Metal particle adsorption and diffusion in a model polymer/metal composite system

We have developed a model polymer/metal composite system based on the adsorption of colloidal gold particles from a dilute aqueous suspension to the surface of poly(2-vinylpyr-idine) (PVP). Particle coverages and tracer diffusion coefficients for the particles within a PVP matrix phase were measured by Rutherford backscattering spectrometry. The adsorption process is quantitatively described by a diffusion-limited mechanism where gold particles irreversibly adsorb to the surface of the polymer film. Model dispersions produced in this way are excellent model systems for studying the fundamental properties of metal particle dispersions, since the particle size and the areal density of particles on the surface are well-controlled. Diffusion coefficients for the gold particles within PVP were also measured. The diffusion of the gold particles was found to be coupled to the bulk viscosity of the polymer, even though the size of the gold particles was only slightly larger than the mesh size of the entanglement network for PVP. © 1995 John Wiley & Sons, Inc.     

Surface patterning via evaporation of ultrathin films containing nanoparticles

The dewetting dynamics of ultrathin films containing potentially surface-active nanoparticles is considered in the presence of evaporation. Evolution equations for the film height and particle surface and bulk concentration are derived using a lubrication model coupled by a constitutive relation for the dependence of the viscosity on local particle concentration. A linear stability analysis and numerical simulations are used to determine how particle mass distribution depends on the various physical parameters such as equilibrium film separation distance, initial packing concentration, rate of evaporation, and particle surface activity. Our results show that when starting from an initially uniform distribution the particles become aligned into distinct "bands" in rectilinear geometry, or "rings" in cylindrical geometry. The functional dependence of the pattern spacing on relevant system parameters is studied and detailed herein.     

The diffusion coefficient of a swollen microgel particle

The drag on a permeable particle traversing through a Newtonian liquid is calculated. This is in terms of a single dimensionless group, Da, the Darcy number, which relates the particle permeability to the radius. For small values of the Darcy number the solution reverts to the well-known Stokes drag for smooth hard particles. For larger values of the Darcy number the drag is reduced. This drag allows calculation of the diffusion coefficient of such particles, again as a function of the Darcy number. The results are discussed in relation to microgel particles, which display swelling under certain conditions. The size of such particles is typically measured with dynamic light scattering, which measures the diffusion coefficient of particles and as such the analysis presented here shows the conditions under which dynamic light scattering is accurate. The Darcy number for microgel particles is estimated to be on the order of 10(-7).     

The effect of gas slip on pressure drop and deposition of submicron particles in model granular filters

The Stokes flow field and aerosol particle deposition from flows in model filters, i.e., separate layers of granules with square and hexagonal structures, have been calculated taking into account the effect of gas slip at granule surface. Approximating formulas have been derived for granule drag forces to a flow. The efficiencies of diffusion collection of particles have been calculated in a wide range of Peclet numbers with allowance for a finite particle size and the existence of a Knudsen boundary layer, the layer thickness being comparable with the particle sizes. The applicability of the cell model to the calculation of granular filters has been discussed.     

Effect of soluble polymer binder on particle distribution in a drying particulate coating

Soluble polymer is frequently added to inorganic particle suspensions to provide mechanical strength and adhesiveness to particulate coatings. To engineer coating microstructure, it is essential to understand how drying conditions and dispersion composition influence particle and polymer distribution in a drying coating. Here, a 1D model revealing the transient concentration profiles of particles and soluble polymer in a drying suspension is proposed. Sedimentation, evaporation and diffusion govern particle movement with the presence of soluble polymer influencing the evaporation rate and solution viscosity. Results are summarized in drying regime maps that predict particle accumulation at the free surface or near the substrate as conditions vary. Calculations and experiments based on a model system of poly(vinyl alcohol) (PVA), silica particles and water reveal that the addition of PVA slows the sedimentation and diffusion of the particles during drying such that accumulation of particles at the free surface is more likely.     

