Miscible Fluids Research Articles

Displacement flows in periodically moving pipe: Understanding multiphase flows hosted in oscillating geometry

In the present work, we experimentally study displacement flows of two Newtonian, miscible fluids in a long, vertical moving pipe while comparing the results with the corresponding displacement flows in a stationary pipe. When in motion, the pipe slowly oscillates like an inverted pendulum. The two fluids have a small density difference and a nearly-identical viscosity. The denser displacing fluid is placed above the displaced fluid. Overall, our buoyant displacement flows in a moving pipe are at least controlled by three dimensionless groups, namely the Reynolds number, the densimetric Froude number, and the Rossby number. Experimental images of the penetrating front of the heavy displacing fluid into the light displaced one have been analyzed for a wide range of the dimensionless groups. In particular, three different flow regimes are observed for displacement flows in a moving pipe: a stable flow that is non-diffusive (for Re/Ro≲O102 &Re/Fr2<35), a stable-diffusive flow (for Re/Ro≳O102 &Re/Fr2<35) and an unstable-diffusive flow (for Re/Fr2>35). In addition, penetration front velocities as well as macroscopic diffusion coefficients have been quantified. The results show in detail that depending on the value of the density difference and the mean imposed displacement flow velocity, the geometrical movement can have different and even opposite effects, e.g., slightly increase or decrease the front velocity. The pipe motion seems to also slightly increase the macroscopic diffusion coefficient. While the findings of this study can help understand the leading order effects associated with a flow geometry movement on displacement flows, they can be of great importance for industrial applications and for development of relevant fluid mechanics theories.

Interaction between shock layer and viscous fingering in a Langmuir adsorbed solute

The nonlinear evolution of the interface between miscible fluids in porous media exhibits different spatiotemporal patterns. The understanding of the physical mechanism behind these patterns is relevant in a wide variety of physicochemical processes. The displacement of a high viscous fluid by a less viscous one in uniform porous medium results in classical viscous fingering (VF) instability. We find that the nonlinear Langmuir-type adsorption of the solute, dissolved in the displacing fluid, leading to the formation of a shock layer can alter the fingering dynamics. The influence of the shock layer on the evolving instability is examined by numerical simulations. Of particular interest are the formation of the shock layer and its impact on the onset of viscous fingering. In this paper, we reveal a critical mechanism of Langmuir-type adsorption that plays a vital role in the speed up of instability. We further infer that by controlling the non-linear adsorption parameter and viscosity contrast of the fluids, the shock layer either ceases to exist or it can be suppressed with VF instability. Hence, the Langmuir adsorption is identified as a strategy to manipulate the instability in a system involving porous media flows.

Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow

Stratified shear flows occur in many geophysical contexts, from oceanic overflows and river estuaries to wind-driven thermocline layers. We explore a turbulent wall-bounded shear flow of lighter miscible fluid into a quiescent fluid of higher density with a range of Richardson numbers$0.05\lesssim Ri\lesssim 1$. In order to find a stability parameter that allows close comparison with linear theory and with idealized experiments and numerics, we investigate different definitions of$Ri$. We find that a gradient Richardson number defined on fluid interface sections where there is no overturning at or adjacent to the maximum density gradient position provides an excellent stability parameter, which captures the Miles–Howard linear stability criterion. For small$Ri$the flow exhibits robust Kelvin–Helmholtz instability, whereas for larger$Ri$interfacial overturning is more intermittent with less frequent Kelvin–Helmholtz events and emerging Holmboe wave instability consistent with a thicker velocity layer compared with the density layer. We compute the perturbed fraction of interface as a quantitative measure of the flow intermittency, which is approximately 1 for the smallest$Ri$but decreases rapidly as$Ri$increases, consistent with linear theory. For the perturbed regions, we use the Thorpe scale to characterize the overturning properties of these flows. The probability distribution of the non-zero Thorpe length yields a universal exponential form, suggesting that much of the overturning results from increasingly intermittent Kelvin–Helmholtz instability events. The distribution of turbulent kinetic energy, conditioned on the intermittency fraction, has a similar form, suggesting an explanation for the universal scaling collapse of the Thorpe length distribution.

