Settling of a charged hydrophobic rigid colloid in aqueous media under generalized gravitational field

The hindrance created by the induced electric filed on the sedimentation of a charged colloid in an aqueous media is studied through numerical modeling. The colloid is considered to be hydrophobic, sedimenting under gravity or a centrifugal force (generalized gravity). The deformation of the charge cloud around the colloid induces an electric field, which generates electrical dipole force on the colloid. The sedimentation velocity is governed by the balance of an electric force, hydrodynamic drag, and gravitational force. Governing equations based on the first principle of electrokinetics is solved numerically through a control volume approach. The dependence of the sedimentation velocity on the electrical properties and slip length of the colloid is investigated. The sedimentation velocity of the charged colloid is slower than the corresponding uncharged particle and this deviation magnifies as the charge density as well as particle slip length is increased. An enhanced g-factor creates a size dependency of the charged colloids. The induced sedimentation field is obtained to analyze the electrokinetics. Surface hydrophobicity enhances the sedimentation velocity, which in turn manifests the induced sedimentation field. However, the sedimentation velocity of a charged hydrophobic colloid is lower than the corresponding uncharged hydrophobic particle and this deviation manifests as slip length is increased.     

Particle adsorption and deposition: role of electrostatic interactions

This work demonstrates how electrostatic interactions, described in terms of the classical DLVO theory, influence colloid particle deposition phenomena at solid/liquid interfaces. Electrostatic interactions governing particle adsorption in both non-polar and polar media (screened interactions) are discussed. Exact and approximate methods for calculating the interaction energy of spherical and non-spherical (anisotropic) particles are presented, including the Derjaguin method. Phenomenological transport equations governing particle deposition under the linear regime are discussed with the limiting analytical expressions for calculating initial flux. Non-linear adsorption regimes appearing for higher coverage of adsorbed particles are analysed. Various theoretical approaches are exposed, aimed at calculating blocking effects appearing due to the presence of adsorbed particles. The significant role of coupling between bulk transport and surface blocking is demonstrated. Experimental data obtained under well-defined transport conditions, such as diffusion and forced convection (impinging-jet cells), are reviewed. Various experimental techniques for detecting particles at interfaces are discussed, such as reflectometry, ellipsometry, streaming potential, atomic force microscopy, electron and optical microscopy, etc. The influence of ionic strength and flow rate on the initial particle deposition rate (limiting flux) is presented. The essential role of electrostatic interactions in particle deposition on heterogeneous surfaces is demonstrated. Experimental data pertinent to the high-coverage adsorption regime are also presented, especially the dependence of the maximum coverage of particles and proteins on the ionic strength. The influence of lateral electrostatic interactions on the structure of particle monolayers is elucidated, and the links between colloid and molecular systems are pointed out.     

Formation of Flocs and Sediments in the Presence of Cationic Polyelectrolytes

Regularities of the flocculation of kaolin suspension with cationic polyelectrolytes based on 1,2-dimethyl-5-vinylpyridinium methyl sulfate were studied by turbidimetry, optical microscopy, and sedimentation methods. It was found that poly(1,2-dimethyl-5-vinylpyridinium methyl sulfate)-co-N-vinylpirrolidone promotes the formation of dense flocs and provide a complete sedimentation of the kaolin suspension at a high rate. The effect of dense floc formation is likely caused by a copolymer hydrophobicity and a compression of adsorbed macrocoils accompanied by squeezing of a dispersion medium out of interparticle space.     

Interfacial interactions and colloid retention under steady flows in a capillary channel

Colloidal interfacial interactions in a capillary channel under different chemical and flow conditions were studied using confocal microscopy. Fluorescent latex microspheres (1.1 microm) were employed as model colloids and the effects of ionic strength and flow conditions on colloidal retention at air-water interface (AWI) and contact line were examined in static and dynamic (flow) experiments. Colloids were preferentially attached to and accumulated at AWI, but their transport with bulk solution was non-negligible. Changing solution ionic strength in the range 1-100 mM had a marginal effect on colloidal accumulation, indicating forces other than electrostatic are involved. Flow through the open channel resembled Poiseuille flow with AWI acting as a non-stress-free boundary, which resulted in near stagnation of AWI and consequently promoted colloid accumulation. Retention on contact line was likely dominated by film-straining and was more significant in flow relative to static experiments due to hydrodynamic driving force. Modeling and dimensionless analysis of the flow behavior in the capillary channel clearly indicate the important role of apparent surface viscosity and surface tension in colloidal interfacial retention at the pore scale, providing insight that could improve understanding of colloid fate and transport in natural unsaturated porous media.     

