Miscible Fluids Research Articles

Harmonic to subharmonic transition of the Faraday instability in miscible fluids

When a stable stratification between two miscible fluids is excited by a vertical and periodic forcing, a turbulent mixing zone can develop, triggered by the Faraday instability. The mixing zone grows and saturates to a recently predicted final value L sat [Grea and Ebo Adou, J. Fluid Mech. 837, 293 (2018)] when resonance conditions are no longer fulfilled. Notably, it is expected from the Mathieu stability diagram that the instability may evolve from a harmonic to a subharmonic regime for particular initial conditions. This transition is evidenced here in the full inhomogeneous system using direct numerical simulations with 1024 3 points: the analysis of one-point statistics and spectra reveals that turbulence is greatly enhanced after the transition, while the global anisotropy of both the velocity and concentration fields is significantly reduced. Furthermore, using the concept of sorted density field, we compute the background potential energy e b p of the flow, which increases only after the transition as a signature of irreversible mixing. While the gain in e b p strongly depends on the control parameters of the instability, the cumulative mixing efficiency is more robust. At saturation of the instability, available potential energy is partially released in the flow as background potential energy. Finally, it is shown numerically that for fixed parameters, a multiple-frequency forcing can modify the duration of the harmonic regime without significantly altering the asymptotic state.

Janus Dimers at Liquid-Liquid Interfaces.

We study the impact of selected parameters on the behavior of Janus-like dimers at liquid-liquid interface. The equilibrium orientation and the adsorption depth of a single Janus dimer are calculated using a simple phenomenological method. We have also performed molecular dynamics simulations for different numbers of Janus dimers trapped at the interface between two partially miscible Lennard-Jones fluids. The particles with different wettabilities of both parts of Janus dimers are considered. Depending on the assumed energy parameters, we observe various structures: orientationally ordered monolayers, fractal-like aggregates, compact clusters, and ordered multilayers containing alternately arranged layers built of Janus particles and molecules of the fluids.

Chemo-mechanical coupling constitutive model for chalk considering chalk–fluid physicochemical interaction

Chalk shows a pronounced water-weakening effect, which can be attributed to the microscopic physicochemical interactions between the pore fluid and the chalk matrix. In this paper a conceptual elastoplastic model is developed for describing the chemo-mechanical behaviour of chalk based on the framework of the modified Cam Clay model. Central to the model is the concept of intergranular stresses, introduced as the substitute for Terzaghi's effective stress to describe the chalk behaviour. In this context, the microscopic physicochemical interactions are characterised by introducing a macroscopic surface force potential. The composition and significance of pore water pressure are analysed, and the intergranular stress tensor is explicitly defined. To address the hardening effect of the microscopic physicochemical interactions, the preconsolidation pressure function is modified by introducing the intrinsic intergranular pressure as an additional hardening variable that accounts solely for the chalk–fluid interaction. It is shown that the proposed concept of intergranular stresses can address the effects of osmosis, adsorption and capillarity on the chalk behaviour in a consistent and systematic way. Comparisons between the theoretical simulations and experimental results demonstrate that the proposed model is capable of capturing the main features of the chemo-mechanical behaviour of chalk saturated with an individual or two (miscible or immiscible) fluids.

Diffusion-driven transition between two regimes of viscous fingering

Diffusion between miscible fluids in the viscous-fingering instability produces an unexpected transition into a novel pattern. Usually thought of as a two-dimensional phenomena, this works shows the importance of three-dimensional structure to the patterns that form.

Interfacial phenomena in immiscible liquids subjected to vibrations in microgravity

We consider the response to periodic forcing between 5 Hz and 50 Hz of an interface separating immiscible fluids under the microgravity conditions of a parabolic flight. Two pairs of liquids with viscosity ratios differing by one order of magnitude are investigated. By combining experimental data with numerical simulations, we describe a variety of dynamics including harmonic and subharmonic (Faraday) waves, frozen waves and drop ejection, determining their thresholds and scaling properties when possible. Interaction between these various modes is facilitated in microgravity by the relative ease with which the interface can move, altering its orientation with respect to the forcing axis. The effects of key factors controlling pattern selection are analysed, including vibrational forcing, viscosity ratio, finite-size effects and residual gravity. Complex behaviour often arises with features on several spatial scales, such as Faraday waves excited on the interface of a larger columnar structure that develops due to the frozen wave instability – this type of state was previously seen in miscible fluid experiments but is described for the first time here in the immiscible case.