Labyrinthine instabilities of miscible magnetic fluids in a rotating Hele-Shaw cell

This study presents the first experimental results of confining miscible magnetic fluids in a rotating Hele-Shaw cell. Variations in the prominence of labyrinthine instabilities are observed under a range of experimental conditions, with different magnetic field strengths, gap depths, and rotation speeds. These instabilities are characterized by two modified Péclect numbers, namely, Pem (the ratio of the characteristic magnetic advection rate and the diffusion rate) and Pec (the ratio of characteristic rotation advection and the diffusion rate). The magnetic effect is characterized by dipolar repulsion, which triggers a distinctive fingering pattern differing from the progressive diffusion pattern that occurs without magnetic fields or rotation. Under the same rotation speed, the magnetoviscous effect will hinder the growth rate of the magnetic drops at the later stage. However, both the rotation effect and the gap depth greatly enhance the growth rate of the magnetic drops, as these conditions help to intensify the labyrinthine instabilities. In contrast, the countering pressure gradient produces an opposite force that constrains the trend toward expansion. Two major phases in the growth of instabilities are defined: a magnetization phase and a rotation phase, which are dominated by the magnetic and the rotation effect, respectively. The significance of the rotation effect is confirmed by the linear regression between the rotation growth rate and Pec. Finally, main fingering structures that evolve from the secondary waves are verified as having a wavelength λ to gap depth h relation of λ≈(7±1)h.

Experimental study on droplet generation in flow focusing devices considering a stratified flow with viscosity contrast

High throughput analysis is highly demanded in a variety of chemical reactions. Droplet microfluidics offers unique advantages over traditional multi-well plate systems for high throughput analysis such as providing a confined and more controllable environment for single particle or cell analysis. Driven by the need to improve the efficiency of encapsulating one particle or cell into one individual droplet without complicating geometric and operating conditions, this study experimentally investigated the effects of viscosity contrast between two miscible fluids that together serve the dispersed fluid on the ordering of particles before they are encapsulated into droplets by another immiscible fluid. Five scenarios with different viscosity contrast were systematically considered and a physical model of droplet size for each scenario was developed based on experimental results and scaling laws. The five different scenarios include two with pure 10% glycerol and pure 80% glycerol as the dispersed phase, respectively, and three others where these two fluids are either side by side or one is accompanied by the other. Droplet size and formation period for these scenarios were compared and analyzed considering the same geometric and flow conditions. It is found that the stratified flow structures formed in the first junction by the two miscible fluids (10% and 80% glycerol solutions) strongly influence droplet formation dynamics such as droplet size and formation frequency. Each scenario finds its own applications. The scenario with 80% glycerol surrounded by 10% glycerol provides the optimized means for particle encapsulation. However, the scenario with two fluids side by side in the first junction generates droplets with high monodispersity for the largest range of flow ratios, which is useful for high throughput reactions involving different reagents.

Incompressible Rayleigh–Taylor Turbulence

Basic fluid equations are the main ingredient in the development of theories of Rayleigh–Taylor buoyancy-induced instability. Turbulence arises in the late stage of the instability evolution as a result of the proliferation of active scales of motion. Fluctuations are maintained by the unceasing conversion of potential energy into kinetic energy. Although the dynamics of turbulent fluctuations is ruled by the same equations controlling the Rayleigh–Taylor instability, here only phenomenological theories are currently available. The present review provides an overview of the most relevant (and often contrasting) theoretical approaches to Rayleigh–Taylor turbulence together with numerical and experimental evidence for their support. Although the focus is mainly on the classical Boussinesq Rayleigh–Taylor turbulence of miscible fluids, the review extends to other fluid systems with viscoelastic behavior, affected by rotation of the reference frame, and, finally, in the presence of reactions.

