Momentum transport of morphological instability in fluid displacement with changes in viscosity.

Saffman-Taylor instability exhibits a stepwise unstable morphology from a stable interface to viscous fingering, eventually leading to tip splitting. The nonlinear dynamics of the destabilized interface depends on various flow properties. However, the physicochemical mechanism that determines the transition point of the flow state is unclear. We studied the interfacial instability transition in miscible displacement from a thermodynamic perspective by calculating the momentum transport and entropy production. Using numerical analysis based on Darcy's law coupled with the convection-diffusion equation, the observed flux-dependent flow state transitions were attributed to the selection of the flow state with a higher entropy production.

Experimental demonstration of the suppression of viscous fingering in a partially miscible system.

Phase separation is ubiquitous in nature and technology. So far, the focus has primarily been on phase separation occurring in the bulk phase. Recently, phase separation taking place in interfacial areas has attracted more attention - in particular, a combination of interfacial phase separation and hydrodynamics. Studies on this combination have been conducted intensively in this past decade; however, the detailed dynamics remain unclear. Here, we perform fluid displacement experiments, where a less viscous solution displaces a more viscous one in a radially confined geometry and phase separation occurs at the interfacial region. We demonstrate that a finger-like pattern, due to the viscosity contrast during the displacement, can be suppressed by the phase separation. We also claim that the direction of a body force, the so-called Korteweg force, which appears during the phase separation and induces convection, determines whether the fingering pattern is suppressed or changed to a droplet pattern. The change of the fingering pattern to the droplet pattern is enhanced by the Korteweg force directed from the less viscous solution to the more viscous one, whereas the fingering is suppressed by the force directed in the opposite direction. These findings will contribute directly to the higher efficiency of processes such as enhanced oil recovery and CO2 sequestration, where interfacial phase separation is considered to occur during the flow.

Tunability of Self-Organized Structures Based on Thermodynamic Flux.

Nature establishes structures and functions via self-organization of constituents, including ions, molecules, and particles. Understanding the selection rule that determines the self-organized structure formed from many possible alternatives is fundamentally and technologically important. In this study, the selection rule for the self-organization associated with a reaction-diffusion system was explored using the Liesegang phenomenon, by which a periodic precipitation pattern is formed as a model system. Experiments were conducted by systematically changing the mass flux. At low mass fluxes, a vertically periodic pattern was formed, whereas at high mass fluxes, a horizontally periodic pattern was formed. The results inferred that a structural vertical-to-horizontal periodicity transition occurred in the self-organized periodic structure at the crossover flux at which the entropy production rate reversed. Numerical analyses attributed the as-observed flux-dependent structural transition to the selection of the self-organized pattern with a higher entropy production rate. These findings contribute to our understanding of how nature controls self-organized structures and geometry, potentially facilitating the development of novel designs, syntheses, and fabrication processes for well-controlled organized functional structures.

Growing Interface with Phase Separation and Spontaneous Convection during Hydrodynamically Stable Displacement.

The displacement of one fluid by another is an important process, not only in industrial and environmental fields, such as chromatography, enhanced oil recovery, and CO2 sequestration, but also material processing, such as Lost Foam Casting. Even during hydrodynamically stable fluid displacement where a more viscous fluid displaces a less viscous fluid in porous media or in Hele-Shaw cells, the growing interface fluctuates slightly. This fluctuation is attributed to thermodynamic conditions, which can be categorized as the following systems: fully miscible, partially miscible, and immiscible. The dynamics of these three systems differ significantly. Here, we analyze interfacial fluctuations under the three systems using Family-Vicsek scaling and calculate the scaling indexes. We discovered that the roughness exponent, α, and growth exponent, ß, of the partially miscible case are larger than those of the immiscible and fully miscible cases due to the effects of the Korteweg convection as induced during phase separation. Moreover, it is confirmed that fluctuations in all systems with steady values of α and ß are represented as a single curve, which implies that accurate predictions for the growing interface with fluctuations in Hele-Shaw flows can be accomplished at any scale and time, regardless of the miscibility conditions.