A Nonlinear Rupture Theory of Thin Liquid Films with Soluble Surfactant

The effects of soluble surfactant on the dynamic rupture of thin liquid films are investigated. A nonlinear coupling evolution equation is used to simulate the motion of thin liquid films on free surfaces. A generalized Frumkin model is adopted to simulate the adsorption/desorption kinetics of the soluble surfactant between the surface and the bulk phases. Numerical simulation results show that the liquid film system with soluble surfactant is more unstable than that with insoluble surfactant. Moreover, a generalized Frumkin model is substituted for the Langmuir model to predict the instability of liquid film with soluble surfactant. A numerical calculation using the generalized Frumkin model shows that the surfactant solubility increases as the values of parameters of absorption/desorption rate constant (J), activation energy desorption (nu(d)), and bulk diffusion constant (D(1)) increase, which consequently causes the film system to become unstable. The surfactant solubility decreases as the rate of equilibrium (lambda) and interaction among molecules (K) are increased, which therefore stabilizes the film system. On the other hand, an increase of relative surface concentration (the index of a power law), beta(n), will initially result in a decrease of corresponding shear drag force as beta and n increase from 0 to 0.3 and 0.85, respectively. This will enhance the Marangoni effect. However, a further increase of beta and n to greater than 0.3 and 0.85, respectively, will conversely result in an increase of the corresponding shear drag force. This will weaken the Marangoni effect and thus result in a reduction of interfacial stability. Copyright 2000 Academic Press.     

The Stokes–Brinkman Flow Field and Diffusion Deposition of Nanoparticles in a Layer of Hollow Permeable Grains

The diffusion deposition of point particles from a Stokes–Brinkman transverse stationary flow in a model monolayer membrane composed of contacting spherical hollow grains (capsules) with porous permeable shells formed from nanoparticles, is calculated. Monolayers with square and hexagonal packings of the grains are considered. Approximation equations are constructed for the dependences of grain drag force on shell thickness, Brinkman permeability parameter S, and internal shell radius ξ. Efficiencies of point particle collection on the grains are calculated as depending on the Peclet number, S, and ξ, and it is shown that layers of hollow permeable grains possess the highest filtration performance criterion among layers of impermeable and permeable uniform porous grains provided that the zero-concentration boundary condition is fulfilled at the outer radius of the grain.     

On hydrodynamic permeability of a membrane built up by porous deformed spheroidal particles

This paper concerns the slow viscous flow of an incompressible fluid past a swarm of identically oriented porous deformed spheroidal particles, using particle-in-cell method. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid region in their stream function formulations are used. Explicit expressions are investigated for both the inside and outside flow fields to the first order in a small parameter characterizing the deformation. The flow through the porous oblate spheroid is considered as the particular case of the porous deformed spheroid. The hydrodynamic drag force experienced by a porous oblate spheroid and permeability of a membrane built up by porous oblate spheroids having parallel axis are evaluated. The dependence of the hydrodynamic drag force and the hydrodynamic permeability on particle volume fraction, deformation parameter and viscosity of porous fluid are also discussed. Four known boundary conditions on the hypothetical surface are considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta-Morse’s condition). Some previous results for hydrodynamic drag force and hydrodynamic permeability have been verified. The model suggested can be used for evaluation of changing hydrodynamic permeability of a membrane under applying unidirectional loading in pressure-driven processes (reverse osmosis, nano-, ultra- and microfiltration).     

Effects of surfactants on wave-induced drainage of foam and emulsion films

It is well established that the plane-parallel models of foam and emulsion films underestimate the velocity of film thinning by up to several orders of magnitude and show an incorrect dependence of thinning velocity on film radius. A new theory of film thinning has been previously formulated for tangentially immobile films [12, 13], and shows that the reason for this discrepancy is the neglect of experimentally observed finite amplitude surface waves. For thin films of relatively large radii (> 1o^–2 cm), the pumping of the fluid generated by oscillations of the surface waves, provides the dominant contribution to film thinning velocity. The present hydrodynamic model includes the effects of surfactants (Marangoni-Gibbs-effect, surface viscosity and surface diffusion) and surface waves on thinning velocity. As in the case of a tangentially immobile film, it is concluded that the thinning velocity varies inversely with less than the first power of the film radius, and not with the square of the film radius, as predicted by the plane-parallel models of thin film. Also, the velocity of thinning is found to be up to several orders of magnitudes larger than that evaluated from the plane-parallel models. The influence of waves in enhancing the thinning velocity is found to be most significant for a tangentially immobile film and this effect decreases by a factor of up to 3, with a decrease in surface elasticity and surface viscosity.     

Mobility of a particle immersed in a liquid film between two fluids

The mobility of a particle immersed in a liquid film between two viscous fluids is calculated in point approximation. The mobility in the direction parallel to the film diverges logarithmically as the ratio of the sum of outside viscosities to the film viscosity tends to zero, as in the [Saffman-Delbruck, Proc. Natl. Acad. Sci. U.S.A. 72, 3111 (1975)] expression for the mobility of a particle embedded in a membrane. A simple expression for the limiting behavior is derived. For any values of the parameters the mobility tensor can be evaluated by numerical quadrature of two one-dimensional integrals.     