Analysis of the impact of CO&lt;SUB align="right"&gt;2 content on the physical properties of the liquid phase mixtures in oil production wells

CO2 injection not only enhances oil recovery dramatically, but it also has a potential to reduce the greenhouse effect. During the process of CO2 displacement, when CO2 breaks through in oil production wells, CO2 content will impact the phase state and physical properties of the liquid phase mixture in wellbore. As a result, it will affect the calculation of temperature and pressure in oil production wells. Therefore, it is unacceptable to use the conventional black-oil model for calculating the phase state of miscible fluids. For dealing with this problem, we use a gas-liquid flash theory and a compositional model to develop a new model. The Jilin oilfield is used as a case study; the phase state (gas, liquid or gas-liquid) and physical properties of the liquid phase mixture (including CO2 and hydrocarbons) under initial conditions are calculated by this new model. The results indicate that the molar content of CO2 has a great impact on the physical properties of the liquid phase mixture in oil production wells under certain temperature and pressure. A scientific guide for the calculation of temperature and pressure in oil production wells can be provided with the developed model.

Analysis of the impact of CO&lt;SUB align="right"&gt;2 content on the physical properties of the liquid phase mixtures in oil production wells

CO2 injection not only enhances oil recovery dramatically, but it also has a potential to reduce the greenhouse effect. During the process of CO2 displacement, when CO2 breaks through in oil production wells, CO2 content will impact the phase state and physical properties of the liquid phase mixture in wellbore. As a result, it will affect the calculation of temperature and pressure in oil production wells. Therefore, it is unacceptable to use the conventional black-oil model for calculating the phase state of miscible fluids. For dealing with this problem, we use a gas-liquid flash theory and a compositional model to develop a new model. The Jilin oilfield is used as a case study; the phase state (gas, liquid or gas-liquid) and physical properties of the liquid phase mixture (including CO2 and hydrocarbons) under initial conditions are calculated by this new model. The results indicate that the molar content of CO2 has a great impact on the physical properties of the liquid phase mixture in oil production wells under certain temperature and pressure. A scientific guide for the calculation of temperature and pressure in oil production wells can be provided with the developed model.

Nonequilibrium Interfacial Tension in Simple and Complex Fluids

Interfacial tension between immiscible phases is a well-known phenomenon, which manifests itself in everyday life, from the shape of droplets and foam bubbles to the capillary rise of sap in plants or the locomotion of insects on a water surface. More than a century ago, Korteweg generalized this notion by arguing that stresses at the interface between two miscible fluids act transiently as an effective, nonequilibrium interfacial tension, before homogenization is eventually reached. In spite of its relevance in fields as diverse as geosciences, polymer physics, multiphase flows, and fluid removal, experiments and theoretical works on the interfacial tension of miscible systems are still scarce, and mostly restricted to molecular fluids. This leaves crucial questions unanswered, concerning the very existence of the effective interfacial tension, its stabilizing or destabilizing character, and its dependence on the fluid's composition and concentration gradients. We present an extensive set of measurements on miscible complex fluids that demonstrate the existence and the stabilizing character of the effective interfacial tension, unveil new regimes beyond Korteweg's predictions, and quantify its dependence on the nature of the fluids and the composition gradient at the interface. We introduce a simple yet general model that rationalizes nonequilibrium interfacial stresses to arbitrary mixtures, beyond Korteweg's small gradient regime, and show that the model captures remarkably well both our new measurements and literature data on molecular and polymer fluids. Finally, we briefly discuss the relevance of our model to a variety of interface-driven problems, from phase separation to fracture, which are not adequately captured by current approaches based on the assumption of small gradients.

A sharp interface method for coupling multiphase flow, heat transfer and multicomponent mass transfer with interphase diffusion

Mixing of partially miscible fluids plays an important role in many physical and chemical processes. The modeling complexities lie in the tight coupling of the multiphase flow, heat transfer and multicomponent mass transfer, as well as diffusions across the phase interface. We present a sharp interface method for modeling such process. The non-ideal equation of state is used to compute the fluid properties such as density, fugacity and enthalpy, and to predict phase equilibrium composition. The phase interface location is tracked using the phase propagation velocity. A third-order one-sided finite difference scheme using a variable grid size according to the interface location is utilized to discretize the partial derivatives immediately next to the interface, while a second-order central scheme is used for the bulk of fluids. An optimization method, the Nelder–Mead method, is applied to search for (1) the phase compositions on both sides of the interface, and (2) the phase propagation velocity based on the coupling of the multicomponent phase equilibrium and the species' balance across the interface. The temperature at the interface is determined by the energy balance. Numerical results are used to demonstrate the convergence of our method and show its capability to simulate the mixing of multicomponent partially miscible fluids.

