarce and/or greatly simplified. In the present model, the density effects are included and the results are compared to direct numerical simulations (DNS) and experimental data for flow instabilities with low to moderate density differences. The quantities compared include Reynolds stresses, turbulent mass flux, mixture density, density-specific-volume covariance, turbulent length scale, turbulence and material mix time scales, turbulence dissipation, and mix widths and/or growth rates. These comparisons are made within the framework of three very different classes of flows: shear-driven, Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Overall, reasonable agreement is seen between experiments, DNS, and averaging models.

Characterization of fracture aperture field heterogeneity by electrical resistance measurement

We use electrical resistance measurements to characterize the aperture field in a rough fracture. This is done by performing displacement experiments using two miscible fluids of different electrical resistivity and monitoring the time variation of the overall fracture resistance. Two fractures have been used: their complementary rough walls are identical but have different relative shear displacements which create “channel” or “barrier” structures in the aperture field, respectively parallel or perpendicular to the mean flow velocity U → . In the “channel” geometry, the resistance displays an initial linear variation followed by a tail part which reflects the velocity contrast between slow and fast flow channels. In the “barrier” geometry, a change in the slope between two linear zones suggests the existence of domains of different characteristic aperture along the fracture. These variations are well reproduced analytically and numerically using simple flow models. For each geometry, we present then a data inversion procedure that allows one to extract the key features of the heterogeneity from the resistance measurement.

Effects of sweep rates of external magnetic fields on the labyrinthine instabilities of miscible magnetic fluids

The interfacial instability of miscible magnetic fluids in a Hele-Shaw Cell is studied experimentally, with different magnitudes and sweep rates of the external magnetic field. The initial circular oil-based magnetic fluid drop is surrounded by the miscible fluid, diesel. The external uniform magnetic fields induce small fingerings around the initial circular interface, so call labyrinthine fingering instability, and secondary waves. When the magnetic field is applied at a given sweep rate, the interfacial length grows significantly at the early stage. It then decreases when the magnetic field reaches the preset values, and finally approaches a certain asymptotic value. In addition, a dimensionless parameter, Pe, which includes the factors of diffusion and sweep rate of the external magnetic field, is found to correlate the experimental data. It is shown that the initial growth rate of the interfacial length is linearly proportional to Pe for the current experimental parameter range and is proportional to the square root of the sweep rate at the onset of labyrinthine instability.

Simulations of Axial Mixing of Liquids in a Long Horizontal Pipe for Industrial Applications

Various industrial applications require the use of common pipelines or tubing to simultaneously or sequentially deliver multiple types of liquids. Dependent upon the application, long pipelines or tubing can range from several meters to several kilometers in length, composed of significant horizontal and vertical sections. Axial mixing is an important aspect of such flows of liquids in succession from a safety and reliability point of view. It is anticipated that mixing is due to turbulence and buoyancy, with the latter as a result of density differences of the mixing fluids. This paper sets out a numerical simulation model based on computational fluid dynamics (CFD) to fundamentally understand the mixing behavior of two miscible fluids under actual industrial-project-specific conditions. To benchmark its accuracy, the simulation model is first verified with respect to its numerical parameters using a short, 10 m pipe. Subsequently, a 100 m horizontal pipe is modeled, and we show that these results can be...

Realistic simulation of mixing fluids

Recently, simulation of mixing fluids, for which wide applications can be found in multimedia, computer games, special effects, virtual reality, etc., is attracting more and more attention. Most previous methods focus separately on binary immiscible mixing fluids or binary miscible mixing fluids. Until now, little attention has been paid to realistic simulation of multiple mixing fluids. In this paper, based on the solution principles in physics, we present a unified framework for realistic simulation of liquid–liquid mixing with different solubility, which is called LLSPH. In our method, the mixing process of miscible fluids is modeled by a heat-conduction-based Smooth Particle Hydrodynamics method. A special self-diffusion coefficient is designed to simulate the interactions between miscible fluids. For immiscible fluids, marching-cube-based method is adopted to trace the interfaces between different types of fluids efficiently. Then, an optimized spatial hashing method is adopted for simulation of boundary-free mixing fluids such as the marine oil spill. Finally, various realistic scenes of mixing fluids are rendered using our method.

Transient surface tension in miscible liquids

Evidence of the existence of a transient surface tension between two miscible fluid phases is given. This is done by making use of a density matched free of gravity perturbations, binary liquid of isobutyric acid and water, which presents a miscibility gap and is studied by light scattering. The experiment is performed very near the critical point of the binary liquid, where the diffusion of phases is extremely slow. The surface tension is deduced from the evolution of the structure factor obtained from low angle light scattering. The latter evolution is successfully analyzed in terms of a local equilibrium diffusive approach that makes explicit how the surface tension decreases with time.

Reaction‐Driven Mixing and Dispersion

Reactions that look after themselves: Interfacial instabilities caused by chemical reactions can increase the area of contact between fluids and enhance their mixing or dispersion. Although instabilities in macroscopic liquid/liquid systems are well-understood, “reactive mixing” at molecular length scales presents a challenge and an opportunity for future research. The picture shows two-dimensional density fields of two miscible reactive fluids.

