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A general multi‐ion diffusion model for liquid slag is developed for silicate melts by combining the tracer diffusivities of ions and chemical potentials from the CALculation of PHAse Diagrams thermodynamic database. For the demonstration of the model, the tracer diffusivities of Ca, Al, Si, and O ions in CaO–Al2O3–SiO2 melts were optimized as functions of temperature and composition using available isotope experimental data. The present model successfully simulates liquid‐junction diffusion in the CaO–Al2O3–SiO2 system and the dissolution of solid SiO2 and Al2O3 particles in CaO–Al2O3–SiO2 melts. Furthermore, the model can be readily expanded to multicomponent systems, making it potentially applicable to refractory dissolution in liquid slag and various other diffusion‐controlled high temperature processes involving liquid oxide melts. [ABSTRACT FROM AUTHOR]

Phospholipid bilayer bending energy is often discarded in the analysis of vesicle adhesion on the basis of a dimensionless parameter w=−ΔUR20/κb >1 (interaction energy ΔU, spherical radius R0, bending rigidity κb), considered a regime of strong adhesion. In this study, we propose a model by which bending energy in a singular proximity of the contact line balances the adhesion energy. This is developed for a regime in which the membrane correlation length ξ is small compared with the vesicle radius R0, so a spherical cap with circular footprint presents an effective contact angle θ. Experiments are conducted in which the adhesion of 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC) vesicles to hyaluronic acid hydrogel substrates is controlled by tuning the van der Waals attraction with systematic change in the hydrogel concentration. Theoretical interpretation of the data furnishes a dimensionless model parameter α ≈2–10 for contact angles θ ≈20–80◦, beyond which vesicles collapse into discs. We show that the van der Waals interaction energy varies in the range −ΔU ≈0.14–0.68 μJm−2 in response to varying the hydrogel concentration in a range cha ≈2–10%. The analysis provides a foundation for exploring vesicle– hydrogel interactions with electro-steric influences; these are poorly understood but pertinent in a wide variety of biological and technological applications. [ABSTRACT FROM AUTHOR]

The electrosteric interaction energy for a charged hydrogel and hard plane, and between two charged hydrogels is derived in the Debye-Hückel approximation. This is combined with a van der Waals potential that explicitly addresses the Hamaker constant for the solvent-mediated hydrogel interactions. Then, in the Derjaguin approximation, DLVO-type interaction potentials are provided for hydrogel and hard/rigid spheres, accounting for elastic deformation that accompanies adhesion. As examples, this furnishes the energy for cohesion of soft polyelectrolyte microspheres, and provides a quantitative interpretation for the adhesion of rigid latex spheres to a soft deformable hydrogel, as reported by Sato et al. (Sato et al. 2017 Sci. Rep. 7, 1-10 (doi:10.1038/s41598-017-06257-1)). The theory demonstrates that weak van der Waals attraction of hydrogels is readily balanced by electrosteric interactions, e.g. making colloidal hydrogel dispersions less stable than their rigid-particulate counterparts. [ABSTRACT FROM AUTHOR]

This paper examines the response of electrolyte-saturated polymer gels, embedded with charged spherical inclusions, to a weak gradient of electrolyte concentration. An electrokinetic model was presented in an earlier publication, and the response of homogeneous composites to a weak electric field was calculated. In this work, the influence of the inclusions on bulk ion fluxes and the strength of an electric field (or membrane diffusion potential) induced by the bulk electrolyte concentration gradient are computed. Effective ion diffusion coefficients are significantly altered by the inclusions, so—depending on the inclusion surface charge or ζ potential—asymmetric electrolytes can behave as symmetrical electrolytes and vice versa. The theory also quantifies the strength of flow driven by concentration-gradient-induced perturbations to the equilibrium diffuse double layers. Similarly to diffusiophoresis, the flow may be either up or down the applied concentration gradient. [ABSTRACT FROM AUTHOR]

Chemically cross-linked polyacrylamide (PA) hydrogels have been studied extensively, but gels with a very low cross-linker ratio have received relatively little attention. In this paper, the rheology of bis-cross-linked PA hydrogels is examined with acrylamide concentrations c a approximately 10 % w/v and cross-linker to acrylamide ratios c bis / c a in the range 0.2 – 0.9 mmol mol − 1 . Linear viscoelastic responses were measured during and following gelation. The effective cross-link formation rate increases with the cross-linker ratio, with a plateau modulus that is weakly quadratic in the cross-linker ratio. The gels exhibit distinctly different features from their counterparts in the literature with higher cross-linker ratios. Plateau regions in the dynamic moduli spectra are less pronounced, and the loss tangents are several orders of magnitude higher than for gels with a higher cross-linker ratio but a comparable plateau modulus. Time-temperature superposition of viscoelastic spectra furnishes a disentanglement activation energy that decreases with increasing temperature, from ≈ 25 to 6 k B T. Time-concentration superposition for samples prepared above the percolation threshold furnishes a critical relaxation exponent Δ ≈ 0.38 , which is much smaller than previously reported for the universal sol-gel transition. These distinct features can be attributed to the predominance of entanglements. We show that a Wiechert model with a power-law distribution of relaxation times faithfully reproduces dynamic moduli spectra from the creep compliance. Together, the results provide a foundation with which to interpret acoustic and electroacoustic rheological responses (at MHz frequencies) and the linear viscoelasticity of DNA-cross-linked gels (to be reported elsewhere). [ABSTRACT FROM AUTHOR]