Confinement effect on the dynamics of non-equilibrium concentration fluctuations far from the onset of convection.

In a recent letter (C. Giraudet et al., EPL 111, 60013 (2015)) we reported preliminary data showing evidence of a slowing-down of non-equilibrium fluctuations of the concentration in thermodiffusion experiments on a binary mixture of miscible fluids. The reason for this slowing-down was attributed to the effect of confinement. Such tentative explanation is here experimentally corroborated by new measurements and theoretically substantiated by studying analytically and numerically the relevant fluctuating hydrodynamics equations. In the new experiments presented here, the magnitude of the temperature gradient is changed, confirming that the system is controlled solely by the solutal Rayleigh number, and that the slowing-down is dominated by a combined effect of the driving force of buoyancy, the dissipating force of diffusion and the confinement provided by the vertical extension of the sample cell. Moreover, a compact phenomenological interpolating formula is proposed for easy analysis of experimental results.

Convective instability in a two-layer system of reacting fluids with concentration-dependent diffusion

The development of convective instability in a two-layer system of miscible fluids placed in a narrow vertical gap has been studied theoretically and experimentally. The upper and lower layers are formed with aqueous solutions of acid and base, respectively. When the layers are brought into contact, the frontal neutralization reaction begins. We have found experimentally a new type of convective instability, which is characterized by the spatial localization and the periodicity of the structure observed for the first time in the miscible systems. We have tested a number of different acid–base systems and have found a similar patterning there. In our opinion, it may indicate that the discovered effect is of a general nature and should be taken into account in reaction–diffusion–convection problems as another tool with which the reaction can govern the movement of the reacting fluids. We have shown that, at least in one case (aqueous solutions of nitric acid and sodium hydroxide), a new type of instability called as the concentration-dependent diffusion convection is responsible for the onset of the fluid flow. It arises when the diffusion coefficients of species are different and depend on their concentrations. This type of instability can be attributed to a variety of double-diffusion convection. A mathematical model of the new phenomenon has been developed using the system of reaction–diffusion–convection equations written in the Hele–Shaw approximation. It is shown that the instability can be reproduced in the numerical experiment if only one takes into account the concentration dependence of the diffusion coefficients of the reagents. The dynamics of the base state, its linear stability and nonlinear development of the instability are presented. It is also shown that by varying the concentration of acid in the upper layer one can achieve the occurrence of chemo-convective solitary cell in the bulk of an almost immobile fluid. Good agreement between the experimental data and the results of numerical simulations is observed.

Nonlinear effects in buoyancy-driven variable-density turbulence

We consider the time dependence of a hierarchy of scaled $L^{2m}$-norms $D_{m,\unicode[STIX]{x1D714}}$ and $D_{m,\unicode[STIX]{x1D703}}$ of the vorticity $\unicode[STIX]{x1D74E}=\unicode[STIX]{x1D735}\times \boldsymbol{u}$ and the density gradient $\unicode[STIX]{x1D735}\unicode[STIX]{x1D703}$, where $\unicode[STIX]{x1D703}=\log (\unicode[STIX]{x1D70C}^{\ast }/\unicode[STIX]{x1D70C}_{0}^{\ast })$, in a buoyancy-driven turbulent flow as simulated by Livescu &amp; Ristorcelli (J. Fluid Mech., vol. 591, 2007, pp. 43–71). Here, $\unicode[STIX]{x1D70C}^{\ast }(\boldsymbol{x},t)$ is the composition density of a mixture of two incompressible miscible fluids with fluid densities $\unicode[STIX]{x1D70C}_{2}^{\ast }&gt;\unicode[STIX]{x1D70C}_{1}^{\ast }$, and $\unicode[STIX]{x1D70C}_{0}^{\ast }$ is a reference normalization density. Using data from the publicly available Johns Hopkins turbulence database, we present evidence that the $L^{2}$-spatial average of the density gradient $\unicode[STIX]{x1D735}\unicode[STIX]{x1D703}$ can reach extremely large values at intermediate times, even in flows with low Atwood number $At=(\unicode[STIX]{x1D70C}_{2}^{\ast }-\unicode[STIX]{x1D70C}_{1}^{\ast })/(\unicode[STIX]{x1D70C}_{2}^{\ast }+\unicode[STIX]{x1D70C}_{1}^{\ast })=0.05$, implying that very strong mixing of the density field at small scales can arise in buoyancy-driven turbulence. This large growth raises the possibility that the density gradient $\unicode[STIX]{x1D735}\unicode[STIX]{x1D703}$ might blow up in a finite time.

