Particle laden fluid interfaces: Dynamics and interfacial rheology

We review the dynamics of particle laden interfaces, both particle monolayers and particle + surfactant monolayers. We also discuss the use of the Brownian motion of microparticles trapped at fluid interfaces for measuring the shear rheology of surfactant and polymer monolayers. We describe the basic concepts of interfacial rheology and the different experimental methods for measuring both dilational and shear surface complex moduli over a broad range of frequencies, with emphasis in the micro-rheology methods. In the case of particles trapped at interfaces the calculation of the diffusion coefficient from the Brownian trajectories of the particles is calculated as a function of particle surface concentration. We describe in detail the calculation in the case of subdiffusive particle dynamics. A comprehensive review of dilational and shear rheology of particle monolayers and particle + surfactant monolayers is presented. Finally the advantages and current open problems of the use of the Brownian motion of microparticles for calculating the shear complex modulus of monolayers are described in detail.     

一组线型聚苯乙烯和星形支化聚苯乙烯的凝胶色谱与热场流分级方法的比较

本文应用热场流分级方法,在两种不同的场强下(△T=30℃、△T=50℃),测试了一系列窄分布聚苯乙烯标样和星形支化聚苯乙烯的淋出体积V_r和分子量M的依赖关系。星形支化物的臂数不同,但臂的分子量相同,上述样品进行了GPC测试,实验表明,由TFFF得到的支化的与线型聚苯乙烯在V_r～M关系上的差别大于GPC的结果,表明链结构对扩散系数的影响大于对分子体积的影响。     

Characterization of macromolecules in liquid solutions by thermal diffusion. I. Dependence of the soret coefficient on the nature of the dispersing medium

Experiments have been carried out on thermal diffusion of macromolecular particles dispersed in various liquids, with the object of checking some predictions of the radiation-pressure theory of Soret effect in liquids and of establishing a method of physical characterization of macromolecules in liquid solutions. The experimental results confirm the importance of the ratio G between thermal conductivity K and (phase) velocity v of high-frequency elastic waves of the materials composing the mixture in determining the thermodiffusive behavior of a liquid solution. We have shown that the migration of the macromolecular component takes place in the same direction in which thermal energy is flowing or opposite to it, depending on whether G of the dispersed particles is smaller or larger relative to the G of the liquid. Another aspect of the same phenomenon may be observed when macroscopic pieces of nonmetallic materials are suspended in a liquid, and heat is made to flow through this solid plunger and the surrounding liquid. The experiments performed with molecular solutions and with macroscopic plungers mutually complement and confirm each other. Anomalous results obtained in the case of solutions of polyvinylpyrrolidone in methanol are also discussed, and the possibility that this might be the consequence of the existence of a marked velocity dispersion in the high-frequency region of the spectrum of thermal waves in both water and methyl alcohol is indicated. Finally the possibility is hinted that thermal diffusion might have been responsible for the phenomena of molecular selection and evolution which ultimately led to the origin of life on our planet.     

COMPARISON OF GPC AND THERMAL FIELDFLOW FRACTIONATION METHODS FOR LINEAR AND STAR BRANCHED POLYSTYRENE SAMPLES

The Thermal Field-Flow Fractionation (TFFF) method was used to determine the elution volumeof a series of star branched polystyrene having different number of arms but the same arm molecularweigh and polystyrene standards with narrow distribution whose molecular weight ranged from5.0×10~4 to 8.6×10~5. Results were obtained by measuring at two temperature difference (△T=30℃and △T=50℃in THF. The same star branched samples were measured by means of GPC method.Comparison of Vr-Mrelationships obtained from TFFF and GPC showed that the displacement of V_r-M curves for star and linear polystyrene is larger than that in GPC. This difference is caused by theentirely different mechanism of separation for these two methods. As the controlling factor is hy-drodynamic volume of the polymer chain in solution for GPC, it is the diffusion coefficient of polymermolecules for TFFF. The experimental results indicate that the influence of variance of chain struc-ture on diffusion coefficient is stronger than that on the hydrodynamic volume and that TFFF tech-nique may be used as a method for characterizing branching of polymer molecules. For this pur-pose a proper theoretical model and more accurate experiments are needed.     

