Immiscible Mixtures Research Articles

Quantitative relationship between tissue composition and scattering of ultrasound.

This study establishes quantitative laws by which the magnitude of ultrasonic scatter is related to the gross chemical composition of tissues, viz., water, fat, and collagen. Tissues are modeled as immiscible mixtures, the constituents of which are uniformly dispersed over the volume. Each component of the mixture causes the ultrasonic velocity of the medium to fluctuate about the mean value. Such localized variations in the refractive index of a medium cause propagating sound waves to scatter. It is proposed that the contribution of each component to the total fluctuation is in proportion to its volume fraction. The analysis shows that the scatter of ultrasound exhibits a complex nonlinear dependence on the concentrations of the individual components. From the knowledge of sound speed of individual components, total velocity fluctuations are determined for binary and three-component models of the tissue. Comparison of these values, with those estimated from scatter measurements, shows a close correlation between the two sets. Collagen, although present in relatively small amounts in soft tissues, contributes a significant portion of the total scatter. However, both fat and collagen fractions must be taken into consideration to account for the major fraction of the observed scatter. In conclusion, there is a direct relationship between tissue composition and scatter from tissues. Such dependence must also be taken into consideration, in addition to the correlation function and correlation lengths to explain backscatter or loss in a transmitted signal due to scatter from tissues.

Characterizing scatterer size via measurements of multiple acoustic parameters

A multiple parameter approach for characterizing mixtures has been investigated. It is found that one can characterize scatterers (droplets) in immiscible mixtures of water, fat (oil), and protein, in term of volume fraction and size, from measurements of the mixture’s effective acoustic parameters (density, sound speed, the acoustic nonlinear parameter, and attenuation). Mixture laws [P. Jiang et al., Ultrasound Med. Biol. 17(8), 829–838 (1991)] were used to determine the composition of a mixture. A procedure for choosing a reliable composition predictor was proposed. Good agreement between the predicted compositions and the known values has been demonstrated. After the volume fraction of the scattering droplet was found, an effective radius of the droplets was obtained by using an appropriate attenuation law with the measured frequency‐dependent attenuation. The deduced radius is close to that of the majority of droplets observed under an optical microscope. A discussion is given on how to apply the tec...

Wave features related to a model of compressible immiscible mixtures of two perfect fluids

The balance equations of a compressible immiscible mixture of two perfect fluids are derived by using a variational principle. It is shown that the equations of such a mixture obey Truesdell's third metaphysical principle. Then the governing equations, specialized by assuming that both phases have the same motion, are studied by means of a suitable asymptotic approach. It is derived an evolution equation representing a generalized Korteweg-de Vries equation containing also nonlinear terms in the higher order derivatives. Finally, the travelling wave solutions of this evolution equation are discussed.

Partitioning of polystyrene latex spheres in immiscible critical liquid mixtures

We have made a systematic survey of the behavior of colloidal polystyrene latex spheres (PLS's) in critical mixtures of 2,6-lutidine plus water at temperatures where the liquid mixture separates into two immiscible phases. By varying the particle size, particle-surface charge density, and global PLS's concentration, we observe a robust and reversible set of phenomena that include the partitioning of the particles into a preferred phase at temperatures close to ${\mathit{T}}_{\mathit{c}}$ with a subsequent population of the interface between the liquid phases as the temperature is quenched deeper into the two-phase region. These results are shown to be in good qualitative agreement with thermodynamic models if the models are extended to include the singular temperature dependence of the particle-liquid and liquid-liquid interactions near the critical point. We also observe crystalline ordering of particles on the interface when the population of PLS's on the liquid-liquid interface is high.

The Flow Characteristics of a Horizontal Immischible Equal-Density Liquid-Liquid Two-Phase Flow. 1st Report. Experimental Results on Flow Pattern, Void Fraction, and Pressure Drop.

The flow characteristics of an immiscible equal-density liquid-liquid two-phase mixture were investigated to clarify the behavior of a gas-liquid two-phase flow under microgravity. The experiments were carried out in a horizontal transparent acrylic resin tube of 4.5m in length and 25mm I.D., using silicone oil (viscosity μ0=55.0 mPa·s, density ρ=980 kg/m3) and water mixture as the working fluid in the range of superficial oil velocities of 0.03 to 0.40m/s and superficial water velocities of 0.0017 to 0.7m/s. Seven kinds of flow patterns were observed. In particular, the inverted annular flow and the inverted slug flow occurred. In these flow patterns the water touched the tube wall and the oil flowed in a core region. The mean void fraction was clarified using the drift flux model. Furthermore, the experimental results of the frictional loss were compared with the Lockhart-Martinelli correlation. As a result, it was found that both agreed well in bubbly, slug, and annular flow regimes when the oil touched the tube wall, but neither agreed in the inverted flow patterns when the water touched the wall.