Fingering instability and mixing of a blob in porous media.

The curvature of the unstable part of the miscible interface between a circular blob and the ambient fluid in two-dimensional homogeneous porous media depends on the viscosity of the fluids. The influence of the interface curvature on the fingering instability and mixing of a miscible blob within a rectilinear displacement is investigated numerically. The fluid velocity in porous media is governed by Darcy's law, coupled with a convection-diffusion equation that determines the evolution of the solute concentration controlling the viscosity of the fluids. Numerical simulations are performed using a Fourier pseudospectral method to determine the dynamics of a miscible blob (circular or square). It is shown that for a less viscous circular blob, there exist three different instability regions without any finite R-window for viscous fingering, unlike the case of a more viscous circular blob. Critical blob radius for the onset of instability is smaller for a less viscous blob as compared to its more viscous counterpart. Fingering enhances spreading and mixing of miscible fluids. Hence a less viscous blob mixes with the ambient fluid quicker than the more viscous one. Furthermore, we show that mixing increases with the viscosity contrast for a less viscous blob, while for a more viscous one mixing depends nonmonotonically on the viscosity contrast. For a more viscous blob mixing depends nonmonotonically on the dispersion anisotropy, while it decreases monotonically with the anisotropic dispersion coefficient for a less viscous blob. We also show that the dynamics of a more viscous square blob is qualitatively similar to that of a circular one, except the existence of the lump-shaped instability region in the R-Pe plane. We have shown that the Rayleigh-Taylor instability in a circular blob (heavier or lighter than the ambient fluid) is independent of the interface curvature.

What Are Some Common Fire Flow Requirements for Municipalities?

Most municipalities are willing to incur higher costs for water distribution system sizing because of the reduction in loss made possible by using the water system for fire protection. Water in sufficient quantity can cool a fire; steam can deprive the fire of oxygen, and in the case of miscible or dense fluids, water can disperse the fuel. The key question for water utilities is how large must distribution system components be to provide sufficient water for fire protection.

Buoyant miscible displacement flows in vertical pipe

The displacement flow of two miscible Newtonian fluids is investigated experimentally in a vertical pipe of long aspect ratio (δ−1 ≈ 210). The fluids have a small density difference and they have the same viscosity. The heavy displacing fluid is initially placed above the light displaced fluid. The displacement flow is downwards. The experiments cover a wide range of the two dimensionless parameters that largely describe the flow: the modified Reynolds number (0 ≤ Ret⪅800) and the densimetric Froude number (0 ≤ Fr ≤ 24). We report on the stabilizing effect of the imposed flow and uncover the existence of two main flow regimes at long times: a stable displacement flow and an unstable displacement flow. The transition between the two regimes occurs at a critical modified Reynolds number RetCritical, as a function of Fr. We study in depth the stable flow regime: First, a lubrication model combined with a simple initial acceleration formulation delivers a reasonable prediction to the time-dependent penetrating displacing front velocity. Second, we find two sub-regimes for stable displacements, namely, sustained-back-flows and no-sustained-back-flows. The transition between the two sub-regimes is a marginal stationary interface flow state, which is also well predicted by the lubrication model. The unstable regime is associated to instabilities and diffusive features of the flow. In addition, particular patterns such as front detachment phenomenon appear in the unstable flow regime, for which we quantify the regions of existence versus the dimensionless groups.