The transport of condensible vapors through a microporous vycor glass membrane

The flow of condensible vapors through microporous Vycor glass was investigated experimentally as well as theoretically. In porous materials, adsorbable gases frequently exhibit higher permeability than predicted from the flow of nonadsorbable gases. This enhanced flow has been attributed to the surface diffusion of adsorbed molecules along the surface of the porous media or to the viscous flow of capillary condensate at high relative pressures. In the present investigation, a new flow model of condensible vapors through microporous material was developed by considering the blocking effect of the adsorbed phase on the basis of a cylindrical capillary structure. Six different flow modes were considered depending on the pressure distribution and the film thickness of the adsorbed layer. Experimental measurements were also conducted on the transport of condensible vapors (Freon-113 and water) through microporous Vycor glass at steady state in the entire range of relative pressure. The maximum peak and scattering phenomena of permeabilities were observed. The estimated values of permeability from the developed model were compared with the experimental results. Also, it was attempted to explain the maximum peak and scattering phenomena of the experimentally observed permeabilities.     

Diffusion of cationic polyelectrolytes into cellulosic fibers

The penetration of cationic polyelectrolytes into anionic cellulosic fibers was evaluated with fluorescent imaging techniques in order to clarify the mechanism and time scales for the diffusion process. The bulk charge of the cellulosic fibers indirectly creates a driving force for diffusion into the porous fiber wall, which is entropic in nature due to a release of counterions as the polyelectrolyte adsorbs. The individual bulk charges in the fiber cell wall also interact with the diffusing polyelectrolyte, such that the polyelectrolyte diffuses to the first available charge and consequently adsorbs and remains fixed. Thus, subsequent polyelectrolyte chains must first diffuse through the adsorbed polyelectrolyte layer before adsorbing to the next available bulk charges. This behavior differs from earlier suggested diffusion mechanisms, by which polyelectrolytes were assumed to first adsorb to the outermost surface and then reptate into the pore structure. The time scales for polyelectrolyte diffusion were highly dependent on the flexibility of the chain, which was estimated from calculations of the persistence length. The persistence length ultimately depended on the charge density and electrolyte concentration. The charge density of the polyelectrolyte had a greater influence on the time scales for diffusion. High charge density polyelectrolytes were observed to diffuse on a time scale of months, whereas the diffusion of low charge density polyelectrolytes was measured on the order of hours. An influence of the chain length, that is, steric interactions due the persistence length of the polyelectrolyte and to the tortuosity of the porous structure of the fiber wall, could only be noted for low charge density polyelectrolytes. Increasing the electrolyte concentration increased the chain flexibility by screening the electrostatic contribution to the persistence length, in turn inducing a faster diffusion process. However, a significant change in the diffusion behavior was observed at high electrolyte concentrations, at which the interaction between the polyelectrolyte charges and the fiber charges was almost completely screened.     

Diffusion through colloidosome shells

Colloidosomes are aqueous cores surrounded by a shell composed of packed colloidal particles. Recent studies suggest that these colloidal shells reduce, or even inhibit, the transport of molecular species (diffusants). However, the effect of the colloidal shell on transport is unclear: In some cases, the reduction in transport of diffusants through the shell was found to be independent of the size of the colloidal particles composing the shell. Other studies find, however, that shells composed of small colloidal particles of order 100nm or less hindered transport of diffusants more than those composed of micro-scale colloidal particles. In this paper we present a simple diffusion model that accounts for three processes that reduce diffusant transport through the shell: (i) a reduction in the penetrable volume available for transport, which also increases the tortuousity of the diffusional path, (ii) narrow pore size which may hinder transport for larger diffusants through size exclusion, and (iii) a reduction in interfacial area due to 'blocking' of the surface by the adsorbed particles. We find that the colloidal particle size does not affect the reduction in transport through the colloidal shell when the shell is a monolayer. However, in closely packed, thick layers where the thickness of the multi-layer shell is fixed, the rate of transport decreases significantly with colloidal particle dimensions. These results are in excellent agreement with previously published experimental results.     