Revisiting the linear stability analysis and absolute–convective transition of two fluid core annular flow

Numerous experimental, numerical and theoretical studies have shown that core annular flows can be unstable. This instability can be convective or absolute in different situations: miscible fluids with matched density but different viscosities, creeping flow of two immiscible fluids or buoyant flow along a fibre. The analysis of the linear stability of the flow equation of two fluids injected in a co-current and concentric manner into a cylindrical tube leads to a rather complex eigenvalue problem. Until now, all analytical solution to this problem has involved strong assumptions (e.g. lack of inertia) or approximations (e.g. developments at long or short wavelengths) even for axisymmetric disturbances. However, in this latter case, following C. Pekeris, who obtained, almost seventy years ago, an elegant explicit solution for the dispersion relationship of the flow of a single fluid, we derive an explicit solution for the more general case of two immiscible fluids of different viscosity, density and inertia separated by a straight interface. This formulation is well adapted to commercial software. First, we review the creeping flow limit (zero Reynolds number) of two immiscible fluids as it is used in microfluidics. Secondly, we consider the case of two fluids of different viscosities but of the same density in the absence of surface tension and also without diffusion (i.e. miscible fluids with infinite Schmidt number). In both cases, we study the transition from convective to absolute instability according to the different control parameters.

Influence of artificial aging on the lubricating ability of water miscible metalworking fluids

The understanding of the complex aging processes of water miscible metalworking fluids and their effect on the performance in machining processes is of high relevance for the metalworking industry. Nevertheless, only little knowledge is available in this context. Due to the highly dynamic interactions in the complex ecosystem “metalworking fluid”, a distinct correlating of the aging process with the performance of the fluid in metalworking processes is hardly possible. Consequences of the aging process on physical, chemical and biological properties of the fluid have been described in several research works. These consequences comprise aspects such as the decrease of the pH-value, the increase of the droplet size, the presence of bacterial cells or the modification of the metalworking fluid composition. The novel approach of the presented work aims to investigate the individual influence of isolated aging aspects on the lubricity of metalworking fluids. Therefore, selected aging aspects were artificially varied separately from each other and evaluated in tribological experiments. It could be shown that the physical presence of bacterial cells as well as extracellular polymeric substances have positive influence on the lubricating ability while the pH-value has no effect and the droplet size only a slight influence on the fluids performance. The results reveal essential knowledge for the design of future monitoring and maintenance strategies for water miscible metalworking fluids.

Quantification and Evaluation of Thermodynamic Miscibility in Nanoconfined Space

In this paper, thermodynamic miscibility in nanoconfined spaces is quantified and evaluated. First, an analytical generalized equation of state (EOS) is developed by considering the effects of pore radius, molecule–molecule interaction, and molecule–wall interaction at nanometer scale, on the basis of which four extended cubic EOS are proposed. Second, the analytical formulations of the confined fluid free energy of mixing and solubility parameter at nanometer scale are developed thermodynamically. Third, the free energy of mixing and solubility parameter are calculated under different conditions, by means of which the conditions and characteristics of the fluid miscibility at nanometer scale are specifically studied. Finally, two important factors, the temperature and molecule–wall (m–w) interaction, are specifically studied to evaluate and compare their effects on miscibility. The fluid miscibility benefits from the reduction of the pore radius, while the m–w interaction is detrimental to the developmen...