Particle self-assembly at ionic liquid-based interfaces

This review presents an overview of the nature of ionic liquid (IL)-based interfaces and self-assembled particle morphologies of IL-in-water, oil- and water-in-IL, and novel IL-in-IL Pickering emulsions with emphasis on their unique phenomena, by means of experimental and computational studies. In IL-in-water Pickering emulsions, particles formed monolayers at ionic liquid–water interfaces and were close-packed on fully covered emulsion droplets or aggregated on partially covered droplets. Interestingly, other than equilibrating at the ionic liquid–water interfaces, microparticles with certain surface chemistries were extracted into the ionic liquid phase with a high efficiency. These experimental findings were supported by potential of mean force calculations, which showed large energy drops as hydrophobic particles crossed the interface into the IL phase. In the oil- and water-in-IL Pickering emulsions, microparticles with acidic surface chemistries formed monolayer bridges between the internal phase droplets rather than residing at the oil/water–ionic liquid interfaces, a significant deviation from traditional Pickering emulsion morphology. Molecular dynamics simulations revealed aspects of the mechanism behind this bridging phenomenon, including the role of the droplet phase, surface chemistry, and inter-particle film. Novel IL-in-IL Pickering emulsions exhibited an array of self-assembled morphologies including the previously observed particle absorption and bridging phenomena. The appearance of these morphologies depended on the particle surface chemistry as well as the ILs used. The incorporation of particle self-assembly with ionic liquid science allows for new applications at the intersection of these two fields, and have the potential to be numerous due to the tunability of the ionic liquids and particles incorporated, as well as the particle morphology by combining certain groups of particle surface chemistry, IL type (protic or aprotic), and whether oil or water is incorporated.     

Micro-thermal field-flow fractionation: new high-performance method for particle size distribution analysis

Micro-thermal field-flow fractionation (mu-TFFF) was applied to the separation of polystyrene latices. This new high-resolution technique allows determination of the particle size distribution (PSD) if carried out under optimized experimental conditions. The optimum temperature of the accumulation wall, which influences the relaxation processes and, consequently, the zone broadening, was chosen on the basis of our prior work. The flow rate was chosen as a compromise between the theoretical optimum value, which is very low because the diffusion coefficients of the colloidal particles are very small, and a value allowing performance of the PSD analysis in a reasonable time. These experimental conditions can be manipulated easily due to the high versatility of mu-TFFF, which follows from a large decrease of the heat energy flux across the channel with its reduced dimensions in comparison with standard TFFF. The PSDs obtained from mu-TFFF data are compared with results from quasi-elastic laser light scattering (QELS) and transmission electron microscopy (TEM). It has been found that a baseline resolution of a model mixture of two samples of close average particle diameters can be achieved by an appropriate choice of the temperature drop in mu-TFFF, whereas only a broad, unresolved PSD of the mixed sample was obtained from the QELS measurement. The TEM of the mixed sample revealed the presence of two particle size populations. However, the number of particles which are practically counted on a TEM picture is several orders of magnitude lower than the number of particles taken into account in mu-TFFF or QELS. Consequently, the PSD obtained from the TEM did not represent the whole sample. Comparison of mu-TFFF with modern hydrodynamic chromatography (HC) has shown that the methods exhibit roughly the same resolution and time of analysis. Nevertheless, mu-TFFF is a more universal technique because the separation of the colloidal particles or of the macromolecules within a broad range of molar masses is carried out on the same channel, as demonstrated previously.     

