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DOE OSTI2020

Empirical correlations for prediction of minimum miscible pressure and near-miscible pressure interval for oil and CO 2 systems

Although near-miscible CO 2 flooding has recently received considerable attention, no criteria are available to predict its applicability to a specific reservoir. Evaluating the viability of near-miscible flooding requires experimental exploration of a specific region in pressure–temperature space. The near-miscible pressure field is bounded on one side in P, T space by the MMP (minimum miscible pressure). This paper provides robust empirical correlations to estimate the MMP for both pure and impure CO 2 and for prediction of the near-miscible pressure region for CO 2 -oil. Many slim tube analyses, lacking high density data points, systematically underestimate the MMP, when the near miscible region is not accounted for. They are based on 147 published data sets that include: slim tube experimental determination of MMP; interfacial tension (IFT) between oil and CO 2 ; concentration of solution gas; and purity of the CO 2 . This paper is the first to begin a systematic exploration of the pressure-temperature space within which near-miscible effects characterize CO 2 floods. Our new correlations provide a basis for identifying and investigating the nature of near miscible effects associated with existing CO 2 floods. For a case study of an offshore field we determined that lower and upper pressure boundaries for effective near-miscible flooding, are 0.87 MMP and 1.07 MMP at reservoir temperatures. The proposed model is the first empirical correlation for the prediction of near-miscible pressure region, it will provide the basis for both screening the relative potential of oil reservoirs for economically viable miscible or near-miscible CO 2 -flooding.

42 ENGINEERING↗

DOE OSTI2021

Separating Miscible Liquid–Liquid Mixtures Using Supported Ionic Liquid Membranes

Supported liquid membranes (SLMs) are promising in separating miscible liquid–liquid mixtures, which has been a key challenge in wastewater treatment and other applications. However, SLMs suffer from poor durability due to the loss of the liquid phase. In current work, ionic liquids (ILs) with high stability have been impregnated into polyvinylidene fluoride membranes to separate miscible benzene–heptane mixtures. The two imidazolium-based ILs, that is, 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF 6 ]) and 1-butyl-3-methylimidazolium tris(pentafluoroethyl) trifluorophosphate ([BMIM][FAP]), were tested in supported ionic liquid membranes (SILMs) for the benzene–heptane separation. Both ILs show successful separation within 48 h as indicated by nuclear magnetic resonance results. Compared to the SILM with [BMIM][FAP], the SILM with [BMIM][PF 6 ] has lower throughput and higher selectivity. The higher selectivity can be attributed to the higher hydrophilicity of [BMIM][PF 6 ], which results in strong repulsion against heptane. The lower throughput can be attributed to the higher hydrophilicity as well since it lowers the solubility of benzene in [BMIM][PF 6 ]. The stability of IL in SILMs has also been investigated via multiple separation cycles. The scanning electron microscopy, weight change of SILMs, and separation results indicate that the separation efficiency of the [BMIM][PF 6 ] SILM does not degrade for up to 144 h. The SILM has been further optimized with curvature design (i.e., curved SILM) to increase the interfacial area and thus increase the separation throughput, where the curved SILM separation device was 3D-printed. Here, the findings here have important implications on design and application of SILMs in separating miscible liquid–liquid mixtures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Continuous Liquid–Liquid Extraction and in-Situ Membrane Separation of Miscible Liquid Mixtures

Separation operations are critical across a wide variety of manufacturing industries and account for about one quarter of all in-plant energy consumption in the United States. Conventional liquid-liquid separation operations require either thermal or chemical treatment, both of which have a large environmental impact and carbon footprint. Consequently, there is a great need to develop sustainable, clean methodologies for separation of miscible liquid mixtures. The greatest opportunities to achieve this lie in replacing high-energy separation operations (e.g., distillation) with low-energy alternatives such as liquid-liquid extraction. One of the primary design challenges in liquid-liquid extraction is to maximize the interfacial area between two immiscible (e.g., polar and non-polar) liquids for efficient mass transfer. However, this often involves energy-intensive methods including ultrasonication, pumping the feed and the extractant through packed columns with high tortuosity, or using a supercritical fluid as an extractant. Emulsifying the feed and the extractant, especially with a surfactant, offers a large interfacial area, but subsequent separation of emulsions can be energy-intensive and expensive. Thus, emulsions are typically avoided in conventional extraction operations. Herein, we discuss a novel, easily scalable, platform separation methodology termed CLEANS (Continuous Liquid-liquid Extraction And iN-situ membrane Separation). CLEANS integrates emulsion-enhanced extraction with continuous, gravity-driven, membrane-based separation of emulsions into a single unit operation. Furthermore, our results demonstrate that the addition of a surfactant and emulsification significantly enhance extraction (by > 250% in certain cases), even for systems where the best extractants for miscible liquid mixtures are known. Utilizing the CLEANS methodology, we demonstrate continuous separation of a wide range of miscible liquid mixtures, including soluble organic molecules from oils, alcohols from esters, and even azeotropes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Membrane synthesis via in-situ pore formation in silica gels through dynamic miscibility with soybean oil