A first-principle predictive theory for a sphere falling through sharply stratified fluid at low Reynolds number

A sphere exhibits a prolonged residence time when settling through a stable stratification of miscible fluids due to the deformation of the fluid-density field. Using a Green's function formulation, a first-principles numerically assisted theoretical model for the sphere–fluid coupled dynamics at low Reynolds number is derived. Predictions of the model, which uses no adjustable parameters, are compared with data from an experimental investigation with spheres of varying sizes and densities settling in stratified corn syrup. The velocity of the sphere as well as the deformation of the density field are tracked using time-lapse images, then compared with the theoretical predictions. A settling rate comparison with spheres in dense homogeneous fluid additionally quantifies the effect of the enhanced residence time. Analysis of our theory identifies parametric trends, which are also partially explored in the experiments, further confirming the predictive capability of the theoretical model. The limit of infinite fluid domain is considered, showing evidence that the Stokes paradox of infinite fluid volume dragged by a moving sphere can be regularized by density stratifications. Comparisons with other possible models under a hierarchy of additional simplifying assumptions are also presented.

Thermal mixing of two miscible fluids in a T-shaped microchannel

In this paper, thermal mixing characteristics of two miscible fluids in a T-shaped microchannel are investigated theoretically, experimentally, and numerically. Thermal mixing processes in a T-shaped microchannel are divided into two zones, consisting of a T-junction and a mixing channel. An analytical two-dimensional model was first built to describe the heat transfer processes in the mixing channel. In the experiments, de-ionized water was employed as the working fluid. Laser induced fluorescence method was used to measure the fluid temperature field in the microchannel. Different combinations of flow rate ratios were studied to investigate the thermal mixing characteristics in the microchannel. At the T-junction, thermal diffusion is found to be dominant in this area due to the striation in the temperature contours. In the mixing channel, heat transfer processes are found to be controlled by thermal diffusion and convection. Measured temperature profiles at the T-junction and mixing channel are compared with analytical model and numerical simulation, respectively.

Fluid-driven fractures in uncemented sediments: Underlying particle-level processes

Granular materials subjected to fluid flow may experience fracture formation and fluid flow localization. Current explanations for hydraulic fracture in soils fail to satisfy the inherent characteristics of granular materials: effective stress-dependent cohesionless-frictional strength. We apply complementary experimental and numerical techniques to identify the underlying particle-scale mechanisms. First, we show that the miscibility of the invading fluid with the host fluid leads to distinct localization processes that depend on the balance between particle-level skeletal forces (effective stress-dependent), capillary forces (the invasion of the interfacial membrane when immiscible fluids are involved), and seepage drag forces (associated with fluid flow velocity). Then, we identify the positive feedback mechanisms at surface defects and fracture tips that promote fracture initiation and sustain fracture propagation. These include increased porosity at the tip due to strains preferentially normal to the fracture alignment, either eased membrane invasion (immiscible fluids) or higher hydraulic conductivity (miscible fluids), and the emergence of particle-level forces that promote opening-mode particle displacement. This effective stress compatible sequence of events helps identify the parameters that govern fluid-driven fracture formation in uncemented sediments, and explain experimental observations.

Diffusive mixing through velocity profile variation in microchannels

Rapid mixing does not readily occur at low Reynolds number flows encountered in microdevices; however, it can be enhanced by passive diffusive mixing schemes. This study of micromixing of two miscible fluids is based on the principle that (1) increased velocity at the interface of co-flowing fluids results in increased diffusive mass flux across their interface, and (2) diffusion interfaces between two liquids progress transversely as the flow proceeds downstream. A passive micromixer is proposed that takes advantage of the peak velocity variation, inducing diffusive mixing. The effect of flow variation on the enhancement of diffusive mixing is investigated analytically and experimentally. Variation of the flow profile is confirmed using micro-Particle Image Velocimetry (μPIV) and mixing is evaluated by color variations resulting from the mixing of pH indicator and basic solutions. Velocity profile variations obtained from μPIV show a shift in peak velocities. The mixing efficiency of the Σ-micromixer is expected to be higher than that for a T-junction channel and can be as high as 80%. The mixing efficiency decreases with Reynolds number and increases with downstream length, exhibiting a power law.

Simulation of flow of mixtures through anisotropic porous media using a lattice Boltzmann model

We propose a description for transient penetration simulations of miscible and immiscible fluid mixtures into anisotropic porous media, using the lattice Boltzmann (LB) method. Our model incorporates hydrodynamic flow, advection-diffusion, surface tension, and the possibility for global and local viscosity variations to consider various types of hardening fluids. The miscible mixture consists of two fluids, one governed by the hydrodynamic equations and one by advection-diffusion equations. We validate our model on standard problems like Poiseuille flow, the collision of a drop with an impermeable, solid interface and the deformation of the fluid due to surface tension forces. To demonstrate the applicability to complex geometries, we simulate the invasion process of mixtures into wood spruce samples.

Lagrangian simulations of unstable gravity-driven flow of fluids with variable density in randomly heterogeneous porous media

A new Lagrangian particle model based on smoothed particle hydrodynamics (SPH) is developed and used to simulate Darcy scale flow and transport in porous media. The method has excellent conservation properties and treats advection exactly. The Lagrangian method is used in stochastic analysis of miscible density-driven fluid flows. Results show that heterogeneity significantly increases dispersion and slows development of Rayleigh–Taylor instability. The presented numerical examples illustrate the advantages of Lagrangian methods for stochastic transport simulations.