Experimental study of 3D Rayleigh–Taylor convection between miscible fluids in a porous medium

The natural convection of miscible fluids in porous media has applications in several fields, such as geoscience and geoengineering, and can be employed for the geological storage of CO2. In this study, we used X-ray computer tomography to visualize 3D fingering structures associated with the Rayleigh–Taylor instability between miscible fluids in a porous medium. In the early stages of the onset of the Rayleigh–Taylor instability, a fine crinkling pattern gradually appeared at the interface. As the wavelength and amplitude increased, descending fingers formed on the interface and extended vertically downward; in addition, ascending and highly symmetric fingers formed. The adjacent fingers were cylindrical in shape and coalesced to form large fingers. The fingers appearing on the interface tended to become finer with increasing Rayleigh number, which is consistent with linear perturbation theory. When the Péclet number exceeded 10, transverse dispersion increased the finger diameter and enhanced the finger coalescence, strongly impacting the decrease in finger number density. When mechanical dispersion was negligible, the finger-extension velocity and the dimensionless mass-transfer rate scaled with the characteristic velocity and the Rayleigh number with an appropriate length scale. Mechanical dispersion not only reduced the onset time but also enhanced the mass transport.

DISTRIBUTION OF SOLUTES NO3 - E Ca IN SOIL COLUMNS WITH VINASSE

Simulation models can provide a better understanding of the processes occurring in the soil displacement relative to solutes, and is applicable to research tools to minimize impacts on the environment. Thus, this study aimed to determine the retardation factors, diffusive-dispersive coefficients involved in the transport and distribution of vinasse effluent curves for the ions Calcium and Nitrate in soil columns. The Alfisol was collected in the rural municipality of Piracicaba-SP, soil samples were collected at 0-0.20 m depth. For the manufacture of columns was used PVC tubing 0.25 m long and 0.05 cm in diameter, wire mesh, and fast filter paper at one end, fastened by a cap bottomless PVC screw. The volumes of 10 mL were collected, defined in terms of pore volume (related to the porosity of the soil, taken generally around 50%) and the amount required to be performed the analysis of chemical components NO3 (nitrate) and Ca (calcium). We used the computer program to calculate the DISP parameters of solute transport in soil miscible fluid displacement. The transport parameters showed the positive effects of adsorption and calcium ion present in the shift vinasse. For the nitrate ion, despite the breakthrough curve not have adjusted the parameters indicate low adsorption to soil may be moved to greater depths.

Three-dimensional structure of natural convection in a porous medium: Effect of dispersion on finger structure

Density-driven natural convection in a porous medium is of great interest in the geoscience and geoengineering fields, especially for carbon dioxide capture and storage (CCS). In this study, we applied a novel experimental approach to three-dimensional (3D) imaging of density-driven natural convection in a porous medium. Miscible fluid pairs with nonlinear density properties (a sodium chloride solution and a mixture of methanol and ethylene glycol doped with sodium iodide) were used to model density-driven natural convection from 3D imaging captured by X-ray computed tomography (CT). Slight fluctuations that appeared at the interface grew into large “fingers,” which interacted and merged with the neighboring fingers. The fingers extended vertically downward without changing their locations, forming a columnar structure. The finger-extension velocity increased in line with the Rayleigh number and was correlated with the characteristic velocity. The 3D images captured the local concentration of fingers in the course of convective mixing. We found that the decrease in finger-number density was not only related to the Rayleigh number but was also affected by transverse dispersion between the downward- and upward-flow regions. There was an exponential relationship between the finger-number density and the transverse dispersion coefficient. Transverse dispersion caused broadening of the fingers and reduction in the finger-number density because of the interaction and merging of fingers. In carbon dioxide (CO2) geological storage applications, this transverse dispersion influences the long-term-dissolution process of CO2 injected into aquifers.

Inertial destabilization of highly viscous microfluidic stratifications

The formation and stability of viscous stratifications made between miscible fluids are experimentally investigated in square microchannels. The authors characterize the appearance and dynamics of traveling interfacial waves, which offer useful features for implementing in-line mixing procedures between highly viscous fluids in microfluidic systems.