The dynamic immiscibility between vegetable oil and organic silica precursors during sol-gel synthesis was used to tailor the microstructure of gels made with tetraethoxysilane (TEOS) or tetraethoxysilane+methyltrimethoxysilane (MTMS). Vegetable oil was investigated as an environmentally friendly and cheaper alternative to many other porogens. Oil concentrations of 9.09 v/v% and 33.33 v/v% were studied. For both TEOS and TEOS+MTMS gels, the miscibility of the oil and precursor decreases as the silica gel network forms, leading to oil-rich regions within the silica matrix. Gels containing MTMS maintained partial miscibility with the oil during gel formation due to the non-hydrolysable methyl groups on the MTMS. The pore structure of MTMS gels appeared more interconnected compared to the isolated pores observed in gels made with only TEOS. To create membranes with hierarchical pore structures, solvent exchanges were performed on gels or dried gels (i.e., xerogels) were calcined. The effect of the methyl group was also observed in the results of the time sweep rheology, as the addition of oil to the TEOS+MTMS gels caused an increase in the time to form the spanning gel. The trend was the opposite for oil additions to TEOS gels, which only contained polar groups. Xerogel membranes made with TEOS+MTMS had higher specific surface areas (SSAs) than those made with TEOS. For oil concentrations of 33.33 v/v%, xerogels made from TEOS+MTMS had an average SSA of 1068 + 113 m2 g-1, an order of magnitude higher than the average SSA of 103 + 6 m2 g-1 for xerogels made with TEOS.

sol-gel, dynamic immiscibility, oil-alkoxide inter↗

DOE OSTI2023

Ion Solvation-Driven Liquid–Liquid Phase Separation in Divalent Electrolytes with Miscible Organic Solvents

Liquid–liquid phase separation (LLPS) is a common phenomenon, but LLPS of electrolytes prepared in miscible organic solvents is rarely documented. Here we report four cases of LLPS that occur in MgTFSI 2 or ZnTFSI 2 electrolytes in mixed organic solvents. The conditions for the formation of this LLPS share four common features: cations with high charge density; bulky anions with low charge density; a strongly coordinating solvent with high compressibility; and a relatively weak coordinating solvent with low relative permittivity and high mobility. With these conditions, the cations tend to draw the strongly coordinating solvents together to form a densely-packed, energetically-favorable ion solvation region, while the cosolvents with low relative permittivity tend to repel ions to form an ion-depleted dilute phase. Furthermore, in the dilute upper layer with more than 300 solvent molecules per cation, ion pairs and large ion aggregates are clearly evidenced, due to the incomplete screening of electrostatic interactions by the weaker cosolvent. This LLPS driven by ion solvation may be more common in multivalent electrolytes and is a design consideration with mixed solvents that should not be overlooked.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2003

Transient Interfacial Phenomena in Miscible Polymer Systems (TIPMPS)