Nanoparticles (NPs) have been demonstrated in recent years to simultaneously enhance polymeric nanocomposite membrane selectivity and permeability according to the polymer/NP/penetrant. With a repulsive polymer-NP interaction, permselectivity is enhanced by NP loading, which is thought to adjust the permeability by locally disturbing polymer conformation. In this paper, we examine another mechanism for controlling nanocomposite permeability. We focus on the interfacial sorption capacity and mobility of water-vapour through nanocomposites comprising spherical silica NPs embedded in cross-linked polyacrylamide. Equilibrium and dynamic moisture sorption data are interpreted with a quantitative theoretical model that addresses equilibrium and dynamic partitioning of the tracer between interfacial and continuous phases. The results demonstrate significant and systematic changes in non-classical diffusion behaviour. Our interpretation indicates that polyacryamide adsorption on silica NPs varies the number of available surface adsorption sites, thus controlling adsorption capacity and interfacial mobility. Such effects can therefore be tuned by varying the specific NP surface area, which increases with NP loading and decreases with NP size. These insights will hopefully improve rational design strategies for nanocomposite membranes. [ABSTRACT FROM AUTHOR]

Pore-resolved computations are undertaken, within a continuum model framework, to explore surface diffusion as a selective mechanism for gas separations using membranes of randomly overlapping parallel cylindrical pores or fibers. Orders of magnitude of the model parameters are established using an intrinsic gas diffusivity that is self-consistent with the Knudsen diffusivity obtained from Monte Carlo simulations reported in the literature. The relative contributions of surface and gas diffusion to the overall permeation show that the surface-diffusion flux increases with the specific surface area, whereas the gas flux increases with porosity. Thus, gas diffusion that is perpendicular to pores and fibers can be hindered by the increasing tortuosity while simultaneously promoting permeation via surface diffusion. The selectivity of pore structures with fibrous networks is examined for the dehumidification of air, natural gas, and carbon dioxide. Selectivities, defined as the ratio of the effective diffusion coefficients for the adsorbed phases (moisture) and the void-diffusing gas (air, natural gas, or carbon dioxide), reveal that selectivity is higher for (i) heavier gases, which have lower gas-diffusion fluxes, and (ii) capillary pores, which have higher surface connectivity than fibers. [ABSTRACT FROM AUTHOR]

Three-dimensional computations of coupled gas and surface diffusion in periodic arrays of solid spheres and spherical cavities are undertaken to assess the role of pore size, void fraction, and pore geometry on permeability. With nano-dimensioned pores, gas-phase diffusion is hindered by the small mean-free path, so the overall permeability hinges on surface diffusion. We prescribe the intrinsic gas-phase diffusivity to be self-consistent with the Knudsen diffusivity obtained from molecular-kinetic simulations reported in the literature. The continuum model of Albaalbaki and Hill then couples the gas and surface phases via an equilibrium adsorption isotherm and kinetic-exchange parameters. Solving these equations in complex pore-scale geometries provides new insights into the coupling. To interpret the results, we decompose the net flux into (i) gas and surface contributions that can be calculated without knowledge of the concentration perturbations to equilibrium, but which depend on the pore geometry, and (ii) counterparts that must be evaluated from integrals of the concentration perturbations to equilibrium. These measures are directly related to the familiar, but less precise, gas and surface tortuosity parameters, which are often used to interpret experiments. The results highlight (i) discontinuous variations in the fluxes when passing through void and solid percolation thresholds, (ii) how the surface flux depends on the specific surface area, and (iii) the pore sizes at which surface transport compares with void transport. [ABSTRACT FROM AUTHOR]

The sol-gel transition of silica-polyacrylamide hydrogel nanocomposites is studied when approaching the gel point by independently varying the nanoparticle (NP) and chemical crosslinker concentrations. Time-concentration-superposition (TCS) principles are applied to ascertain the effect of NPs on dynamics at the gel point. Doping dilute and concentrated polyacrylamide (PA) solutions with silica NPs indicates that these particles do not crosslink PA; neither do they form percolating networks. Nevertheless, silica NPs interact with PA to influence the storage and loss moduli to a much greater degree than expected for passive fillers. Interestingly, when silica NPs are embedded in very weakly chemically crosslinked PA (with a bis crosslinker concentration that would otherwise not form PA hydrogels), they significantly enhance the effective degree of crosslinking, forming viscoelastic solids. From TCS analysis of dynamics at the gel point, the bond probability is found to scale with the NP volume fraction as p ∼ ϕ 1.5 , whereas chemical crosslinking furnishes a bond probability that is linear in the crosslinker concentration. [ABSTRACT FROM AUTHOR]

Literature interpretations of the electrophoretic mobility of spherical polyelectrolytes are revisited using the capillary-electrophoresis data of Duval et al. (2006) for the extracellular polysaccharide succinoglycan as an example. Subtle changes in the polyelectrolyte mobility have recently been attributed to new electrokinetic theories that feature multi-component electrolytes, charge regulation, and the so-called polarization and relaxation phenomena. However, these calculations exhibit several unusual trends that have yet to be explained, and so the conclusions drawn from them are controversial. Here, independent computations strengthen conclusions drawn from the original model of Duval et al., i.e., the discrepancies between experiments and all the presently available electrokinetic theories reflect changes in the conformation of succinoglycan arising from changes in the electrolyte pH and ionic strength. [ABSTRACT FROM AUTHOR]