Electric field mediated von Kármán vortices in stratified microflows: transition from linear instabilities to coherent mixing

Application of an electric field across the pressure-driven stratified flow of a pair of miscible fluids inside a microchannel manifests interesting electrohydrodynamic (EHD) instabilities. Experiments uncover distinctive instability regimes with an increase in electric field Rayleigh number ($Ra^{\unicode[STIX]{x1D713}}$) – a linear-onset regime, a time-periodic nonlinear regime analogous to the von Kármán vortex street in the downstream and a regime with coherent flow patterns. The experiments also reveal that such linear and nonlinear instabilities can be stimulated non-invasively in a microchannel to mix or de-mix fluids simply by turning the electric field on or off, indicating the suitability of the process for on-demand micromixing. The characteristics of these instabilities have been theoretically investigated with the help of an Orr–Sommerfeld framework, which discloses the possibility of five distinctive finite-wavenumber modes for the instability. The EHD stresses originating due to the application of electric field stimulate a pair of shorter-wavelength electric field modes beyond a critical value of $Ra^{\unicode[STIX]{x1D713}}$. Increase in the levels of charge injection and EHD stresses lower the critical $Ra^{\unicode[STIX]{x1D713}}$ of these modes. The relatively longer-wavelength viscous mode is found to appear when the viscosity stratification between the fluid layers is high. Beyond a threshold Schmidt number ($Sc$), a diffusive mode is also found to appear near the mixed interfacial region. A thinner interface between the fluids at a higher $Sc$ helps this mode to behave as the interfacial mode of immiscible fluids. Contrast of ionic mobility in the fluids leads to the appearance of the K-mode of instability at much shorter wavelengths. The reported phenomena can be of significance in the domains of microscale mixing, pumping, heat exchange, mass transfer and reaction engineering.

Characterization of fluid mixing in a closed container under horizontal vibrations

The mixing characteristics of two initially stratified miscible fluids in a closed container vibrated horizontally are studied numerically by a validated computational fluid dynamics model. The flow characteristics and interfacial dynamics in the closed vibrating container are analyzed, and the effects of vibration parameters and gravity on mixing efficiency are evaluated both quantitatively and qualitatively. The results show that interfacial instability occurs in the closed container, which leads to interfacial deformation and breakup and quickens mixing. Two distinct stages of the mixing process can be observed in the closed vibrating container. During the macro‐mixing, an increasingly sharp gradient of the concentration field is generated. During the micro‐mixing, the mixing process is dominated by the diffusion of the concentration field and ends up with a nearly homogeneous mixture. The intensification of mixing process by vibration is most pronounced in the absence of static gravity. The gravity can suppress the interfacial instability and retard the mixing process. Over the range of conditions investigated in this paper, vibration is an efficient approach for mixing miscible liquids in a closed container.

Mixing process of two miscible fluids in a lid-driven cavity

A laminar lid-driven cavity flow was constructed to represent the fundamental characteristics of an industrial dynamic mixer. The flow patterns and mixing process in the cavity were measured by using particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) experiments respectively. The refractive indices of the two miscible liquids involved were carefully matched to allow for unhindered optical access. The mixing process was predicted by using computational fluid dynamics (CFD) including models for species transport. The simulated flow and mixing results are in good agreement with the experimental data. The effects of density difference and viscosity of the two miscible fluids on the mixing process were evaluated. Minor variations in the densities of the fluids have significant influence on the mixing process in terms of the coefficient of variation as a function of time. The dimensionless group ArRe (Archimedes number over Reynolds number) is proposed to characterize the mixing process in the cavity.

Thermal convection instability of two miscible viscous fluids in a Hele-Shaw cell

The onset of convection in two superimposed miscible fluid layers is investigated in the configuration of a geometric Hele-Shaw cell using linear stability analysis. The two fluids have different densities. We neglect the surface tension and chemical diffusion at the interface which is assumed of small amplitude. We consider only the asymptotic case, where the Prandtl number’s order is of the order of unity or larger than unity. We show, in the Hele-Shaw configuration, which can simulate convection in porous media, that the onset of convection can be either stationary or oscillatory depending on the Buoyancy number, B (the ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly), which depends on the viscosity and layer height ratios. When the buoyancy number is lower than a critical value, Bc, oscillating convection occurs in the whole cell height, however beyond Bc, the stratified regime develops without deformation of the interface and convection occurs separately in each layer. In this paper, the transition from oscillatory regime to stratified regime is visualised by using the streamlines at the onset of convection

Controllable production of Janus ligaments by AC fields in a flow-focusing junction