Almost one hundred years ago Korteweg published a theory of how stresses could be induced in miscible fluids by concentration gradients, causing phenomena that would appear to be the same as with immiscible fluids. Miscible fluids could manifest a transient or effective interfacial tension (EIT). To this day, there has been no definitive experiment to confirm Korteweg's model but numerous fascinating and suggestive experiments have been reported. The goal of TIPMPS is to answer the question: Can concentration and temperature gradients in miscible materials induce stresses that cause convection? Many polymer processes involving miscible monomer and polymer systems could be affected by fluid flow and so this work could help understand miscible polymer processing, not only in microgravity, but also on earth. Demonstrating the existence of this phenomenon in miscible fluids will open up a new area of study for materials science. The science objectives of TIPMPS are: (1) Determine if convection can be induced by variation of the width of a miscible interface; (2) Determine if convection can be induced by variation of temperature along a miscible interface; (3) Determine if convection can be induced by variation of conversion along a miscible interface An interface between two miscible fluids can best be created via a spatially-selective photopolymerization of dodecyl acrylate with a photoinitiator, which allows the creation of precise and accurate concentration gradients between polymer and monomer. Optical techniques will be used to measure the refractive index variation caused by the resultant temperature and concentration fields. The viscosity of the polymer will be measured from the increase in the fluorescence of pyrene. Because the large concentration and temperature gradients cause buoyancy-driven convection that prevents the observation of the predicted flows, the experiment must be done in microgravity. In this report, we will consider our efforts to estimate the square gradient parameter, k, and our use of the estimates in modeling of the planned TIPMPS experiments. We developed a model consisting of the heat and diffusion equations with convective terms and of the Navier-Stokes equations with an additional volume force written in the form of the Korteweg stresses arising from nonlocal interaction in the fluid. The fluid's viscosity dependence on polymer conversion and temperature was taken from measurements of poly(dodecyl acrylate). Numerical modeling demonstrated that significant flows would arise for conditions corresponding to the planned experiments.

Pojman, John A.↗

DOE OSTI2026

Miscibility and Cocrystallization in Ethylene–Vinyl Alcohol Copolymer Blends

The compatibility among different ethylene−vinyl alcohol (EVOH) copolymer grades plays a crucial role in determining how easily they can be recycled when present together in a mixed waste stream. In this work, melt miscibility and cocrystallization in 50/50 wt/wt binary blends of EVOH copolymers with differing ethylene content were studied. Blends with up to a 21 mol % difference in composition were analyzed. Thin films of miscible blends appeared homogeneous in the melt as observed under an optical microscope, whereas AFM height images showed that immiscible blends underwent surface roughening due to phase separation. For copolymers with modest composition differences, the blend behaved as a single component, showing single, narrow melting and crystallization peaks in DSC thermograms, indicating cocrystallization at the level of crystal stems. Interestingly, even phase-separated blends demonstrated partial cocrystallization due to partial miscibility of the components in the molten phase-separated domains. The extent of cocrystallization is governed by the difference in freezing points of the components; rapid cooling increased cocrystallization in the blends. The maximum compositional difference allowed for miscibility is not constant but depends on the blend’s average comonomer content, in agreement with the “miscibility window” calculated from literature pressure−volume−temperature behavior for the individual EVOH copolymers and regular mixing theory. This study helps illuminate the effect of copolymer composition on miscibility, as well as cocrystallization behavior in blends of random copolymers with cocrystallizable units.

Cocrystallization↗

DOE OSTI2024

Complete miscibility of immiscible elements at the nanometre scale

Understanding the mixing behaviour of elements in a multielement material is important to control its structure and property. When the size of a multielement material is decreased to the nanoscale, the miscibility of elements in the nanomaterial often changes from its bulk counterpart. However, there is a lack of comprehensive and quantitative experimental insight into this process. Here, in this study, we explored how the miscibility of Au and Rh evolves in nanoparticles of sizes varying from 4 to 1 nm and composition changing from 15% Au to 85% Au. We found that the two immiscible elements exhibit a phase-separation-to-alloy transition in nanoparticles with decreased size and become completely miscible in sub-2 nm particles across the entire compositional range. Quantitative electron microscopy analysis and theoretical calculations were used to show that the observed immiscibility-to-miscibility transition is dictated by particle size, composition and possible surface adsorbates present under the synthesis conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Using phase boundary mapping to resolve discrepancies in the Mg 2 Si–Mg 2 Sn miscibility gap