A Monte Carlo study of phase separation processes in immiscible binary mixtures with a surfactant

Phase separation processes of an immiscible binary mixture, which contains amphiphilic molecules (surfactants) or impurity molecules, have been investigated by Monte Carlo (MC) simulations on a 2-dimensional square lattice. The scattering structure function is calculated, which shows a slowing down of the growth rate of its peak height as a function of the increasing surfactant or impurity concentrations. Such a slowing down has actually been observed in real experiments on polymer blends containing amphiphilic block copolymers. The excluded volume effects of surfactant molecules are discussed.

Effect of Methyl tert-Butyl Ether to Homogenize Immiscible Binary-Component Fuels of Three Types; Ethanol Mixed with Diesel Fuel, Soybean Oil, or Rape Oil.

Homogenization was observed for immiscible mixtures with a small addition of methyl tert-butyl ether (MTBE). Three ternary solubility curves were measured at 298.15K for mixtures of three types; MTBE-ethanol-diesel fuel, MTBE-ethanol-soybean oil, and MTBE-ethanol-rape oil.

Dynamics of ordering processes in immiscible binary mixtures with a surfactant. I. Computer experiments

The time evolution of scattering structure functions is obtained by computer simulation experiments for the hybrid model of immiscible binary mixtures containing surfactant molecules, which are undergoing phase separation. The structure functions have a shoulder reflecting the existence of the two distinct characteristic lengths: the characteristic wavelength of the spinodally decomposing binary mixture and that induced by surfactant molecules.

Dynamics of ordering processes in immiscible binary mixtures with a surfactant. II. Analytical treatments

The early stage dynamics of phase separation processes in immiscible binary mixtures with surfactant molecules are investigated by a linear theory of fluctuations in order to explain the behavior of the system found by our computer experiments for the hybrid model. Excluded volume effects of surfactant molecules are also discussed.

Heat Transfer Enhancement by Bubble Formation near the Heating Surface.

The convective boiling heat transfer of an immiscible binary liquid mixture has been investigated by using water as a main fluid. R113 and R11 were atomized into the water as volatile material. When the boiling of the volatile material occurs, the heat transfer is cohanced by the bubble formation near the heating surface. The heat transfer enhancement occurs by the addition of a small amount of volatile material, and is insensitive to further increases in its concentration. The enhancement is remarkable in the case of low Reynolds number. The heat transfer enhancement was also observed under the condition that gas bubbles were generated on the heating surface by electrolysis, and it was clarified that the enhancement is caused by the agitation effect of bubbles near the wall.

Density behavior of alcohol-diesel fuel mixtures.

Liquid densities of six alcohol-diesel fuel systems were measured at 298.15K. The six alcohols are: methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, and 2-methyl-1-propanol. Immiscible liquid ranges were observed for the methanol-diesel fuel and ethanol-diesel fuel mixtures. The systems of methanol-cetane and ethanol-cetane were further investigated, selecting cetane as a representative component of diesel fuel. Solubilities were evaluated from the intersections of experimental density data for the four mixtures: methanol-diesel fuel, methanol-cetane, ethanol-diesel fuel, and ethanol-cetane. By addition of water to the immiscible mixtures of methanol-diesel fuel and of ethanol-diesel fuel, equidensity two-liquid phases were observed. The equi-density behavior makes it possible to feed the fuels continually to the engine.

A lattice-gas model for three immiscible fluids

Lattice-gas methods have recently proven very useful for the study of immiscible mixtures of two fluids, with applications ranging from two-phase flow in porous media to spinodal decomposition of binary fluids. Whereas the original one-phase lattice gas models the fluid as a collection of identical particles, in the immiscible two-phase lattice gas the particles are colored red or blue and the collisions between particles are chosen to achieve surface tension. We introduce a new lattice-gas model which extends the two-phase immiscible lattice gas to the simulation of a mixture of three immiscible fluids, i.e., red, green and blue. This extension achieves more than the obvious generalization: immiscible mixtures of three fluids yield phenomena that can be qualitatively different from analogous phenomena observed with two fluids. To demonstrate this point, we show simulations of phase separation of three immiscible fluids and three-phase flow in porous media.