We report the production of bicomponent Janus filaments of miscible aqueous fluids in a microfluidic electro-flow-focusing device under the action of an AC electric field. The production of liquid filaments can lead to the generation of microfibers by adding a subsequent process of polymerization. Janus microfibers are of paramount importance in biomedical applications such as tissue production on crimped scaffolds. We show that the filament length is a function of the frequency signal, voltage amplitude and of the viscosity and conductivity of the dispersed phase. In particular, Janus filaments with diameters $$\sim 10\,\upmu$$ m and longer than 1 mm are produced by AC voltages with frequencies below 150 kHz and a viscosity of the dispersed phase $$\sim 10\,$$ cP.

Fingering of Miscible Fluids Associated with Gel Formation Reaction

Fingering of Miscible Fluids Associated with Gel Formation Reaction

In Situ Partial Treatment of Single Cells by Laminar Flow in the "Open Space".

Regional difference of a single cell is nonignorable, which means it is not precise to investigate the single cell as a homogeneous object. A convenient method to investigate cellular response to the treatment at the subcellular level is still needed. In this work, we developed a microfluidic approach for manipulating a partial region of a single adherent cell by generating a stable distribution of microenvironments. By controlling flow rates and the gap between the probe and substrate, the diffusion effect can be adjusted as needed. Distribution of the solute was revealed by fluorescein, demonstrating the stability of the interface between two miscible fluids. Partial lysis of single cells (Caco-2, MCF-7, U87 cells) was successfully performed, and partial staining (Mito-Tracker Green FM, Mito-Tracker Red CMXRos, ER-Tracker Green) of a single cell (U87) was explored. Self-healing and regeneration of a single U87 cell after partial lysis was also observed. All of those results demonstrated the feasibility and significance of our idea. The method would be a promising tool for further single-cell analysis and subcellular research.

Sensitivity analyses in a buoyancy-driven closed system with high resolution CFD using Boussinesq approximation and variable density models

The influences of the Schmidt number and fluid models of the Boussinesq approximation and variable density (low-Mach formulation) are investigated using large eddy simulation (LES) where fluid naturally advects between two tanks connected by a pipe. The geometry resembles a reactor-like vessel which comprises of a cold leg-downcomer region. The closed system consists of two miscible fluids with different densities and viscosities separated by a valve. Analysis with Reynolds-Averaged Navier–Stokes (RANS) is used for calculating Taylor length scales to establish minimum grid resolution for LES. Using particle image velocimetry (PIV) data, validation is conducted for four different magnitudes of Schmidt numbers. Evidence indicates that capturing the effects from the highest Schmidt number is essential for properly predicting fluctuations and instabilities in the flow. Although downcomer comparisons with PIV consist of larger errors, they are explained through additional sensitivity analyses involving initial conditions, geometry, and residual energy. Lastly, the influence of larger density differences is demonstrated using simulations with a higher Atwood number, temporally scaled using the fluid front velocity. Recommendations are made regarding future experiments and simulations for design of similar buoyant mixing problems.

Dissolution-driven convection in a heterogeneous porous medium

Motivated by subsurface carbon sequestration, an experimental investigation of dissolution-driven Rayleigh–Darcy convection using two miscible fluids in a Hele-Shaw cell is conducted. A thin horizontal layer of circular impermeable discs is inserted to create an environment with heterogeneous and anisotropic permeability. The Sherwood number that measures the convective mass transfer rate between two fluids at the interface is linked to different parameters of the disc layer, including the disc size, spacing, layer permeability and its relative height with respect to the fluid interface. It is surprising that the convective mass transfer rate in our configuration is dominated by the disc spacing, but almost independent of either the disc size or the mean permeability of the layer. To explain this dependence, the convective mass transfer rate is decomposed into the number, velocity and density contrast of fingers travelling through the disc layer. Both the number and density contrast of fingers show dependences on the disc layer permeability, even though the product of them, the mass transfer rate, does not. In addition, the density contrast also shows a non-monotonic dependence on the disc spacing. The transition point is at a spacing that is close to the finger width. Based on this observation, a simple model based on mixing and scale competition is proposed, and it shows an excellent agreement with the experimental results.