Mg 2 Si–Mg 2 Sn compositions within the Mg–Si–Sn materials system have potential as inexpensive, efficient thermoelectrics. These compositions lie specifically along the pseudobinary line with compositions of Mg 2 Si 1-x Sn x . The alloying and possible nanostructuring within the miscibility gap could further increase the thermoelectric figure of merit (zT) for these materials. However, the solubility limits of the miscibility gap differ greatly in the literature. Such a discrepancy could be a result of differing Mg-compositions due to excess magnesium added during sample annealing. To define these limits better and explain the change in proposed solubility limits based on magnesium content, the three-phase regions on either side of the pseudobinary phase region are phase boundary mapped and defect energy calculations are performed. This study presents a new understanding of the Mg–Si–Sn ternary phase diagram around the pseudobinary phase region. The solubility limits on either side of the pseudobinary should be essentially identical between the Mg-rich and Mg-poor three-phase regions unless the system temperature is brought above about 565 °C, at which eutectic liquid Mg 0.9 Sn 0.1 forms. This creates a second Mg-rich three-phase region which intersects the pseudobinary with a lower Sn solubility. Thus, samples prepared along the pseudobinary line are not well-defined thermodynamically when excess magnesium is added. Excess Mg can push the system into a new three phase region with Mg 2 Si 1-x Sn x composition different from that of the true miscibility gap. This understanding presents new guidelines for evaluating the miscibility gap and assists strategies for microstructure engineering and thermoelectric material processing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1999

Surface Tension and Fingering of Miscible Interfaces

Experiments on miscible, buoyantly unstable reaction-diffusion fronts and non-reacting displacement fronts in Hele-Shaw cells show a fingering-type instability whose wavelengths (lambda*) are consistent with an interfacial tension (sigma) at the front caused by the change in chemical composition, even though the solutions are miscible in all proportions. In conjunction with the Saffman-Taylor model, the relation sigma = K/tau, where tau is the interface thickness and K approximately equal 4 +/- 2 x 10(exp -6) dyne, enables prediction of our measured values of lambda* as well as results from prior experiments on miscible interfaces. These results indicate that even for miscible fluids, surface tension is generally a more significant factor than diffusion in interfacial stability and flow characteristics.

Abib, Mohammed↗

NASA NTRS2002

The Dynamics of Miscible Interfaces: Simulations

The goal of this experimental/computational investigation (joint with Prof Maxworthy at USC) has been to study the dynamics of miscible interfaces, both from a scientific and a practical point of view, and to prepare a related experiment to be flown on the International Space Station. In order to address these effects, we have focused experimental and computational investigations on miscible displacements in cylindrical capillary tubes, as well as in Hele-Shaw cells. Regarding the flow in a capillary tube, the question was addressed as to whether Korteweg stresses and/or divergence effects can potentially account for discrepancies observed between conventional Stokes flow simulations and experiments for miscible flows in capillary tubes. An estimate of the vorticity and streamfunction fields induced by the Kortewegs stresses was derived, which shows these stresses to result in the formation of a vortex ring structure near the tip of the concentration front. Through this mechanism the propagation velocity of the concentration front is reduced, in agreement with the experimental observations. Divergence effects, on the other hand, were seen to be very small, and they have a negligible influence on the tip velocity. As a result, it can be concluded that they are not responsible for the discrepancies between experiments and conventional Stokes simulations. A further part of our investigation focussed on the development of high-accuracy three-dimensional spectral element simulation techniques for miscible flows in capillary tubes, including the effects of variable density and viscosity. Towards this end, the conservation equations are treated in cylindrical coordinates.

Meiburg, Eckart↗

DOE OSTI2021

High Miscibility Compatible with Ordered Molecular Packing Enables an Excellent Efficiency of 16.2% in All-Small-Molecule Organic Solar Cells

In all-small-molecule organic solar cells (ASM-OSCs), a high short-circuit current (Jsc) usually needs a small phase separation, while a high fill factor (FF) is generally realized in a highly ordered packing system. However, small domain and ordered packing always conflicted each other in ASM-OSCs, leading to a mutually restricted J sc and FF. Here, in this study, alleviation of the previous dilemma by the strategy of obtaining simultaneous good miscibility and ordered packing through modulating homo- and heteromolecular interactions is proposed. By moving the alkyl-thiolation side chains from the para- to the meta-position in the small-molecule donor, the surface tension and molecular planarity are synchronously enhanced, resulting in compatible properties of good miscibility with acceptor BTP-eC9 and strong self-assembly ability. As a result, an optimized morphology with multi-length-scale domains and highly ordered packing is realized. The device exhibits a long carrier lifetime (39.8 μs) and fast charge collection (15.5 ns). A record efficiency of 16.2% with a high FF of 75.6% and a J sc of 25.4 mA cm –2 in the ASM-OSCs is obtained. These results demonstrate that the strategy of simultaneously obtaining good miscibility with high crystallinity could be an efficient photovoltaic material design principle for high-performance ASM-OSCs.