Free-energy computations for mixtures of Stockmayer and polarizable Lennard-Jones fluids

Molecular-dynamics calculations are presented for mixtures of polarizable Lennard-Jones and Stockmayer particles. The free energy of mixing is determined as a function of the polarizability. These calculations show that an immiscible mixture of (non-polarizable) Lennard-Jones and Stockmayer molecules can become miscible by adding a sufficiently high polarizability to the Lennard-Jones molecules.

Hybrid models for the dynamics of an immiscible binary mixture with surfactant molecules

For the purpose of studying pattern formation processes in a binary mixture with surfactant molecules such as the formation of a microemulsion, we propose dynamical models which comprise a continuous field representing an immiscible binary fluid mixture and discrete surfactant molecules. In order to demonstrate the efficiency of such a hybrid approach, computer experiments on pattern formation processes are performed combining the cell dynamics method and the molecular dynamics method.

Macroscopic laws for immiscible two‐phase flow in porous media: Results From numerical experiments

Flow through porous media may be described at either of two length scales. At the scale of a single pore, fluids flow according to the Navier‐Stokes equations and the appropriate boundary conditions. At a larger, volume‐averaged scale, the flow is usually thought to obey a linear Darcy law relating flow rates to pressure gradients and body forces via phenomenological permeability coefficients. Aside from the value of the permeability coefficient, the slow flow of a single fluid in a porous medium is well‐understood within this framework. The situation is considerably different, however, for the simultaneous flow of two or more fluids: not only are the phenomenological coefficients poorly understood, but the form of the macroscopic laws themselves is subject to question. I describe a numerical study of immiscible two‐phase flow in an idealized two‐dimensional porous medium constructed at the pore scale. Results show that the macroscopic flow is a nonlinear function of the applied forces for sufficiently low levels of forcing, but linear thereafter. The crossover, which is not predicted by conventional models, occurs when viscous forces begin to dominate capillary forces; i.e., at a sufficiently high capillary number. In the linear regime, the flow may be described by the linear phenomenological law ui = ΣjLijfj, where the flow rate ui of the ith fluid is related to the force fj applied to the jth fluid by the matrix of phenomenological coefficients Lij which depends on the relative concentrations of the two fluids. The diagonal terms are proportional to quantities commonly referred to as “relative permeabilities.” The cross terms represent viscous coupling between the two fluids; they are conventionally assumed to be negligible and require special experimental procedures to observe in a laboratory. In contrast, in this numerical study the cross terms are straightforward to measure and are found to be of significant size. The cross terms are additionally observed to be approximately equal, which is the behavior predicted by Onsager's reciprocity theorem. However, persistent transient effects can render the reciprocity unobservable. The numerical study is performed with a discrete numerical model of the molecular dynamics of immiscible mixtures called the immiscible lattice gas. The immiscible lattice gas models both the Navier‐Stokes equations and surface tension. Numerical tests presented here additionally provide quantitative validation of the method's ability to simulate wetting phenomena and the effects of capillary pressure. Whereas the numerical study of the linear phenomenological laws utilizes a highly simplified porous medium with one pore and two throats, numerical examples of wetting and nonwetting invasion experiments in a geometrically complex 2‐D porous medium are also provided.

Spherical silica gels precipitated from acid catalyzed TEOS solutions

Silica gel particles were obtained from the immiscible mixtures of TEOS and H 2O with nitric acid, in which the H 2O/TEOS molar ratio was less than 2. In the emulsion in which water was dispersed as the droplets in TEOS by stirring, TEOS dissolved into the droplets in proportion to time and was hydrolyzed by an excess of nitric acid water. The hydrolysis and polycondensation reactions of TEOS were restricted inside the droplets, and when the ratio of water to the dissolved TEOS for the droplets reached about 4.5 dense spherical particles were formed in TEOS.

Characterization of red blood cells using inverse acoustic scattering

Three mechanical parameters—volume, compressibility, and density—of human erythrocytes (red blood cells) are measured. The experimental apparatus consists of two confocally positioned high‐frequency acoustic transducers and an on‐line Coulter‐type volume sensing zone [J Acoust. Soc. Am. Suppl. 1 84, S163 (1988)]. Different scattering theories are used to invert the experimental data. Normal red blood cells suspended in saline solutions of varying salinity are tested. A red blood cell is modeled as an immiscible mixture of a protein and saline solution, and perfect mixture laws for compressibility and density as functions of a protein fraction for such a mixture are derived. The mean corpuscular hemoglobin concentration is then calculated from the compressibility and density data. Abnormal red blood cells, e.g., red blood cells from anemic patients, are also tested, and results are correlated to the patients' pathological states. The system is calibrated by adding monodispersed polystyrene spheres to the sample. [Work supported by the U.S. National Institutes of Health through Grant 2R01GM30419.]