Tunable Hydrodynamic Interfacial Instability by Controlling a Thermodynamic Parameter of Liquid-Liquid Phase Separation.

Herein, we report on the hydrodynamic interfacial instability controlled by a thermodynamic parameter driving the liquid-liquid phase separation during fluid displacement in a Hele-Shaw cell. This instability remains even when the solution is guaranteed to be hydrodynamically stable. Adjusting the salt concentration helps control the miscibility of the solutions and change the pattern of the interface. We observe stable circular, fingering, and droplet formation patterns as the salt concentration is decreased from equilibrium. In addition, we analyze this interfacial instability using thermodynamic flux, which is determined from the growth rate of the interface, and provide a theoretical framework to quantitatively predict the transition points between the patterns. We find that the patterns transition to a state having higher entropy production.

Anomalous patterns of Saffman-Taylor fingering instability during a metastable phase separation.

Phase separation is important in biology, biochemistry, industry, and other areas and is divided into two types: a spinodal decomposition type and a nucleation and growth type. The spinodal decomposition type phase separation occurs under the thermodynamically unstable conditions, and the nucleation and growth type phase separation occurs under thermodynamically metastable conditions. On the other hand, when a less viscous fluid displaces a more viscous one in porous media, the interface of the two fluids becomes hydrodynamically unstable and forms a finger-like pattern. The coupling of the hydrodynamic instability with the thermodynamic instability has been studied. It is reported that the hydrodynamic instability under thermodynamically unstable conditions, where spinodal decomposition type phase separation occurs, creates multiple moving droplets with a radius of 3-4 mm because of the spontaneous convection induced by the Korteweg force, which is driven by a compositional gradient during phase separation. However, the hydrodynamic instability under metastable conditions, where the phase separation of nucleation and growth type occurs, is still unrevealed. In this study, we applied fingering instability (hydrodynamic instability) under the metastable conditions, where the patterns are changed from fingering or droplets to anomalous patterns such as tip-widening or needle-like (top-pointed) fingering patterns when the initial concentration is metastable, which is considered near a binodal curve. These patterns are ubiquitous in nature, similar to dendrite crystals (snowflakes) or our body's cells. Thus, the patterns created can be controlled through hydrodynamic conditions such as the injection flow and thermodynamic conditions such as spinodal decomposition (thermodynamically unstable conditions) and metastable conditions.

Thermodynamic Analysis of Bistability in Rayleigh-Bénard Convection.

Bistability is often encountered in association with dissipative systems far from equilibrium, such as biological, physical, and chemical phenomena. There have been various attempts to theoretically analyze the bistabilities of dissipative systems. However, there is no universal theoretical approach to determine the development of a bistable system far from equilibrium. This study shows that thermodynamic analysis based on entropy production can be used to predict the transition point in the bistable region during Rayleigh-Bénard convection using the experimental relationship between the thermodynamic flux and driving force. The bistable region is characterized by two distinct features: the flux of the second state is higher than that of the first state, and the entropy production of the second state is lower than that of the first state. This thermodynamic interpretation provides new insights that can be used to predict bistable behaviors in various dissipative systems.

Thermodynamic analysis of thermal convection based on entropy production.

Flow patterns have a tendency to break the symmetry of an initial state of a system and form another spatiotemporal pattern when the system is driven far from equilibrium by temperature difference. For an annular channel, the axially symmetric flow becomes unstable beyond a given temperature difference threshold imposed in the system, leading to rotational oscillating waves. Many researchers have investigated this transition via linear stability analysis using the fundamental conservation equations and the generic model amplitude equation, i.e., the complex Ginzburg-Landau equation. Here, we present a quantitative study conducted of the thermal convection transition using thermodynamic analysis based on the maximum entropy production principle. Our analysis results reveal that the fluid system under nonequilibrium maximizes the entropy production induced by the thermodynamic flux in a direction perpendicular to the temperature difference. Further, we show that the thermodynamic flux as well as the entropy production can uniquely specify the thermodynamic states of the entire fluid system and propose an entropy production selection rule that can be used to specify the thermodynamic state of a nonequilibrium system.

Motion-Based Detection of Lanthanides(III) Using Self-Propelled Droplets.