14 SOLAR ENERGY↗

DOE OSTI2020

Molecular insights into photostability of fluorinated organic photovoltaic blends: role of fullerene electron affinity and donor–acceptor miscibility

In this report, the photostability of certain organic photovoltaic (OPV) active layers was demonstrated to improve by as much as a factor of five under white light illumination in air with the use of 1,7-bis-trifluoromethylfullerene (C 60 (CF 3 ) 2 ) as the acceptor in place of PC 60 BM. However, the results were highly dependent on the structure and functionality within the donor material. Twelve combinations of active layer blends were studied, comprised of six different high-performance donor polymers (two fluorinated and four non-fluorinated donors) and two fullerene acceptors (PC 60 BM and C 60 (CF 3 ) 2 ). The relative rates of irreversible photobleaching of the active layer blends were found to correlate well with the electron affinity of the fullerene when the polymer and fullerene were well blended, but a full rationalization of the photobleaching data requires consideration of both the electron affinity of the fullerene as well as the relative miscibility of the polymer–fullerene components in the blend. Miscibility of those components was probed using a combination of time-resolved photoluminescence (TRPL) measurements and scanning tunneling microscopy (STM) imaging. The presence of fluorinated aromatic units in the donor materials tend to promote more intimate mixing with C 60 (CF 3 ) 2 as compared to PC 60 BM. The full results of these photobleaching studies and measurements of donor–acceptor miscibility, considered alongside additional photoconductance measurements and preliminary device work, provide new molecular optimization insights for improving the long-term stability of OPV active layers.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Critical Role of Polymer Aggregation and Miscibility in Nonfullerene‐Based Organic Photovoltaics

Abstract Understanding the correlation between polymer aggregation, miscibility, and device performance is important to establish a set of chemistry design rules for donor polymers with nonfullerene acceptors (NFAs). Employing a donor polymer with strong temperature‐dependent aggregation, namely PffBT4T‐2OD [poly[(5,6‐difluoro‐2,1,3‐benzothiadiazol‐4,7‐diyl)‐ alt ‐(3,3″′‐di(2‐octyldodecyl)‐2,2′;5′,2″;5″,2″′‐quaterthiophen‐5,5‐diyl)], also known as PCE‐11 as a base polymer, five copolymer derivatives having a different thiophene linker composition are blended with the common NFA O‐IDTBR to investigate their photovoltaic performance. While the donor polymers have similar optoelectronic properties, it is found that the device power conversion efficiency changes drastically from 1.8% to 8.7% as a function of thiophene content in the donor polymer. Results of structural characterization show that polymer aggregation and miscibility with O‐IDTBR are a strong function of the chemical composition, leading to different donor–acceptor blend morphology. Polymers having a strong tendency to aggregate are found to undergo fast aggregation prior to liquid–liquid phase separation and have a higher miscibility with NFA. These properties result in smaller mixed donor–acceptor domains, stronger PL quenching, and more efficient exciton dissociation in the resulting cells. This work indicates the importance of both polymer aggregation and donor–acceptor interaction on the formation of bulk heterojunctions in polymer:NFA blends.

Yi, Xueping↗

DOE OSTI2021

Temperature and radiation effects on brittle versus ductile fracture behavior in miscible phase boundaries: insight from atomistic simulations

Temperature- and irradiation-assisted failure mechanisms in miscible phase boundaries are clarified via atomistic calculations. We first establish the temperature-dependent brittle-to-ductile transition in U–Zr miscible phase boundaries. Our results confirm that these boundaries are mostly brittle at low temperatures and ductile at elevated temperatures. We then investigate the changes induced by irradiation on the fracture mechanisms in such phase boundaries. The irradiation-induced defect accumulation follows a multi-stage process that starts with the accumulation of isolated small dislocation loops before transitioning to the saturation and growth of larger dislocation loops and end up with a reorganization into forest dislocations. The accumulation of loops is the primary feature to participate in the delineation between brittle and ductile interfacial fracture in irradiated phase boundaries. At low damage levels, radiation defect interactions with the crack tip are limited and U–Zr miscible boundaries fail through the emission of dislocations ahead of the crack tip followed by brittle cleavage in agreement with the classical Griffith’s criterion for crack stability. At higher damage levels, the failure mode transitions from brittle crack growth to ductile void growth. In this case, the microcrack tip is blunted by the high density of pre-existing, radiation-induced defects in the vicinity of the crack. This interaction leads to the development and growth of a cavity at the interface as opposed to interfacial cleavage.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Miscibility of rock and ice in the interiors of water worlds