Influence of process and formulation parameters on the formation of submicron particles by solvent displacement and emulsification-diffusion methods critical comparison

Solvent displacement and emulsification–diffusion are the methods used most often for preparing biodegradable submicron particles. The major difference between them is the procedure, which results from the total or partial water miscibility of the organic solvents used. This review is devoted to a critical and a comparative analysis based on the mechanistic aspects of particle formation and reported data on the influence of operating conditions, polymers, stabilizing agents and solvents on the size and zeta-potential of particles. In addition, a systematic study was carried out experimentally in order to obtain experimental data not previously reported and compare the data pertaining to the different methods. Thus the discussion of the behaviors reported in the light of the results obtained from the literature takes into account a wide range of theoretical and practical information. This leads to discussion on the formation mechanism of the particles and provides criteria for selecting the adequate method and raw materials for satisfying specific objectives in submicron particle design.     

Predicting adsorption isotherms of asphaltenes in porous materials

In this paper we present a molecular thermodynamics approach for the modeling of adsorption isotherms of asphaltenes adsorbed on Berea sandstone, Bedford limestone and dolomite rock, using a model for bulk asphaltenes precipitation and a quasi-two-dimensional approach for confined fluids [E. Buenrostro-González, C. Lira-Galeana, A. Gil-Villegas, J. Wu, AIChE J., 50 (2004) 2552–2570; A. Martínez, M. Castro, C. McCabe A. Gil-Villegas, J. Chem. Phys. 126 (2007) 074707, respectively], both based on the Statistical Associating Fluid Theory for Potentials of Variable Range [A. Gil-Villegas, A. Galindo, P.J. Whitehead, S.J. Mills, G. Jackson, A.N. Burgess, J. Chem. Phys. 106 (1997) 4168–4186]. The theory is applied to model adsorption isotherms from experimental data of asphaltenes extracted from a dead sample of heavy crude oil from a Mexican reservoir. The theoretical results give the right Langmuir Type II adsorption isotherms observed experimentally. The model requires the determination of ten molecular parameters related to the size of the particles and the square-well potentials used to describe the particle–surface and particle–particle interactions at the bulk and adsorbed phases. Nine parameters are taken from previous published results about the behavior of asphaltenes in bulk phases and the adsorption of several molecular fluids onto activated carbon and graphite surfaces. The remaining parameter, the energy strength of the particle–surface interaction, is adjusted to reproduce the experimental data, obtaining values that are consistent with Molecular Mechanics calculations for asphaltenes adsorbed on different surfaces and solutions. Although the agreement between theory and experiments shows some deviations at low bulk concentrations, the model reproduces adsorption data at high concentrations where other semi-empirical approaches fail.     

Polarization, steric, and focusing micro-thermal field-flow fractionation principles, theory, instrumentation, and applications in polymers and particles analysis

The benefits of the miniaturization of the separation channel for Thermal field-flow fractionation (TFFF) are analyzed theoretically and studied experimentally. It is found that the operational variables influencing the efficiency and resolution of the separation can be optimized and that the concept of a micro-TFFF is meaningful. A miniaturized TFFF channel was proposed and constructed. It has been demonstrated experimentally that micro-TFFF allows one to carry out high-performance separations under carefully chosen experimental conditions. This new technique is highly competitive in comparison with size-exclusion chromatography (SEC) of macromolecules with molar masses up to roughly one million gram per mole. However, the versatility of micro-TFFF is superior to SEC for macromolecules of ultra-high molar masses, as well as colloidal sub-micron, and micron-sized particles of synthetic, natural, or biological origin. The free choice of the carrier liquids without any modification of the separation system affords an advantage to micro-TFFF. The experimental implementation and application to polymer and particle analysis confirmed the potential of micro-TFFF.     