Polyacrylamide (PA) hydrogels have been studied extensively, but fundamental aspects of their gelation kinetics, percolation dynamics, and viscoelasticity are still not well understood. This paper focuses on the rheology of PA hydrogels having unusually low monomer concentrations (ca≈3 w% equivalent to 0.42 mol l-1). These furnish loss tangents that span 4 orders of magnitude when varying the crosslinker concentration. An optimum crosslinker concentration (cbis/ca≈2.5 mol. % equivalent to 5.3 w%) is identified, below which the storage modulus G' increases almost linearly, and the loss modulus G" acquires a local maximum. Above the optimum crosslinker concentration, G' and G" both plateau, accompanied by a notable decrease in the maximum strain (increase in brittleness) before breaking. The dynamic shear moduli reveal universal dynamics at the gel point, as indicated by (i) scaling exponents (y=3.1±0.1, z=2.1±0.1 and D=0.70±0.02) that are consistent with the de Gennes ["On a relation between percolation theory and the elasticity of gels," J. Phys. Lett. 37, L1-L2 (1976)] electrical network analogy, and (ii) a critical relaxation exponent that is close to the Rouse limit Δ=2/3 from the scaling theory of Martin. A close correspondence of the exponents with that of Adam and Delsanti [Macromolecules 18, 2285-2290 (1985)] for the radical copolymerization of a different material supports the long-standing hypothesis that dynamics at the gel point are universal for a prescribed gelation mechanism. [ABSTRACT FROM AUTHOR]

We examine the equilibrium and stability of an elastocapillary system to model drying-induced structural failures. The model comprises a circular elastic membrane with a hole at the center that is deformed by the capillary pressure of simply connected and doubly connected menisci. Using variational and spectral methods, stability is related to the slope of equilibrium branches in the liquid content versus pressure diagram for the constrained and unconstrained problems. The second-variation spectra are separately determined for the membrane and meniscus, showing that the membrane out-of-plane spectrum and the in-plane spectrum at large elastocapillary numbers are both positive, so that only meniscus perturbations can cause instability. At small elastocapillary numbers, the in-plane spectrum has a negative eigenvalue, inducing wrinkling instabilities in thin membranes. In contrast, the smallest eigenvalue of the meniscus spectrum always changes sign at a pressure turning point where stability exchange occurs in the unconstrained problem. We also examine configurations in which the meniscus and membrane are individually stable, while the elastocapillary system as a whole is not; this emphasizes the connection between stability and the coupling of elastic and capillary forces. [ABSTRACT FROM AUTHOR]

Anchoringpoly(ethylene glycol) (PEG) to inorganic nanoparticles(NPs) permits control over NP properties for a variety of technologicalapplications. However, the core–shell structure tremendouslycomplicates the interpretation of the ubiquitous ζ-potential,as furnished by electrophoretic light-scattering, capillary electrophoresisor gel electrophoresis. To advance the ζ-potentialandthe more fundamental electrophoretic mobilityas a quantitativediagnostic for PEGylated NPs, we synthesized and characterized AuNPs bearing terminally anchored 5 kDa PEG ligands with univalent carboxymethylend groups. Using the electrophoretic mobilities, acquired over awide range of ionic strengths, we developed a theoretical model forthe distributions of polymer segments, charge, electrostatic potential,and osmotic pressure that envelop the core: knowledge that will helpto improve the performance of soft NPs in fundamental research andtechnological applications. [ABSTRACT FROM AUTHOR]

We analytically study the stability of catenoids pinned at one contact line, with the other free to move on a substrate subject to axisymmetric and nonaxisymmetric perturbations. A variational formulation is applied to derive the corresponding stability criteria. The maximal stability region and the stability region are represented in the favorable and canonical phase diagrams, providing a complete description of catenoid equilibrium and stability. All catenoids are stable with respect to nonaxisymmetric perturbations. For a fixed contact angle, there exists a critical volume below which catenoids are unstable to axisymmetric perturbations. Equilibrium solution multiplicity is discussed in detail, and we elucidate how geometrical symmetry is reflected in the maximal stability and stability regions. [ABSTRACT FROM AUTHOR]

Gel electrophoresis of spherical nanoparticles (NPs) is studied using an electrokinetic model that couples the ion conservation equations to the Poisson and fluid momentum equations, thus including the socalled polarization and relaxation processes. This model is therefore the charged gel electrophoresis analogue of the well-known O'Brien and White solution of the standard electrokinetic model for free-solution electrophoresis. Results are provided for the small NPs (size around 10 nm) to which gel electrophoresis is relevant, because particles must be small enough to permeate the gel: these include the particle drag coefficient (or Brownian diffusivity), which is subject to hydrodynamic screening and electroviscous effects, and the electrophoretic mobility, which is subject to nonlinear electrostatic and charge polarization influences. Also addressed are the influences of charge-regulating gels and the accompanying particle-induced immobile charge-density perturbations. Ion-concentration perturbations attenuate the electrophoretic mobility and enhance the drag coefficient according to the particle charge and the mobility of the most abundant counterion. However, dynamic regulation of the hydrogel charge--termed the secondary immobile charge-density perturbation--has a negligible influence on the particle mobility, and may therefore be neglected for most practical purposes. [ABSTRACT FROM AUTHOR]