The directional and controllable transportation of self-propelled chemical objects in response to chemical signals in environmental media holds considerable promise for diverse applications. We investigated the chemotaxis of oil droplets loaded with surfactants to detect spatial gradients of lanthanide(III) ions, among which Dy3+ and Tm3+ were the most effective chemoattractants for steering droplets toward the targets. Patterns within a chemotactic index of the lanthanide series exhibited a convex tetrad effect and a breakpoint at Gd3+. The Jørgensen-Kawabe equation, which is based on the refined spin-pairing energy theory, quantitatively demonstrated the tetrad effect. The self-propelled droplets served as a motion-based detection mechanism for lanthanides(III).

Propagating Precipitation Waves in Disordered Media.

The study presented in this paper investigates form changes of propagating waves generated through precipitation reactions in a gel matrix that possesses an inhomogeneous microstructure. The waves demonstrate form changes from a single ring-like pattern to multiple target-like waves. Subsequently, the waves take up a spiral form and ultimately manifest themselves in the form of a turbulence pattern that intensifies with increasing fluctuations within the gel structure. An investigation into the dynamics of the precipitation waves reveals the existence of an anomalous diffusion. The effective diffusion coefficients are found to increase linearly with the quenching temperature. Further, it is revealed through the analysis of the anomalous diffusion dynamics that precipitation patterns could be adequately controlled by adjusting the permeability fluctuations within the gel structure. The findings of this study lead to a greater understanding of the spontaneous creation of precipitation patterns by a system driven by disorder.

Self-Propelled Vesicles Induced by the Mixing of Two Polymeric Aqueous Solutions through a Vesicle Membrane Far from Equilibrium.

This study describes the development of self-propelled vesicles using transient interfacial energy in an aqueous two-phase system composed of polyethylene glycol (PEG), dextran (DEX), and water. The transient interfacial energy was generated at the mixing boundary between the PEG and DEX solutions when the two miscible liquids were in contact with each other far from equilibrium. Vesicles encapsulating 20 wt % DEX solution traveled spontaneously when the PEG concentration in the environmental media was >15 wt %. The motility of the vesicles varied with the permeability of the vesicle membrane. The permeability increased significantly when the concentration of PEG was >15 wt %. PEG had a profound effect not only on mass transfer through the membrane but also on the motility of the vesicles.

Propagation Properties of the Precipitation Band in an AlCl3/NaOH System.

When inherently immobile solid particles collectively form precipitates in a reaction-diffusion system involving a redissolution reaction, a propagation phenomenon may occur in which a dynamic pattern of precipitation bands forms. This propagating precipitation phenomenon has been studied by many researchers. However, two completely different processes-i.e., the reaction-diffusion of reactants and the crystal growth of products-progress simultaneously in the system, thereby rendering the phenomenon complex. There are no well-established experimental laws for this propagating precipitation phenomenon, such as the spacing, time, and width laws associated with the well-known Liesegang phenomenon, which is static in the sense that precipitation bands form and remain at the same position. In fact, it has not been clarified which of the processes controls the propagation phenomenon. Accordingly, we have investigated the apparent diffusion coefficient associated with the dynamics of propagating precipitation band in an AlCl3/NaOH system for the case in which a large excess of outer electrolytes (i.e., OH(-)) diffuses into gel in which inner electrolytes (i.e.,Al(3+)) are homogeneously distributed. An isolated precipitation band of Al(OH)3 was formed horizontally in a test tube and propagated vertically in proportion to the square root of time. In our experimental results, we found that the apparent diffusion coefficient, D(p), possesses an exponential dependence on the initial concentrations of the outer electrolyte, and the inner electrolyte; the measured relation was D(p) = D[Al(3+)](-0.6)[OH(-)](0.6), where D = (0.63 ± 0.04) × 10(5) cm(2)/s. From our model equations based on the prenucleation theory, which take into account a redissolution reaction, we found that the dynamics of the reaction front of the outer and the inner electrolytes was an important factor in controlling the propagation of the precipitation band. In our simulation results, we obtained a similar dependence of the apparent diffusion coefficient on the electrolyte concentrations.