Interfacial colloidal sedimentation equilibrium. I. Intensity based confocal microscopy

This paper reports confocal microscopy measurements of inhomogeneous colloidal sedimentation equilibrium profiles near planar wall surfaces for conditions when colloid dimensions are comparable to the characteristic gravitational length scale. The intensity based confocal method developed in this work enables real-space measurements of one-dimensional density profiles of Brownian colloids without identifying many single colloid centers in large imaging volumes. Measured sedimentation equilibrium profiles for single-phase interfacial fluids and for coexisting inhomogeneous fluid and solid phases are in agreement with a perturbation theory and Monte Carlo simulations within the local density approximation. Monte Carlo simulated colloid scale density profiles display some minor differences with confocal images in terms of microstructural transitions involving the onset of interfacial crystallization and the precise elevation of the fluid-solid interface. These discrepancies are attributed to polydispersity unaccounted for in the analyses, sensitivity of the perturbation theory to the effective hard sphere size, and the influence of ensemble, system size, and box shape in Monte Carlo simulations involving anisotropic/inhomogeneous solids. Successful demonstration of intensity based confocal microscopy provides a basis for future measurements of three-dimensional colloidal interactions, dynamics, and structure near surfaces.     

Well-Characterized Monodisperse Latexes as Model Colloids

Monodisperse polystyrene latexes prepared with persulfate-ion initiator can be ion exchanged to remove the adsorbed emulsifier and solute electrolyte. Rigorous purification of the ion-exchange'resins is necessary to avoid contamination with leached polyelectrolytes. These ion-exchanged latexes are stabilized with the residual sulfate end-groups of the polymer molecules, the number of which is determined by conductoroetric titration. The result is a dispersion of monodisperse spheres with-a constant and known surface charge due to chemically-bound strong-acid groups. These latexes are ideal models for colloidal studies. Preliminary experiments of stability, adsorption, sedimentation, viscosity, interference colors, and conductance give consistent results, e.g., the particle double-layer interactions determined by viscosity are in accord -with the particle spacings estimated from interference colors, the double-layer parameters estimated from conductometric titration and conductance measurements account for the measured decrease in sedimentation rate due to double-layer interactions, and the molecular area of sodium dodecyl sulfate measured by adsorption in latex is in agreement with literature values.     

Colloid dispersion in a uniform-aperture fracture

This research investigates the dispersion of colloids through fracture systems by exploring experimentally and numerically the transport and dispersion of 1.0-, 0.11-, and 0.043-mum diameter fluorescent carboxylate-modified microspheres and chloride at various flow rates through variable-length, synthetic Plexiglas fractures (flow cells). A dimensionless number describing each experiment is varied by changing the colloid size, flow rate, and fracture length. Surface characteristics of the microspheres and Plexiglas favor repulsive interactions, thereby minimizing the chance of colloid filtration and remobilization. Full recovery of the colloids is typically observed, thereby supporting the assumption of negligible colloid filtration. In comparison to chloride transport, there is increased tailing for colloid plumes traveling through the flow cell. This increased tailing is attributed to Taylor dispersion phenomena (dispersion due to an advection gradient). In the synthetic fractures investigated here, colloid dispersion due to the velocity gradient is evident, but fully developed Taylor conditions are not realized. A particle-tracking algorithm is run inversely to estimate the effective dispersion rate for the colloid plume in each experiment as a function of the experimental parameters (flow rate, fracture length, and colloid size). Results suggest that the log of the effective dispersion rate of the colloid plume increases linearly with the log of the dimensionless number comprising experimental parameters.     

Transient phoretic migration of a permselective colloidal particle

We quantify the phoretic migration of a spherical cation-permselective colloidal particle immersed in a binary electrolyte under a time-dependent electric field. We invoke the thin-Debye-layer approximation, where the size of ionic Debye layer enveloping the particle is much smaller than the particle radius. The imposed electric field generates ion concentration gradients, or concentration polarization, in the bulk (electroneutral) electrolyte outside the Debye layer. The bulk ion concentration polarization--and consequently the particle's phoretic velocity--evolves on the time scale for ion diffusion around the particle, which can be on the order of milliseconds for typical colloidal dimensions. Notably, concentration polarization arises here solely due to the permselectivity of the particle; it does not require non-uniform ionic transport in the Debye layer (i.e., surface conduction). Thus, the phoretic transport of a permselective particle is significantly different to that of a inert, dielectric particle, since surface conduction is necessary to achieve bulk concentration polarization in the (more commonly studied) latter case. Calculations are presented for a permselective particle under oscillatory (ac) and suddenly applied electric fields. In the former case, the particle velocity possesses frequency-dependent components in phase and out of phase with the driving field; in the latter case, the particle approaches its terminal velocity with a long-time (algebraic) tail.     