Strukturviskosität von verdünnten Lösungen von Biopolymeren

The importance of the rheological behaviour of solutions of macromolecules is briefly evaluated. The viscosity of the solutions depends on concentration, shear rate and time of shear, this relation being determined by the structure of the dissolved molecules. In dilute solutions shear dependence of viscosity is very frequently caused by the preferential orientation of anisotropic molecules. In such a case the particle dimensions can be calculated from the true limiting viscosity number, an anisotropy factor, the rotational diffusion constant and the effective particle density. These numbers can be derived from the flow curve, which has been extrapolated to zero concentration. It is necessary to measure the flow curve at shear gradients, which are sufficiently low to allow for an extrapolation to vanishing shear rate. By comparing the experimental flow curve with a choice of theoretical ones, the rotational diffusion constant and the anisotropy factor (axial ratio) can be found. From the limiting viscosity number and the axial ratio, the particle density can be calculated.     

A model for the drying process during film formation in waterborne acrylic coatings

Establishing drying mechanisms during film formation in waterborne acrylic coatings is a technologically important problem, however complex, and still poorly understood. A model for the prediction of evaporation kinetics is proposed in this paper, where films are supposed to dry normally with respect to the film surface, and a drying front separates a top dry region from a bottom wet region. The model accounts for the competition between water evaporation and particle diffusion that determines the degree of vertical homogeneity, but also for the competition between water evaporation and particle deformation that ultimately establishes the rate-determining step in film formation processes. The model was validated by performing gravimetric water-loss experiments on latexes of acrylic polymers of various composition, various particle size and stabilizing systems, under different environmental temperatures and humidity, and various initial film thicknesses in order to evaluate the effect of the different factors that can in principle influence the film formation process.     

Computational electrochemistry: finite element simulation of a disk electrode with ultrasonic acoustic streaming

Computer simulations using the finite element method (FEM) are used to predict the correlation between the transport limiting current (I(lim)) and parameters such as diffusion coefficient, source to electrode separation, source power, and medium viscosity for a sonicated disk electrode in "face on" mode. The fluid dynamics and diffusion layer are modeled directly using FEM and predict that the electrode is uniformly accessible, I(lim) is proportional to the diffusion coefficient to the 2/3 power and I(lim) is proportional to the square root of the source power. Curves are also calculated relating I(lim) to the source to electrode separation and liquid viscosity.     

An Insoluble Surfactant Model for a Vertical Draining Free Film

A mathematical model is constructed to study the evolution of a vertically oriented thin liquid film draining under gravity when there is an insoluble surfactant with finite surface viscosity on its free surface. Lubrication theory for this free film results in three coupled nonlinear partial differential equations describing the free surface shape, the surface velocity, and the surfactant transport at leading order. We will show that in the limit of large surface viscosity, the evolution of the free surface is that obtained for the tangentially immobile case. For mobile films with small surface viscosity, transition from a mobile to an essentially immobile film is observed for large Marangoni effects. It is verified that increasing surface viscosity and the Marangoni effect retard drainage, thereby enhancing film stability. The theoretical results are compared with experiment; the purpose of both is to act as a model problem to evaluate the effectiveness of surfactants for potential use in foam-fabrication processes. Copyright 2000 Academic Press.     

Mobility of permeable fractal agglomerates in slip regime

Hydrodynamic drag and mobility of fractal aggregates in the slip creeping flow regime are calculated. A theoretical continuum model of the gas slip flow past and within agglomerates is developed. It accounts for effects of flow rarefaction and porous fractal structure upon the molecular mean free path, apparent viscosity, and effective permeability of agglomerates. It is shown that flow rarefaction significantly diminishes the aggregates' drag to an extent that cannot be predicted by the Cunningham's drag correction factor. The developed model allows calculation the agglomerates' transport properties in a wide range of fractal dimensions. For low D(f) agglomerates the drag force agrees with the Friedlander's expression based on the Epstein's single sphere drag in the free molecular regime.     

Thinning of drying latex films due to surfactant

Lateral non-uniformities in surfactant distribution in drying latex films induce surface tension gradients at the film surface and lead to film thinning through surfactant spreading. Here we investigate the influence of the surfactant driven to the air-water interface, during the early stages of latex film drying, on the film thinning process which could possibly lead to film rupture. A film height evolution equation is coupled with conservation equations for particles and surfactant, within the lubrication approximation, and solved numerically, to obtain the film height, particle volume fraction, and surfactant concentration profiles. Parametric analysis identifies the effect of drying rate, dispersion viscosity and initial particle volume fraction on film thinning and reveals the conditions under which films could rupture. The results from surface profilometry conform qualitatively to the model predictions.     