Metal-Ion-Dependent Motion of Self-Propelled Droplets Due to the Marangoni Effect.

Chemically driven self-propulsion of soft matter is useful for various applications because it can move toward a desired location, without external power fields, in response to chemical signals in environmental media. We have developed a suitable steering mechanism to maintain the orientation of self-propelled droplets loaded with surfactant in fluidic environments. A spatial gradient of alkaline-earth metal ions induces directional sensing. These metal ions can be arranged in descending order of directional sensing as Ba(2+) ∼ Sr(2+) > Ca(2+) > Mg(2+). On the other hand, the affinity between metal ions and di-(2-ethylhexyl)phosphoric acid (DEHPA) decreases in the order as Ca(2+) > Ba(2+) > Sr(2+) > Mg(2+). To clarify the difference between the order of directional sensing and that of affinity, we investigated the effect of metal ions on the driving force to create asymmetric convection. We found that changes in the interfacial tension under nonequilibrium conditions play an important role in directional sensing.

Self-propelled droplets for extracting rare-earth metal ions.

We have developed self-propelled droplets having the abilities to detect a chemical gradient, to move toward a higher concentration of a specific metal ion (particularly the dysprosium ion), and to extract it. Such abilities rely on the high surface activity of di(2-ethylhexyl) phosphoric acid (DEHPA) in response to pH and the affinity of DEHPA for the dysprosium ion. We used two external stimuli as chemical signals to control droplet motion: a pH signal to induce motility and metal ions to induce directional sensing. The oil droplets loaded with DEHPA spontaneously move around beyond the threshold of pH even in a homogeneous pH field. In the presence of a gel block containing metal ions, the droplets show directional sensing and their motility is biased toward higher concentrations. The metal ions investigated can be arranged in decreasing order of directional sensing as Dy(3+)≫ Nd(3+) > Y(3+) > Gd(3+). Furthermore, the analysis of components by using an atomic absorption spectrophotometer reveals that the metal ions can be extracted from the environmental media to the interiors of the droplets. This system may offer alternative self-propelled nano/microscale machines to bubble thrust engines powered by asymmetrical catalysts.

pH-dependent motion of self-propelled droplets due to Marangoni effect at neutral pH.

Oil droplets loaded with surfactant propel themselves with a velocity up to 6 mm s(-1) when they are placed in an aqueous phase of NaOH solution or buffer solution. The required driving force for such motion is generated on the interface of the droplets by the change in interfacial tension, due to deprotonation of the surfactant. This force induces Marangoni convection, which gives rise to a circulating flow inside the droplets. The droplets begin to move when the axis of this circulation deviates from the vertical line. This motion depends on the pH condition of the aqueous phase. When the initial value of pH is adjusted such that the pH exceeds the threshold at the equilibrium state, the droplets move spontaneously. It was seen that the droplets were independent of the material of the solid substrates because the droplets were not directly in contact with the surface of the substrate. The condition for the onset of this spontaneous motion was verified by comparing the prediction from the linear stability analysis with experiments. The stability analysis overestimates the value of the driving force, causing instability.

Transient pore dynamics in pH-responsive liquid membrane.

We have investigated the transient pore dynamics in a chemically destabilized liquid membrane in buffer solutions at macroscopic scale. A hole opened and closed repeatedly in response to pH in the surrounding media when the concentration of surfactant in the liquid membrane was sufficiently high to form emulsion at equilibrium and the membrane was larger than a critical value. The analysis of pore dynamics allowed us to estimate some physicochemical properties such as membrane tension, line tension, and membrane viscosity.

Ion-selective Marangoni instability coupled with the nonlinear adsorption/desorption rate.