NMR studies of sorption and adsorption phenomena in colloidal systems

NMR methods provide chemically selective tools, particularly suitable to detect the molecular environment of molecular species in micro-heterogeneous materials. They are consequently applied to solve many questions in colloid science. The present review covers NMR studies of molecular adsorption onto particle surfaces as well as sorption into colloidal particles. Various methods ranging from liquid or solid state spectral analysis over spin relaxation to pulsed field gradient diffusion NMR have been employed in this field, monitoring either the chemical environment or the restricted dynamics of adsorbed or encapsulated guest molecules. Adsorption systems include surfactant layers, stabilizing ligands, small molecules, polymer layers or polyelectrolyte multilayers at the surface of various types of particles. Sorption into colloidal particles and detection of their position in specific compartments of the colloid are particularly relevant in systems employed as colloidal carriers, such as micelles, vesicles, or hollow polymeric capsules. With guest molecules considered as model compounds for drugs these studies have large relevance for the development of nanoparticle drug delivery systems.     

Dense colloid transport in a bifurcating fracture

In this work, the transport of dense colloids through a water-saturated, bifurcating fracture is investigated using a constant spatial step particle tracking technique. The size of the constituents of a colloid plume is an important factor affecting the partitioning of dense colloids at the bifurcation. While neutrally buoyant colloids partition between daughter fractures in proportion to flow rates, dense colloids will preferentially exit fractures that are gravitationally downgradient, notwithstanding that the majority of the interstitial fluid may flow through the upper fracture. Comparison of the partitioning ratio between daughter fractures with the ratios of characteristic settling, diffusion, and advection time reveal that these parameters control how colloids behave at fracture bifurcations.     

Effect of colloidal particle size on adsorbed monodisperse and bidisperse monolayers

Coating hydrogel films or microspheres by an adsorbed colloidal shell is one synthesis method for forming colloidosomes. The colloidal shell allows control of the release rate of encapsulated materials, as well as selective transport. Previous studies found that the packing density of self-assembled, adsorbed colloidal monolayers is independent of the colloidal particle size. In this paper we develop an equilibrium model that correlates the packing density of charged colloidal particles in an adsorbed shell to the particle dimensions in monodisperse and bidisperse systems. In systems where the molar concentration in solution is fixed, the increase in adsorption energy with increasing particle size leads to a monotonic increase in the monolayer packing density with particle radius. However, in systems where the mass fraction of the particles in the adsorbing solutions is fixed, increasing particle size also reduces the molar concentration of particles in solution, thereby reducing the probability of adsorption. The result is a nonmonotonic dependence of the packing density in the adsorbed layer on the particle radius. In bidisperse monolayers composed of two particle sizes, the packing density in the layer increases significantly with size asymmetry. These results may be utilized to design the properties of colloidal shells and coatings to achieve specific properties such as transport rate and selectivity.     

Colloid particle and protein deposition - electrokinetic studies

Recent developments in the electrokinetic determination of particle, polyelectrolyte and protein deposition at solid/electrolyte interfaces, are reviewed. In the first section basic theoretical results are discussed enabling a quantitative interpretation of the streaming current/potential and microelectrophoretic measurements. Experimental results are presented, pertinent to electrokinetic characteristics of simple (homogeneous) surfaces such as mica, silica and various polymeric surfaces used in protein studies. The influence of the ionic strength, background electrolyte composition and pH is discussed, and the effective (electrokientic) charge of these interfaces is evaluated. In the next section, experimental data obtained by streaming potential measurements for colloid particle mono- and bilayers are presented and interpreted successfully in terms of available theoretical approaches. These results, obtained for model systems of monodisperse colloid particles are used as reference data for discussion of more complicated experiments performed for polyelectrolyte and protein covered surfaces. Results are discussed, obtained for cationic polyelectrolytes (PEI, PAH) and fibrinogen adsorbing on mica, interpreted quantitatively in terms of the theoretical approach postulating a heterogeneous 3D charge distribution. The Gouy-Chapman model, based on the continuous charge distribution proved inadequate. Interesting experimental data are also discussed, obtained by electrophoretic methods in the case of protein adsorption on colloid latex particles. In the last section, supplementary results on particle deposition on heterogeneous surfaces produced by controlled protein adsorption are discussed. Quantitative relationships between the amount of adsorbed protein, zeta potential of the interface and the particle coverage are specified. Possibility of evaluating the heterogeneity of protein charge distribution is pointed out. The anomalous deposition of colloid particles on protein molecules bearing the same sign of zeta potential, which contradicts classical DLVO theory, is interpreted in terms of the fluctuation theory. It is concluded that theoretical and experimental results obtained for model colloid systems and flat interfaces can be effectively used for interpretation of protein adsorption phenomena, studied by electrophoresis. In this way the universality of electrokinetic phenomena is underlined.     