The static stability of weightless liquid bridges with a free contact line with respect to axisymmetric and nonaxisymmetric perturbations is studied. Constant-volume and constant-pressure stability regions are constnicted in slenderness versus cylindrical volume diagrams for fixed contact angles. Bifurcations along the stability-region boundaries are characterized by the structure of axisymmetric bridge branches and families of equilibria. A wave-number definition is presented based on the pieces-of-sphere states at branch terminal points to classify equilibrium branches and identify branch connections. Compared with liquid bridges pinned at two equal disks, the free contact line breaks the equatorial and reflective symmetries, affecting the lower boundary of the constant-volume stability region where axisymmetric perturbations are critical. Stability is lost at transcritical bifurcations and turning points along this boundary. Our results furnish the maximum-slenderness stability limit for drop deposition on real surfaces when the contact angle approaches the receding contact angle. [ABSTRACT FROM AUTHOR]

An elastocapillary model for drying-induced collapse is proposed. We consider a circular elastic membrane with a hole at the centre that is deformed by the capillary pressure of simply and doubly connected menisci. The membrane overlays a cylindrical cavity with rigid walls, trapping a prescribed volume of water. This geometry may be suitable for studying structural failures and stiction in microelectromechanical systems during wet etching, where capillary surfaces experience catastrophic transitions. The dry state is determined using the dihedral-angle and volume-turning-point stability criteria. Open and collapsed conformations are predicted from the scaled hole radius, cavity aspect ratio, meniscus contact angle with the membrane and cavity walls, and an elastocapillary number measuring the membrane stretching rigidity relative to the water surface tension. For a given scaled hole radius and cavity aspect ratio, there is a critical elastocapillary number above which the system does not collapse upon drying. The critical elastocapillary number is weakly influenced by the contact angle over a wide range of the scaled hole radius, thus indicating a limitation of surface hydrophobization for controlling the dry-state conformation. The model is applied to the drying of wood fibres above the fibre saturation point, determining the conditions leading to collapse. [ABSTRACT FROM AUTHOR]

This paper probes the nanoparticle(NP) interaction with hydrogelsusing electroacoustic spectroscopy at MHz frequencies. We measureddynamic electrophoretic mobility spectra of silica NPs in polyacrylamidegels for a variety of NP sizes and gel concentrations. The spectraare exquisitely sensitive to NP entrapment, size, and charge as wellas to gel rheology and gelation kinetics. For NPs that are large comparedto the gel mesh size, many of these influences can be quantified usingelectrokinetic theory, which furnishes the apparent NP ζ-potentialand a complex gel shear modulus at MHz frequencies. The methodologyprovides new insights into the NP–hydrogel interaction, sinceit noninvasively probes the nanostructure and the combined influencesof particle and gel properties. Electroacoustic spectroscopy may thereforebe a valuable new tool for characterizing soft nanocompositesonethat complements other noninvasive methods, such as bulk rheometryand microrheology. [ABSTRACT FROM AUTHOR]

Abstract: Nanoparticle gel electrophoresis has recently emerged as an attractive means of separating and characterizing nanoparticles. Consequently, a theory that accounts for electroosmotic flow in the gel, and coupling of the nanoparticle and hydrogel electrostatics and hydrodynamics, is required, particularly for gels in which the mesh size is comparable to or smaller than the particle radii. Here, we present an electrokinetic model for charged, spherical colloidal particles undergoing electrophoresis in charged (polyelectrolyte) hydrogels: the gel-electrophoresis analogue of Henry’s theory for electrophoresis in Newtonian electrolytes. We compare numerically exact solutions of the model with several independent asymptotic approximations, identifying regions in the parameter space where these approximations are accurate or break down. As previously assumed in the literature, Henry’s formula, modified by the addition of a constant electroosmotic flow mobility, is accurate only for nanoparticles that are small compared to the hydrogel mesh size. We derived an exact analytical solution of the full model by judiciously modifying the theory of Allison et al. [15] for uncharged gels, drawing on the superposition methodology of Doane et al. [14] to account for hydrogel charge. This furnishes accurate and economical mobility predictions for the entire parameter space. The present model suggests that nanoparticle size separations (with diameters ≲40nm) are optimal at low ionic strength, with a gel mesh size that is selected according to the particle charging mechanism. For weakly charged particles, optimal size separation is achieved when the Brinkman screening length is matched to the mean particle size. [Copyright &y& Elsevier]

Abstract: Nanoparticle transport in porous materials, including nanoparticle gel electrophoresis, hinges on knowledge of the hydrodynamic drag coefficient. Here, we compute the drag force on a soft core–shell sphere translating in a porous medium from a continuum hydrodynamic model in which slow viscous flow in the soft shell and embedding porous medium are modelled using Brinkman''s equations. This model unifies the Brinkman force for bare spheres in porous media and the drag force of Masliyah et al. (1987) for soft core–shell spheres in pure viscous fluids. We compare the drag force with the Brinkman force evaluated using the composite sphere hydrodynamic radius, showing that this convenient approximation is reasonable when the Brinkman screening length of the embedding porous medium is large compared to the core radius; otherwise, the Brinkman force can significantly underestimate the force. [Copyright &y& Elsevier]