Dynamic adhesion behavior of micrometer-scale particles flowing over patchy surfaces with nanoscale electrostatic heterogeneity

The dynamic adhesion behavior of micrometer-scale silica particles is investigated numerically for a low Reynolds number shear flow over a planar collecting wall with randomly distributed electrostatic heterogeneity at the 10-nanometer scale. The hydrodynamic forces and torques on a particle are coupled to spatially varying colloidal interactions between the particle and wall. Contact and frictional forces are included in the force and torque balances to capture particle skipping, rolling, and arrest. These dynamic adhesion signatures are consistent with experimental results and are reminiscent of motion signatures observed in cell adhesion under flowing conditions, although for the synthetic system the particle–wall interactions are controlled by colloidal forces rather than physical bonds between cells and a functionalized surface. As the fraction of the surface (Θ) covered by the cationic patches is increased from zero, particle behavior sequentially transitions from no contact with the surface to skipping, rolling, and arrest, with the threshold patch density for adhesion (Θ_crit) always greater than zero and in quantitative agreement with experimental results. The ionic strength of the flowing solution determines the extent of the electrostatic interactions and can be used to tune selectively the dynamic adhesion behavior by modulating two competing effects. The extent of electrostatic interactions in the plane of the wall, or electrostatic zone of influence, governs the importance of spatial fluctuations in the cationic patch density and thus determines if flowing particles contact the wall. The distance these interactions extend into solution normal to the wall determines the strength of the particle–wall attraction, which governs the transition from skipping and rolling to arrest. The influence of Θ, particle size, Debye length, and shear rate is quantified through the construction of adhesion regime diagrams, which delineate the regions in parameter space that give rise to different dynamic adhesion signatures and illustrate selective adhesion based on particle size or curvature. The results of this study are suggestive of novel ways to control particle–wall interactions using randomly distributed surface heterogeneity.     

Measurement and modeling on hydrodynamic forces and deformation of an air bubble approaching a solid sphere in liquids

The interaction between bubbles and solid surfaces is central to a broad range of industrial and biological processes. Various experimental techniques have been developed to measure the interactions of bubbles approaching solids in a liquid. A main challenge is to accurately and reliably control the relative motion over a wide range of hydrodynamic conditions and at the same time to determine the interaction forces, bubble–solid separation and bubble deformation. Existing experimental methods are able to focus only on one of the aspects of this problem, mostly for bubbles and particles with characteristic dimensions either below 100 μm or above 1 cm. As a result, either the interfacial deformations are measured directly with the forces being inferred from a model, or the forces are measured directly with the deformations to be deduced from the theory. The recently developed integrated thin film drainage apparatus (ITFDA) filled the gap of intermediate bubble/particle size ranges that are commonly encountered in mineral and oil recovery applications. Equipped with side-view digital cameras along with a bimorph cantilever as force sensor and speaker diaphragm as the driver for bubble to approach a solid sphere, the ITFDA has the capacity to measure simultaneously and independently the forces and interfacial deformations as a bubble approaches a solid sphere in a liquid. Coupled with the thin liquid film drainage modeling, the ITFDA measurement allows the critical role of surface tension, fluid viscosity and bubble approach speed in determining bubble deformation (profile) and hydrodynamic forces to be elucidated. Here we compare the available methods of studying bubble–solid interactions and demonstrate unique features and advantages of the ITFDA for measuring both forces and bubble deformations in systems of Reynolds numbers as high as 10. The consistency and accuracy of such measurement are tested against the well established Stokes–Reynolds–Young–Laplace model. The potential to use the design principles of the ITFDA for fundamental and developmental research is demonstrated.     

Separation of Isotopes in the Thermal Diffusion Column

Abstract

Gas liquid and solid mixtures undergo a slight demixing in the presence of a temperature difference. This phenomenon, known as thermal diffusion, is illustrated in Figure 1 for the isotopes of neon in the gas phase and for isotopically substituted carbon disulfide in the liquid phase. The separation effect, which is quite small even for relatively large temperature differences, was of no practical significance prior to the invention by Clusius and Dickel of the thermogravitational thermal diffusion column in 1938¹. In the thermal diffusion column (Figure 2) the fluid is confined between closely spaced vertical walls maintained at different temperatures. A convection current is set up with the fluid rising along the hot wall and descending along the cold wall. Thermal diffusion takes place In the horizontal direction. The combined effects of vertical countercurrent thermogravitational circulation and horizontal thermal diffusion lead to large separations in the vertical direction. The equivalent of several hundred separation stages can be obtained in apparatus no more than a few meters in length.     