Continuum theory of an immiscible binary fluid mixture with a surfactant

A Ginzburg-Landau type continuum theory is proposed for an immiscible binary fluid mixture with a surfactant. The field variables that enter are the relative concentration of the binary mixture, and the density and director fields of the surfactant. This model reduces to the sharp interface model in a certain limit. The dynamical extensions of our model are also presented, some of which may be used for the purpose of computer modelling of fluids containing amphiphiles such as microemulsions.

Partition of parinaroylphosphatidylethanolamines and parinaroylphosphatidylglycerols in immiscible phospholipid mixtures

Partitioning of two parinaroyl phosphatidylethanolamines and two parinaroyl phosphatidylglycerols between solid and fluid phase phospholipids was examined. Fluorescence quantum yields and fluorescence polarization measurements were used to calculate K p s/t, the solid to fluid partition coefficient of each probe (Sklar, L.A., Miljanich, G.P. and Dratz, E.A. (1979) Biochemistry 18, 1707–1716). In the immiscible mixture dipalmitoylphosphatidylcholine and dilinoleylphosphatidylcholine, both 1-palmitoyl-2- trans-parinaroylphosphatidylethanolamine and 1-palmitoyl-2- trans-parinaroylphosphatidylglycerol partitioned preferentially into solid phase lipid with mean K p s/t values (calculated from quantum yields) of 3.4 ± 1.5 and 2.1 ± 0.7, respectively. In contrast, 1-oleoyl-2- cis-parinaroylphosphatidylethanolamine and 1-oleoyl-2- cis-parinaroylphosphatidylglycerol partitioned preferentially into fluid phase lipid in the same model system with mean K p s/t values (calculated from quantum yields) of 0.44 ± 0.26 and 0.16 ± 0.07, respectively. Fluorescence polarization data on the same four parinaroyl phospholipids in mixtures of solid-phase dimyristoylphosphatidyl ethanolamine and fluid-phase dilinoleoylphosphatidylglycerol were similar to those obtained in the immiscible phosphatidylcholine system, demonstrating that the partitioning of these probes is not strongly dependent on head group. Knowledge of the partition properties of these fluorescent probes is relevant to use of these probes in investigation of the phase behavior of Escherichia coli inner membrane lipids, since phosphatidylethanolamine and phosphatidylglycerol species account for approximately 95% of these lipids.

Eulerian kinematics of flow through spatially periodic models of porous media

For spatially periodic models of porous media, and incompressible fluids, we consider here in detail thephysical interpretation of averaged velocity fields in terms of a purely continuum-level Eulerian seepage flux relation involving the mass flow across an arbitrarily oriented ‘macroscale’ surface element. We prove that the appropriately averaged microscale velocities do indeed satisfy a macroscale Eulerian flux relation (albeit to some approximation), provided that the surface ‘element’ is large compared with the pore lengthscale (microscale). A quantitative discussion of an ‘intermediate scale’ (lying between the pore scale and a characteristic macroscale) is achieved through the use of locally periodic velocity fields. Within the context of seepage velocity kinematics, our developments provide a conceptual foundation that renders continuum theories of flow of incompressible fluids through (periodic) porous media entirely selfcontained on the macroscale—free from any details of the discrete microscale structure (inaccessible to macroscopic observers) from which this continuum theory sprang. The error bounds and scaling laws derived are of special interest when the macroscale/microscale disparity is not very ‘wide’. With reference to current rational mechanical theories of ‘immiscible mixtures,’ our analysis provides aconstructive existence proof, at least for periodic models of porous media, for phase-specific velocities; heretofore, such velocities were usually accepted, in a Lagrangian sense, on an axiomatic basis. Thus, clarification and quantification of thekinematical aspects of the continuum hypothesis for certain classes of multiphase systems can be effecteda priori by our arguments, independently of any subsequent macroscaledynamical modelling. Our analysis, whereby we systematically proceed from a discrete picture of the underlying geometry to a purely continuum picture, may be likened to that achieved in classical statistical mechanics. As in that case, we hope that the general results obtained transcend the underlying discrete (i.e. spatially periodic) model of the subcontinuum structure.