Abstract: This paper addresses the dynamic electrical response of a charged or uncharged hydrogel that is sandwiched between a bottom fixed plate and a top floating, parallel plate. We demonstrate how this configuration might be adopted as a novel chemical- or bio-sensing platform. It might also be used for nano-positioning, or for studying the rheology and physiochemical characteristics of hydrogels. Here, the gel is modelled as a continuum composite comprising a porous, charged, elastic skeleton saturated by an aqueous electrolyte. Electrostatics satisfy the Debye–Hückel approximation, with zero-slip boundary conditions between the skeleton, solvent, and walls. For large channel gaps, the steady electric-field-induced displacement of the top plate is proportional to the difference between the top- and bottom-wall ζ-potentials. Under oscillatory electrical stimulation, resonant peaks, with amplitudes from picometers to micrometers, reflect hydrogel elasticity and charge density. Such displacements are within the detection range of modern interferometric displacement sensors. [Copyright &y& Elsevier]

Abstract: Polystyrene microspheres were functionalized by covalent binding of 250kDa linear PEI and ethanolamine, acting as a blocking agent, through bioconjugation with EDAC. The functionalized spheres were found to become less susceptible to salt-induced flocculation due to electrosteric stability, caused by the PEI chains at low NaCl concentrations, and at high salt concentration, by steric repulsion by the ethanolamine layer, which in combination with van der Waals attraction results in a shallow energy minimum and the formation of a few unstable aggregates. The latex aggregated in the presence of nanocrystalline cellulose (NCC) with varying efficiencies, depending on the ratio of NCC to latex particles in solution. Polyelectrolyte titration showed that each latex sphere contained about 15 grafted PEI chains. The fastest aggregation was detected when about half of these chains were covered by a single NCC particle. [Copyright &y& Elsevier]

Abstract: Electroosmotic pumping through uncharged hydrogels can be achieved by embedding the polymer network with charged colloidal inclusions. Matos et al. [M.A. Matos, L.R. White, R.D. Tilton, J. Colloid Interface Sci. 300 (2006) 429–436], recently used the concept to enhance the diffusion-limited flux of uncharged molecules across polyacrylamide hydrogel membranes for the purpose of improving the performance of biosensors. This paper seeks to link their reported macroscale diagnostics to physicochemical characteristics of the composite microstructure. The experiments are characterized by a Debye screening length that is much larger than the radius of the silica nanoinclusions and the Brinkman screening length of the polymer skeleton. Accordingly, closed-form expressions for the incremental pore mobility are derived, and these are evaluated by comparison with numerically exact solutions of the full electrokinetic model. A mathematical model for the bulk electroosmotically enhanced tracer flux is proposed, which is combined with the electrokinetic model to ascertain the electroosmotic pumping velocity from measured flux enhancements. Because the experiments are performed with a known current density, but unknown bulk conductivity and electric field strength, theoretical estimates of the bulk electrical conductivity are adopted. These account for nanoparticle polarization, added counterions, and non-specific adsorption. Theoretical predictions of the flux enhancement, achieved without any fitting parameters, are within a factor of two of the experiments. Alternatively, if the Brinkman screening length of the polymer skeleton is treated as a fitting parameter, then the best-fit values are bounded by the range 0.9–1.6 nm, depending on the inclusion size and volume fraction. Independent pressure-driven flow experiments reported in the literature for polyacrylamide gels without inclusions suggest 0.4 or 0.8 nm. The comparison can be improved by allowing for hindered ion migration, while uncertainties regarding the inclusion surface charge are demonstrated to have a negligible influence on the electroosmotic flow. Finally, and perhaps most importantly, anomalous variations in the flux enhancement with particle size and volume fraction can be rationalized at present only by acknowledging that particle–particle and particle–polymer interactions increase the effective permeability of the hydrogel skeleton. This bears similarities to the increase in polymer free volume that accompanies the addition of silica nanoparticles to certain polymeric membranes. [Copyright &y& Elsevier]

Abstract: In papermaking, many colloidal particles are added to a pulp fiber suspension to improve paper properties. Given the right conditions, these different colloids can interact and flocculate. Examples of papermaking colloids are fillers and internal sizing agents, which improve opacity and hydrophobicity of paper, respectively. Internal sizing agents (added at the wet end of a paper machine) are commonly solidified emulsion droplets, stabilized by cationic starch and other stabilizers. We studied the interaction of a common internal sizing agent, alkyl ketene dimer (AKD), with calcium carbonate fillers. AKD is a liquid above 50–65 °C (depending on alkyl chain length), which can be emulsified above its melting point in the presence of a stabilizer, resulting, after cooling, in solid colloidal particles close to 1 μm in size. We investigated the interaction of AKD particles, stabilized by cationic starch, with precipitated calcium carbonate (PCC) particles. Pure PCC particles are positively charged, but they become negative in process waters. Flocculation experiments with positively charged AKD and negatively charged PCC were performed using a photometric dispersion analyzer. Instead of the expected heteroflocculation between AKD and PCC, we observed PCC homoflocculation and AKD homoflocculation, results confirmed by SEM. The results are explained by the transfer of starch from AKD to PCC, resulting in PCC flocculation by starch and AKD destabilization due to depletion of the stabilizer. [Copyright &y& Elsevier]