Multivariate curve resolution-particle swarm optimization: A high-throughput approach to exploit pure information from multi-component hyphenated chromatographic signals

Multivariate curve resolution-particle swarm optimization (MCR-PSO) algorithm is proposed to exploit pure chromatographic and spectroscopic information from multi-component hyphenated chromatographic signals. This new MCR method is based on rotation of mathematically unique PCA solutions into the chemically meaningful MCR solutions. To obtain a proper rotation matrix, an objective function based on non-fulfillment of constraints is defined and is optimized using particle swarm optimization (PSO) algorithm. Initial values of rotation matrix are calculated using local rank analysis and heuristic evolving latent projection (HELP) method. The ability of MCR-PSO in resolving the chromatographic data is evaluated using simulated gas chromatography–mass spectrometry (GC–MS) and high-performance liquid chromatography–diode array detection (HPLC–DAD) data. To present a comprehensive study, different number of components and various levels of noise under proper constraints of non-negativity, unimodality and spectral normalization are considered. Calculation of the extent of rotational ambiguity in MCR solutions for different chromatographic systems using MCR-BANDS method showed that MCR-PSO solutions are always in the range of feasible solutions like true solutions. In addition, the performance of MCR-PSO is compared with other popular MCR methods of multivariate curve resolution-objective function minimization (MCR-FMIN) and multivariate curve resolution-alternating least squares (MCR-ALS). The results showed that MCR-PSO solutions are rather similar or better (in some cases) than other MCR methods in terms of statistical parameters. Finally MCR-PSO is successfully applied in the resolution of real GC–MS data. It should be pointed out that in addition to multivariate resolution of hyphenated chromatographic signals, MCR-PSO algorithm can be straightforwardly applied to other types of separation, spectroscopic and electrochemical data.     

Numerical simulations of viscoelastic particle migration in a microchannel with triangular cross-section

The migration of a spherical particle immersed in a viscoelastic liquid flowing in a microchannel with a triangular cross-section is investigated by direct numerical simulations under inertialess conditions. The viscoelastic fluid is modeled through two constitutive equations to investigate the effect of the second normal stress difference and the resulting secondary flows on the migration phenomenon. The results are presented in terms of trajectories followed by the particles released at different initial positions over the channel cross-section in a wide range of Weissenberg numbers and confinement ratios. Particles suspended in a fluid with a negligible second normal stress difference migrate toward the channel centerline or the closest wall, depending on their initial position. A much more complex dynamics is found for particles suspended in a fluid with a relevant second normal stress difference due to the appearance of secondary flows that compete with the migration phenomenon. Depending on the Weissenberg number and confinement ratio, additional equilibrium positions (points or closed orbits) may appear. In this case, the channel centerline becomes unstable and the particles are driven to the corners or “entrapped” in recirculation regions within the channel cross-section. The inversion of the centerline stability can be exploited to design efficient size-based separation devices.     

STOCHASTIC MODEL OF PERIODIC OPERATION PERFORMANCE FOR THE CONTINUOUS COUNTER—CURRENT ADSORPTION PROCESS

A stochastic model is developed to predict the periodic operation per formance of the continuous counter-current adsorption process.The model takes into account the effects of random backmixing of particles,axial dispersion of liquid phase,liquid-film mass transfer,intraparticle diffusion and particle shape,and can reveal clearly the behavior of solid and liquid phase in adsorption process.The simulation results agree with the experimental data rather well.     