Abstract Super-Earths and sub-Neptunes are the most common planet types in our galaxy. A subset of these planets is predicted to be water worlds, bodies that are rich in water and poor in hydrogen gas. The interior structures of water worlds have been assumed to consist of water surrounding a rocky mantle and iron core. In small planets, water and rock form distinct layers with limited incorporation of water into silicate phases, but these materials may interact differently during the growth and evolution of water worlds due to greater interior pressures and temperatures. Here, we use density functional molecular dynamics (DFT-MD) simulations to study the miscibility and interactions of enstatite (MgSiO 3 ), a major end-member silicate phase, and water (H 2 O) at extreme conditions in water world interiors. We explore pressures ranging from 30 to 120 GPa and temperatures from 500 to 8000 K. Our results demonstrate that enstatite and water are miscible in all proportions if the temperature exceeds the melting point of MgSiO 3 . Furthermore, we performed smoothed particle hydrodynamics simulations to demonstrate that the conditions necessary for rock-water miscibility are reached during giant impacts between water-rich bodies of 0.7–4.7 Earth masses. Our simulations lead to water worlds that include a mixed layer of rock and water.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2005

The Dynamics of Miscible Interfaces: Simulations

This research project focuses on the dynamics of interfacial regions between miscible fluids. While much attention has focused on immiscible interfaces in the past, miscible interfaces have been explored to a much lesser degree, so that there are many open questions regarding their dynamics at this time. Among the more pressing issues is the role that nonconventional stresses can play in such interfacial regions. Such stresses are typically not accounted for in efforts to model the dynamics of miscible flows. Our research aims to clarify under which circumstances these stresses do have to be taken into account, and what quantitative approaches are most suitable in this regard. In order to address these issues, we have focused on conducting linear stability analyses and nonlinear simulations for capillary tube and Hele-Shaw flows, and to compare the results with corresponding experiments performed in the labs of our co-investigators Prof. Maxworthy at USC, and Dr. Balasubramaniam at NASA. Over the duration of the project we have, among other things, focused on the effects of variable diffusion coefficients in such flows, and specifically on their influence in the growth of instabilities. Furthermore, our three-dimensional spectral element simulations have made good progress, so that we have come to a point where we can conduct more detailed comparisons with experimental observations. We are currently focusing our efforts on reproducing the tip-splitting instability observed by Maxworthy. Finally, we have discovered a new core-annular flow instability in the Stokes flow regime during the last year. This represents a significant finding, as this instability does not have an immiscible counterpart.

Meiburg, Eckart↗

NASA NTRS2001

Novel Shapes of Miscible Interfaces Observed

The dynamics of miscible displacements in a cylindrical tube are being investigated experimentally and numerically, with a view to understand the complex processes that occur, for example, in enhanced oil recovery, hydrology, and filtration. We have observed complex shapes of the interface between two liquids that mix with each other when the less viscous liquid is displaced by the more viscous one in a tube. A less viscous fluid that displaces a more viscous fluid is known to propagate in the form of a "finger," and a flight experiment proposed by Maxworthy et al. to investigate the miscible-interface dynamics is currently being developed by NASA. From the current theory of miscible displacements, which was developed for a porous medium satisfying Darcy's law, it can be shown that in the absence of gravity the interface between the fluids is destabilized and thus susceptible to fingering only when a more viscous fluid is displaced by a less viscous one. Therefore, if the interface is initially flat and the more viscous fluid displaces the less viscous fluid, the interface ought to be stable and remain flat. However, numerical simulations by Chen and Meiburg for such displacement in a cylindrical tube show that the interface is unstable and a finger of the more viscous fluid is indeed formed. Preliminary experiments performed at the NASA Glenn Research Center show that not only can fingering occur when the more viscous fluid displaces a less viscous one in a cylindrical tube, but also that under certain conditions the advancing finger achieves a sinuous or snakelike shape. These experiments were performed using silicone oils in a vertical pipette of small diameter. In the initial configuration, the more viscous fluid rested on top of the less viscous one, and the interface was nominally flat. A dye was added to the upper liquid for ease of observation of the interface between the fluids. The flow was initiated by draining the lower fluid from the bottom of the pipette, at speeds less than 0.1 mm/sec.

Balasubramaniam, Ramaswamy↗