When an electric field is applied to an electrolyte-saturated polymer gel immobilizing charged colloidal particles, the force that must be exerted by the hydrogel on each particle reflects a delicate balance of electrical and hydrodynamic stresses. This article adopts a simple boundary-layer analysis to derive a convenient formula for the force in terms of the particle, electrolyte and gel characteristics. Comparisons with numerically exact solutions of the full set of electrokinetic transport equations are presented. These reveal that a fortuitous cancellation of errors leads to reasonably accurate predictions of the force over a much wider range of the parameter space than should be expected. It is noteworthy that, in gels with low permeability, an adverse pressure gradient yields a net force that exceeds the bare electrical force. The analytical theory also provides a convenient formula for the incremental pore mobility, which is a convenient measure of the electro-osmotic pumping capacity of dilute random arrays of charged inclusions. [ABSTRACT FROM AUTHOR]

Abstract: Numerical solutions of the standard electrokinetic model provide a basis for interpreting a variety of electrokinetic phenomena involving ‘bare’ colloids. However, the model rests on the classical notion of a shear or slipping plane, whose location is unknown when surfaces are coated with permeable polymer. Consequently, an electrokinetic model for ‘soft’, ‘hairy’ or ‘fuzzy’ colloids has been developed, but until recently solutions were available only for several restricted cases, most notably for particles with thin, uniform layers, and without polarization and relaxation. Here we present numerically exact solutions of the full model for a variety of soft colloids, including PEG-coated liposomes, PEO-coated latices, human erythrocytes, and polyelectrolyte micelles. Particular attention is given to linking the thickness, density and permeability of the coatings, which are key parameters in the model, to “physical” quantities, such as the polymer molecular weight, adsorbed amount, and hydrodynamic layer thickness. This paper also identifies limits – on the ionic strength, particle size, layer thickness and permeability – beyond which earlier theories breakdown. In short, polarization and relaxation are as influential on the mobility of soft colloids as they are for ‘bare’ particles. [Copyright &y& Elsevier]

The polarizability of polymer-coated colloidal particles, as measured via dielectric relaxation spectroscopy, reflects on the degree to which convection, diffusion, and electromigration deform the equilibrium double layer. With a polymer coating, convection and electro-osmosis are resisted by hydrodynamic drag on the polymer segments. The electro-osmotic flow near the underlying bare surface is therefore diminished. Characteristics of the particles and the adsorbed polymer can, in principle, be inferred by measuring the frequency-dependent polarizability. In this work, “exact” numerical solutions of the electrokinetic equations are used to examine how adsorbed polymer changes the particle polarizability and, hence, the conductivity and dielectric constant increments of dilute suspensions. For neutral polymer coatings, the conductivity and dielectric constant increments are found to be very similar to those of the underlying bare particles, so the response depends mostly on the underlying bare particles. These observations suggest that dielectric spectroscopy is best used to determine the underlying surface charge, with characteristics of the coating inferred from the electrophoretic or dynamic mobility, together with the hydrodynamic radius obtained from sedimentation or dynamic light scattering. Addressed briefly are the effects of added counterions and nonspecific adsorption. The electrokinetic model explored in this work can be used to guide experiments (frequency and ionic strength, for example) to either minimize or maximize the sensitivity of the complex conductivity to the coating thickness or permeability. [Copyright &y& Elsevier]

The dielectric relaxation of polyelectrolyte-coated colloidal particles is examined via “exact” numerical solutions of the governing electrokinetic equations. The charged polymer coatings are characterized by a nominal charge density, thickness, and permeability. Brush-like segment density profiles are considered here, but more sophisticated segment and charge density profiles are accommodated by the model. The role of added counterions and nonspecific adsorption is considered briefly before examining how the experimentally measured conductivity and dielectric constant increments reflect the frequency of the applied electric field, the strength of the electrolyte, and characteristics of the polymer coatings, namely the charge, charge density, and permeability. Finally, a strategy is suggested by which dielectric spectroscopy and electrophoresis can be used to characterize polymer-coated particles. This approach complements experiments where electroviscous effects such as dynamic light scattering and sedimentation are weak. [Copyright &y& Elsevier]

The motion of a spherical polymer-coated colloidal particle in a steady electric field is studied via “exact” numerical solutions of the electrokinetic equations. The hydrodynamic influence of the polymer is represented by a distribution of Stokes resistance centers. With neutral polymer, charge resides on the underlying bare particle, whereas for polyelectrolytes, the charge is distributed throughout the coating. The coatings may be brush-like or have long tails. As expected, neutral coatings lower the mobility because of increased drag and a decrease in the effective charge behind the shear surface. For polyelectrolyte coatings, the behavior is more complex. For example, the mobility becomes independent of the ionic strength and particle size when Donnan equilibrium prevails inside the coating and the coating is thick relative to the Brinkman screening length (square root of the coating permeability). In this limit, the mobility follows from a simple balance of forces within the coating and, therefore, becomes proportional to the fixed charge density and the coating permeability. If the permeability is sufficiently high, the mobility of a polyelectrolyte-coated particle may exceed that of its bare counterpart with the same net charge. In general, the effects of polarization and relaxation are as important for coated particles as they are for bare particles. [Copyright &y& Elsevier]

Examines the average flow properties of packed beds and particle suspensions in which inertia plays a significant role in particle length scale. Features of inertial suspensions; Difficulties in understanding inertial suspensions; Discussion on gas-solid suspensions; Types of inertial suspension.