Thiol-functionalized silica–mixed matrix membranes for silver capture from aqueous solutions: Experimental results and modeling

The study deals with an aqueous phase application of mixed matrix membranes (MMMs) for silver ion (Ag⁺) capture. Silica particles were functionalized with 3-mercaptopropyltrimethoxy silane (MPTMS) to introduce free thiol (–SH) groups on the surface. The particles were used as the dispersed phase in the polysulfone or cellulose acetate polymer matrix. The membranes were prepared by the phase inversion method to create more open and interconnected porous structures suitable for liquid phase applications. The effects of the silica properties such as particle size, specific surface area, and porous/nonporous morphology on the silver ion capture capacity were studied. It was demonstrated that the membranes are capable of selectively capturing silver from a solution containing significant concentrations of other metal ions like Ca²⁺. The membranes were studied to quantify the dynamic capacity for silver ion capture and its dependence on residence time through the adjustment of transmembrane pressure. The thiol–Ag⁺ interaction was quantified with quartz crystal microbalance in a continuous flow mode experiment and the observations were compared with the membrane results. One-dimensional unsteady state model with overall volumetric mass transfer coefficient was developed and solved to predict the silver concentration in the liquid phase and the solid silica phase along the membrane thickness at varying time. The breakthrough data predicted using the model is comparable with the experimental observations. The study demonstrates successful application of the functionalized silica–mixed matrix membranes for selective aqueous phase Ag⁺ capture with high capacity at low transmembrane pressures. The technique can be easily extended to other applications by altering the functionalized groups on the silica particles.     

Role of the shape of various bacteria in their separation by Microthermal Field-Flow Fractionation

The steady-state movement of the spherical and non-spherical particles, such as prolate or oblate rotational ellipsoids, cylinders, or parallelepipeds, suspended in a liquid and exposed to a unidirectional temperature gradient, is analyzed theoretically. The differences in the ratios of the rotational to translational diffusion coefficients of the non-spherical to spherical particles, the heterogeneity of thermal conductivity of the particle body, and the heterogeneity in surface chemical nature make possible to separate the particles according to differences in shape. Preliminary experimental separations of Gram-positive and Gram-negative, nearly spherical and rod-shaped bacteria performed by Microthermal Field-Flow Fractionation confirmed that the fractionation of the cells according to differences in shape is possible.     

Heat Effects in ZLC Experiments

The problem of nonisothermal desorption in a zero length column (ZLC) experiment is considered theoretically. Simple analytical expressions for the ZLC desorption curve are derived for certain limiting situations in which the governing equations reduce to a linear form. More general numerical solutions are calculated for a wide range of experimental conditions assuming both negligible mass transfer resistance and finite mass transfer resistance controlled by intraparticle diffusion. A simple criterion for negligible thermal effects is developed. It is shown that when the ZLC technique is applied to the measurement of diffusion in unaggregated zeolite crystals, as originally intended, heat effects are generally insignificant. However, when applied to the measurement of macropore diffusion in relatively large adsorbent particles heat effects can become important and may cause major modification of both the desorption rate and the shape of the desorption curve. A recent experimental ZLC study carried out with commercial adsorbent particles, under conditions of macropore diffusion control, showed an anomalous dependence of the desorption rate on both temperature and particle size. These effects can be qualitatively explained by the nonisothermal model. A more precise quantitative representation of these experiments will require a more refined model incorporating a nonlinear equilibrium isotherm as well as intraparticle diffusional resistance.     

Ultrafast relaxation and exciton–exciton annihilation in PTCDA thin films at high excitation densities

Femtosecond pump–probe spectroscopy is applied to thin films of the quasi-one-dimensional organic semiconductor 3,4,9,10-perylene tetracarboxylic dianhydride (PTCDA). We present transient absorption spectra over a broad spectral range. Ultrafast intraband relaxation in the S₁ manifold towards the border of the Brillouin zone is shown to depend on temperature and excitation density. The intraband relaxation time is of the order of 100 fs. At high excitation densities (>10¹⁹ cm⁻³), the major de-excitation mechanism for the relaxed excitons is exciton–exciton annihilation. The experimental decay dynamics can be explained very well by two alternative annihilation models: one-dimensional diffusion limited bimolecular recombination or single-step long range Förster-type annihilation. In contrast, a three-dimensional diffusion limited annihilation model is significantly inferior. For all three models, we extract annihilation rates, diffusion constants, diffusion lengths, and Förster radii for room and liquid Helium temperature.