An oil/water interface containing bis(2-ethylhexyl)phosphate and Ca(2+) or Fe(3+) exhibits spontaneous Marangoni instability associated with the fluctuation in interfacial tension. This instability rarely appears for oil/water systems with Mg(2+), Sr(2+), Ba(2+), Cu(2+), or Co(2+). The same ion selectivity is observed for n-heptane and nitrobenzene despite their significant differences in density, viscosity, and the dielectric constant of oil. We studied this instability under acidic pH conditions to avoid the neutralization reaction effects. The result of the equilibrium interfacial tension and the extraction ratio of cations indicates that a large number of oil-soluble complexes form at the interfaces of Ca(2+)-containing systems and probably for Fe(3+)-containing systems. The results obtained by oscillating drop tensiometry and Brewster angle microscopy indicate that desorption, rather than adsorption, is more significant to the onset of instability and that the resulting complex tends to form aggregates in the interface. This aggregation gives the nonlinear desorption rate of the oil-soluble complex. Then, exfoliation of the aggregating matter occurs, which triggers the Marangoni instability. The induced convection removes the oil-soluble complex accumulated at the interface, creating a renewed interface, which is necessary for the successive occurrence of the Marangoni instability. For the other cations, the oil-soluble compounds are insignificant, and they rarely form aggregates. In such cases, adsorption/desorption proceeds without instability.

Spontaneous periodic pulsation of contact line in oil/water system--frequency control with divalent cations and applied voltage.

Periodic oscillatory change of hydrophilicity (or hydrophobicity) of a glass surface was studied. A glass capillary was immersed normally at an oil/water interface. The water phase contained the cationic surfactant trimethyloctadecylammoniumchloride, and the oil phase contained bis(2ethylhexyl) phosphate. Adsorption of the surfactant molecules and their desorption via anionic chemicals dissolved in the oil generated a gradual wetting by the water, followed by a rapid wetting by oil. The three phase contact line exhibited a pulse-like motion that continued, at least for a few minutes. The frequency depended on the cation species dissolved in water and the applied voltage across the oil/water interface. Four kinds of cations, Mg(2+), Ca(2+), Sr(2+) and Ba(2+) were used. While the frequency order was Ba(2+)>Sr(2+)>Mg(2+), the Ca(2+)-containing interface did not show any motion irrespective of the applied voltage. There was a threshold voltage and concentration of anionic chemical that was necessary for the onset of this motion. The pulsation mechanism and its ion selectivity are also discussed. This interfacial motion was a typical nonlinear oscillation with an ion-selective nature. In this regard, this interfacial motion had biomimetic characteristics.

Protrusion and rising of a gel-based precipitation layer.

Two types of unstable growth of a precipitation layer in gel are discussed. A cation and an anion that are reactive diffuse from opposite ends of the gel to its center. A white turbid zone forms due to their reactions. When the concentration ratios for both the ions are far from stoichiometry, the turbid zone expands toward the lower-concentration side. However, when the ratio is nearly stoichiometric, unstable growth occurs. In a glass tube, a protrusion of the precipitation region from the turbid zone grows, which forms a long needle-like shape. When a free surface is present on the gel, the precipitation region protrudes from the gel surface to form a rising structure. Mapping the growing structure on a concentration diagram and using scanning electron microscopy to examine contained particles suggest that the reaction is restricted to a narrow region and the reaction product migrates through a path formed in the protrusive structure to form a bulk solid at the edge.

Autonomous motion of vesicle via ion exchange.

The autonomous motion of vesicle is observed in a simple chemical system. A vesicle composed of didodecyldimethylammonium bromide DDAB breaks down by ion exchange from Br(-) to I(-). When an electrolyte is supplied to vesicles, some of them begin to move after an induction period. They continue to move, leaving behind the reaction products on the trail. The ion exchange decreases the vesicle size, and smaller vesicles remain after the motion. We examine the characteristics of this motion. The surface tension of the DDAB-containing aqueous phase depends on the KI concentration. Considering this result carefully, we conclude that vesicles can move when the ion exchange from Br(-) to I(-) proceeds irreversibly. Then, inhomogeneity in the vesicle membrane develops because of the coagulating nature of the product, didodecyldimethylammonium iodide (DDAI), which is sparingly soluble in water. Inhomogeneous properties of vesicle membranes are then generated, which induce surface transport of the reaction product and flow in the water pool. As a result, a couple of convection rolls appear in the water pool of the vesicle. The convection rolls drive vesicle motion. A simple model for the semiquantitative description is proposed.