A general flux equation for multicomponent diffusion in oxide melts is presented. An explicit method was developed to calculate the gradients of single-ion activities from those of oxides with the constraints of local equilibrium and electroneutrality. This resolves ambiguity in quantifying the thermochemical driving force for ionic diffusion. A model equation for multicomponent ionic diffusion was derived within the framework of non-equilibrium thermodynamics by de Groot and Mazur. The proposed model takes empirically measurable quantities as input variables, so the diffusion calculations are consistent with thermochemical data, as furnished by the CALPHAD (CALculation of PHAse Diagrams) method, as well as ionic mobility measurements. Although the model is derived for oxides, it can be applied to diffusion in other concentrated liquid electrolytes, such as chloride and fluoride melts. Formulas for multicomponent ionic diffusion in various reference frames are presented with respect to mole fraction. • A framework was developed to assess single-ion activity gradients in ionic melts. • The proposed ionic flux takes empirically measurable quantities as input variables. • Formulas were derived for stationary coordinates and mean-velocity reference frames. [ABSTRACT FROM AUTHOR]

A correction to a previously published article "Transport in Polymer-Gel Composites: Response to a Bulk Concentration Gradient," by Reghan J. Hill is presented

Discusses the role played by the phenomenon of Brinkman screening in limiting the range of velocity correlations in porous media and fixed beds. Attenuation of fluid velocity disturbance produced by each particle in a fixed bed by the forces that the fluid exerts on surrounding particles; Finite hydrodynamic diffusion coefficient.

The effective diffusivity of two-dimensional, anisotropic porous materials with surface diffusion is studied. The continuum model of Albaalbaki and Hill (2012), which couples diffusion in the bulk and surface domains via interfacial exchange fluxes, is implemented to couple the phases. Using a cell model, a new analytical solution is developed for aligned fibres with elliptic cross-sections and arbitrary orientation with respect to the mean gradient. The anisotropic boundary-value-problem is solved using an isotropic approximation to furnish concentration distributions in the three phases. Therefore, the model is more accurate near the isotropic limit and at lower inclusion volume fractions. When surface diffusion is significant, the present anisotropic model reproduces the isotropic model of Albaalbaki and Hill (2012) for unit aspect ratio and a variety of physical parameters. For a sphere with negligible surface flux, the model agrees with Maxwell’s theory, and reproduces the model of Akbari et al. (2013) with various aspect ratios. To test the model for several parameters and other aspect ratios, direct numerical computations of the effective diffusivity, using spatially periodic unit cells, are undertaken, and a comparison with experimental data is presented. This model serves as a two-dimensional solution for the effective diffusivity of dilute anisotropic structures with surface diffusion. [ABSTRACT FROM AUTHOR]

A variety of observations—sometimes controversial—have been made in recent decades when attempting to elucidate the roles of interfacial slip on tracer diffusion in phospholipid membranes. Evans–Sackmann theory (1988) has furnished membrane viscosities and lubrication-film thicknesses for supported membranes from experimentally measured lateral diffusion coefficients. Similar to the Saffman and Delbrück model, which is the well-known counterpart for freely supported membranes, the bilayer is modelled as a single two-dimensional fluid. However, the Evans–Sackman model cannot interpret the mobilities of monotopic tracers, such as individual lipids or rigidly bound lipid assemblies; neither does it account for tracer–leaflet and inter-leaflet slip. To address these limitations, we solve the model of Wang and Hill, in which two leaflets of a bilayer membrane, a circular tracer and supports are coupled by interfacial friction, using phenomenological friction/slip coefficients. This furnishes an exact solution that can be readily adopted to interpret the mobilities of a variety of mosaic elements—including lipids, integral monotopic and polytopic proteins, and lipid rafts—in supported bilayer membranes. [ABSTRACT FROM AUTHOR]

A computational framework is developed for applying interfacial kinetic transport theory to predict water vapour permeability of porous media. Modified conservation equations furnish spatially periodic disturbances from which the average flux and, thus, the effective diffusivity is obtained. The equations are solved exactly for a model porous medium comprising parallel layers of gas and solid with arbitrary solid volume fraction. From the microscale effective diffusivity, a two-point boundary-value problem is solved at the macroscale to furnish the water vapour transport rate in membranes subjected to a finite RH differential. Then, the microscale model is implemented using a computational framework (extended finite-element method) to examine the role of particle size, aspect ratio and positioning for periodic arrays of aligned super-ellipses (model particles that pack with high density). We show that the transverse water vapour permeability can be reduced by an order of magnitude only when fibres with a high-aspect ratio cross section are packed in a periodic staggered configuration. Maximum permeability is achieved at intermediate micro-structural length scales, where gas-phase diffusion is enhanced by surface diffusion, but not limited by interfacial-exchange kinetics. The two-dimensional computations demonstrated here are intended to motivate further efforts to develop efficient computational solutions for realistic three-dimensional microstructures. [ABSTRACT FROM AUTHOR]