Review on subsurface colloids and colloid-associated contaminant transport in saturated porous media

In this review article, the authors present up-to-date developments on experimental, modeling and field studies on the role of subsurface colloidal fines on contaminant transport in saturated porous media. It is a complex phenomenon in porous media involving several basic processes such as colloidal fines release, dispersion stabilization, migration and fines entrapment/plugging at the pore constrictions and adsorption at solid/liquid interface. The effects of these basic processes on the contaminant transport have been compiled. Here the authors first present the compilation on in situ colloidal fines sources, release, stabilization of colloidal dispersion and migration which are a function of physical and chemical conditions of subsurface environment and finally their role in inorganic and organic contaminants transport in porous media. The important aspects of this article are as follows: (i) it gives not only complete compilation on colloidal fines-facilitated contaminant transport but also reviews the new role of colloidal fines in contaminant retardation due to plugging of pore constrictions. This plugging phenomenon also depends on various factors such as concentration of colloidal fines, superficial velocity and bead-to-particle size ratio. This plugging-based contaminant transport can be used to develop containment technique in soil and groundwater remediation. (ii) It also presents the importance of critical salt concentration (CSC), critical ionic strength for mixed salt, critical shear stressor critical particle concentration (CPC) on in situ colloidal fines release and migration and consequently their role on contaminant transport in porous media. (iii) It also reviews another class of colloidal fines called biocolloids and their transport in porous media. Finally, the authors highlight the future research based on their critical review on colloid-associated contaminant transport in saturated porous media.     

Macroscopic analysis of the behavior of colloidal suspensions

Three distinct and separate scales of discourse relevant to systems such as porous media and colloidal suspensions are identified: 1) the molecular scale; 2) the microscopic or Navier-Stokes scale; and 3) the macroscopic or Darcy scale. This article reviews the macroscopic mode of analysis which had its origins in problems of flow in porous media and which has been generalized and extended to apply to the behavior of colloidal suspensions. Applied to suspensions, the central concepts concern the energetics and hydrodynamics of the liquid phase.The approach leads to a non-linear Fokker-Planck equation, which reduces to a non-linear diffusion equation in some contexts. Simple experiments yield two functions characterizing the suspension. These functions express the dependence on particle volume fraction (or, equivalently, on ?, the ‘liquid ratio’) of ψ, the relevant chemical potential of the liquid, and κ, the permeability for flow relative to the particles. With these functions known, the analysis enables quantitative prediction of the time course of various flow, filtration, and sedimentation processes undergone by colloidal suspensions.The great generality and adaptability of the approach is emphasized. The necessary and sufficient condition for its application is simply that the characterizing functions exist and are measurable. The approach has been found to apply to a range of colloidal suspensions occurring in practical contexts in nature and industry. The analysis is free of the abstractions, simplifications, and assumptions required for quantitative theoretical studies on the molecular and microscopic scales. We may remain completely agnostic about particle shape, size distribution, and interactions. All information required is embodied in the ψ(?) and κ(?) functions.     

Diffusiophoretic mobility of charged porous spheres in electrolyte gradients

The diffusiophoretic motion of a polyelectrolyte molecule or charged floc in an unbounded solution of a symmetrically charged electrolyte with a uniform prescribed concentration gradient is analytically studied. The model used for the particle is a porous sphere in which the density of the hydrodynamic frictional segments, and therefore also that of the fixed charges, is constant. The electrokinetic equations which govern the electrostatic potential profile, the ionic concentration distributions (or electrochemical potential energies), and the fluid velocity field inside and outside the porous particle are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved for a charged porous sphere with the density of the fixed charges as the small perturbation parameter. An analytical expression for the diffusiophoretic mobility of the charged porous sphere in closed form is obtained from a balance between its electrostatic and hydrodynamic forces. This expression, which is correct to the second order of the fixed charge density of the particle, is valid for arbitrary values of kappaa and lambdaa, where kappa is the reciprocal of the Debye screening length, lambda is the reciprocal of the length characterizing the extent of flow penetration inside the particle, and a is the particle radius. Our result to the first order of the fixed charge density agrees with the corresponding solution for the electrophoretic mobility obtained in the literature. In general, the diffusiophoretic mobility of a porous particle becomes greater as the hindrance to the diffusive transport of the solute species inside the particle is more significant.