Non-modal stability analysis of miscible viscous fingering with non-monotonic viscosity profiles

A non-modal linear stability analysis (NMA) of the miscible viscous fingering in a porous medium is studied for a toy model of non-monotonic viscosity variation. The onset of instability and its physical mechanism are captured in terms of the singular values of the propagator matrix corresponding to the non-autonomous linear equations. We discuss two types of non-monotonic viscosity profiles, namely, with unfavourable (when a less viscous fluid displaces a high viscous fluid) and with favourable (when a more viscous fluid displaces a less viscous fluid) endpoint viscosities. A linear stability analysis yields instabilities for such viscosity variations. Using the optimal perturbation structure, we are able to show that an initially unconditional stable state becomes unstable corresponding to the most unstable initial disturbance. In addition, we also show that to understand the spatio-temporal evolution of the perturbations it is necessary to analyse the viscosity gradient with respect to the concentration and the location of the maximum concentration $c_{m}$. For the favourable endpoint viscosities, a weak transient instability is observed when the viscosity maximum moves close to the pure invading or defending fluid. This instability is attributed to an interplay between the sharp viscosity gradient and the favourable endpoint viscosity contrast. Further, the usefulness of the non-modal analysis demonstrating the physical mechanism of the quadruple structure of the perturbations from the optimal concentration disturbances is discussed. We demonstrate the dissimilarity between the quasi-steady-state approach and NMA in finding the correct perturbation structure and the onset, for both the favourable and unfavourable viscosity profiles. The correctness of the linear perturbation structure obtained from the non-modal stability analysis is validated through nonlinear simulations. We have found that the nonlinear simulations and NMA results are in good agreement. In summary, a non-monotonic variation of the viscosity of a miscible fluid pair is seen to have a larger influence on the onset of fingering instabilities than the corresponding Arrhenius type relationship.

How surfactant-decorated nanoparticles contribute to thermodynamic miscibility

In this study, mineral oil–water fluid miscibility without and with the addition of surfactant-decorated nanoparticles is experimentally and theoretically studied. First, three series of interfacial tension (IFT) tests are conducted using a spinning drop tensiometer (SDT) with the addition of hexadecyltrimethylammonium bromide (CTAB) surfactant-decorated SiO2 nanoparticles at different concentrations. Second, a new comprehensive thermodynamic model is developed to describe the fluid miscibility without and with the addition of these surfactant-decorated nanoparticles, which is also applied theoretically to reveal how the surfactant-decorated nanoparticles contribute to the thermodynamic miscibility state. The thermodynamic model developed is proven to be accurate and physically meaningful by comparing its calculated free energy of mixing with the experimental results and examples from the literature. A series of optimum conditions for the improvement of fluid miscibility by the addition of such surfactant-decorated nanoparticles are determined: a lower temperature, a higher pressure, more wetting conditions, a smaller nanoparticle radius (rNP < 40 nm), a larger surfactant concentration, and a nanoparticle concentration in the range of 0.5–0.6 wt.%. It should be noted that a higher nanoparticle concentration is required with the addition of more CTAB surfactants in order to reach the most miscible state. Moreover, the effect of surfactant concentration on the miscibility development is found to be independent of the nanoparticle radius, whereas the optimum nanoparticle concentration is reduced with increasing particle size.

Analysis of MHD micro-mixers with differential pumping capabilities for two different miscible fluids

In this study, newly devised is a magneto-hydrodynamic (MHD) micro-mixer capable of differential pumping of two different miscible fluids, and numerically investigated are the mixing performance and the mass flow rates of the two fluids. By artfully applying different potentials to different electrode pairs, Lorentz-force with different sizes can be created, driving the liquids in a desired direction for pumping, and inducing fluid circulation at a cross-section for mixing. The results show that the micro-mixer proposed in this study can achieve high mixing performance for electrolytes, together with differential pumping capabilities for the two different miscible fluids. The effect of the total difference in potential applied to the electrodes in pumping section on the mixing performance is numerically analyzed. Also, rectangular and H-shaped cross-sections for pumping section have been examined to explore the geometrical effect on the differential pumping capability.