Deformation controlled assembly of binary microgel thin films

We describe the assembly of two-component, hydrogel microparticle (microgel) monolayer films onto solid substrates via passive Coulombic adsorption from solution. By using two different microgel types with nearly identical sizes but different degrees of softness, the influence of particle deformation on film composition was determined. Determination of the microgel properties using a variety of light scattering techniques allowed for predictions of the film composition as a function of solution composition using a random sequential adsorption (RSA) model. The films were then studied via atomic force microscopy (AFM), and surface coverage and population statistics were determined from the images and compared to the model predictions. Deviations from the predicted particle adsorption behavior can be directly traced to differences in particle softness, deformation, and particle footprint following adsorption, which biases the particle coverage to the more rigid (smaller footprint) particles. Furthermore, by using a mixture of degradable and nondegradable core/shell particles, the identity of the particles can be unambiguously determined by measuring AFM height changes following erosion of the core from the microgels. These results show that, regardless of the solution diffusion properties of soft particles, their competition for surface adsorption from a binary mixture is largely dictated by their interactions with the surface and their deformation at the surface.     

Hydrodynamic force on a microparticle approaching a wall in a nanoparticle dispersion: observation of a separation-dependent effective viscosity

Colloid probe atomic force microscopy was used to measure the hydrodynamic force exerted on a 30-μm-diameter silica particle being moved toward or away from a silica plate in aqueous dispersions of 22-nm-diameter silica nanoparticles (6 or 8 vol %). Upon comparing the measured force to predictions made using the well-known expression of Cox and Brenner (Cox, R. G.; Brenner, H. Chem. Eng. Sci.1967, 22, 1753-1777) assuming a constant viscosity equal to that of the bulk dispersion, the measured drag force was found to become significantly less than that predicted at smaller particle-plate separation distances (e.g., <500 nm). A recent theoretical paper by Bhattacharya and Blawzdziewicz (Bhattacharya, S.; Blawzdziewicz, J. J. Chem. Phys.2008, 128, 214704) predicted that in a solution of dispersed nanoparticles the effective viscosity characterizing the hydrodynamic force on the particle should vary from that of the solvent at contact to that of the bulk dispersion at large separations. By adjusting the viscosity in the Cox and Brenner expression to make the predicted hydrodynamic force match that measured (i.e., the effective viscosity), a curve showing these exact characteristics was obtained. The effective viscosity profile was not a function of particle speed, and changes in the effective viscosity extended to separation distances of as large as 2 μm (nearly 100 times the hard diameter of the nanoparticles). These results suggest that in the range of typical colloidal forces (on the order of 100 nm), the dynamics of particle motion in such systems are determined by the viscosity of the solvent and not that of the bulk dispersion.     

Use of a Cross-Sectional Model for Determining Rheology in Settling Slurries: Effect of Solvent,Particle Size,and Density

Transport models for partially settling slurries need accurate rheology correlations, particularly describing viscosity relationship to the particle concentration. A method is needed to untangle the effects of settling on apparent viscosity and the real effects of particle concentration on viscosity during rheology measurements. Our approach is based on model inversion of a cross-section model for the vertical particle concentration gradient and the local rheologies in the gap of a Couette type rheometer, established by a balance between gravitational particle settling and shear induced migration of the particles. The Krieger-Dougherty rheology correlation with adjustable parameters has been applied, where the parameters are determined by minimizing the difference between the measured viscosity data and those calculated by the model. Fairly mono-disperse silver coated polystyrene particles with two sizes and densities were used in both the aqueous and oil phase. In the raw data an apparent shear thinning tendency is observed. Through the model inversion process, this is accounted for by the shear dependent settling and the steep increase of viscosity with particle concentration. Maximum packing fraction was obtained through settling experiments. The difference between this value and the maximum packing fraction from the model inversion was less than 3% for oil-based suspensions. The larger difference was found for smaller particle size in water which is attributed to the larger effect of interparticle forces.     

Diffusion of liquid domains in lipid bilayer membranes

We report diffusion coefficients of micron-scale liquid domains in giant unilamellar vesicles of phospholipids and cholesterol. The trajectory of each domain is tracked, and the mean square displacement grows linearly in time, as expected for Brownian motion. We study domain diffusion as a function of composition and temperature and measure how diffusion depends on domain size. We find mechanisms of domain diffusion which are consistent with membrane-dominated drag in viscous L(o) phases and bulk-dominated drag for less viscous L(alpha) phases. Where applicable, we obtain the membrane viscosity and report activation energies of diffusion.