Nanoparticle-hydrogel interactions are important in many applications. In drug delivery, for example, these control the release rate and may prevent nanoparticle (NP) migration from a targeted site. In this paper, electroacoustic spectroscopy is used to study the NP-hydrogel interaction, focusing on the influence of polymer adsorption and hydrogel composition. Electroacoustic spectroscopy is a powerful noninvasive tool to complement microrheological characterization. We study the interaction of polyacrylamide (PA) with laponite and silica NPs as model systems with strong and weak attraction, respectively. Stronger adsorption of PA on laponite compared to silica imparts distinctly different rheological properties to PA solutions and decreases the laponite mobility significantly more than silica when embedded in PA hydrogels. However, the mobilities of both NPs exhibit qualitatively similar variations with acrylamide and chemical cross-linker concentrations, as indicated by viscoelastic and electrokinetic characterizations. The electrokinetic charge changes with polymer concentration more than with the chemical cross-linker concentration, whereas elastic coupling increases with the polymer concentration and decreases with the chemical cross-linker concentration. These reflect significant physicochemical changes to the hydrogel microstructure from the NP doping, so optimization of material properties for a specific application must explicitly consider the NP-polymer pairing. [ABSTRACT FROM AUTHOR]

Electro-dewatering (ED) is a novel technology to reduce the overall costs of residual biosolids processing, transport, and disposal. In this study, we investigated Joule heating and pH as parameters controlling the dewaterability limit, dewatering rate, and energy efficiency. Temperature controlled electrodes revealed that Joule heating enhances water removal by increasing evaporation and electro-osmotic flow. High temperatures increased the dewatering rate, but had little impact on the dewaterability limit and energy efficiency. Analysis of horizontal layers after 15-min ED suggests electroosmotic flow reversal, as evidenced by a shifting of the point of minimum moisture content from the anode toward the cathode. This flow reversal was also confirmed by the pH at the anode being below the isoelectric point, as ascertained by pH titration. The important role of pH on ED was further studied by adding acid/base solutions to biosolids prior to ED. An acidic pH reduced the biosolids charge while simultaneously increasing die dewatering efficiency. Thus, process optimization depends on trade-offs between speed and efficiency, according to physicochemical properties of the biosolids microstructure. [ABSTRACT FROM AUTHOR]

The electrophoretic mobility of adilute, weakly charged “soft”particle in a charged hydrogel modeled as an effective medium is investigatedin this work. This is closely related to previous work (Li, F.; Allison,S. A.; Hill, R. J. J. Colloid Interface Sci.2014, 423, 129–142) but approachedin a different way using the Lorentz reciprocal theorem. Under thelimiting conditions of the present work, it is possible to avoid numericalsolution of differential equations. An analytical equation is derivedfor the mobility and applied to a number of cases. [ABSTRACT FROM AUTHOR]

Highlights: [•] Electrokinetic theory furnishes the soft-sphere electrophoretic mobility in polyelectrolyte gels. [•] Mobility is sensitive to the gel charge and permeability. [•] Mobility is sensitive to the core dielectric constant when gels are charged. [•] Matlab routines are available for parametric studies and interpretation of experiments. [Copyright &y& Elsevier]

Abstract: The effective thermal conductivity of anisotropic two-phase media is studied. Using Chang’s unit cell, a new analytical solution is developed for anisotropic materials based on the self-consistent field concept. The structure comprises randomly distributed aligned elliptical inclusions embedded in a continuous medium. Inclusions have arbitrary aspect ratio and arbitrary orientation relative to the coordinate system of interest. The temperature distribution is solved and averaged in the unit cell to obtain all the components. The model shows correct limiting properties in all its independent variables. In particular, it yields Maxwell’s theory in the limit where the inclusion aspect ratio approaches unity. Compact expressions for the components of the effective thermal conductivity are presented. The present model is compared with available expressions for anisotropic systems based on an equivalent inclusion model. To assess the accuracy of these, the closure problem associated with the volume averaging method with periodic boundary condition is numerically solved. The present model agrees well with the result of the periodic unit cell compared with equivalent inclusion based methods, particularly for low aspect ratios and moderate particle volume fractions. This is consistent with Ochoa-Tapia’s analysis for isotropic systems that Chang’s unit cell can accurately approximate spatially periodic models in a wider range of porosities compared to Maxwell’s theory. The present solution can serve as a general 2D model for anisotropic structures with dilute to moderate inclusion concentrations. [Copyright &y& Elsevier]

Abstract: Electro-dewatering is an energy-efficient technology in which an electric field can increase the dryness of biosolids from secondary wastewater treatment from 15% w/w to 30–50% w/w. Here, we address bacterial pathogen indicators inactivation (total coliforms, Escherichia coli and aerobic endospores) during electro-dewatering, investigating the roles of electrochemically generated oxidants, extreme pH, and high temperature (from Joule heating). Our results demonstrate that temperature is the primary factor affecting total coliforms and E. coli inactivation. First, several electro-dewatering cycles were used to increase sludge temperature to about 100 °C after 6 min, during which time the average pH decreased from 7 to 3.6 after 10 min. Total coliforms and E. coli MPNs reached their detection limits after 6 min (with 4–5 logs of inactivation for total coliforms and 3–4 logs for E. coli). In contrast, aerobic endospores were not inactivated under these conditions; rather, their germination appeared to be stimulated by 6–8 min of electro-dewatering. Second, the dewatering cake was separated into four horizontal layers. After 8 min of electro-dewatering, the pH in the top layers decreased to 3, whereas the pH in the bottom layers increased to 8. Inactivation of total coliforms and E. coli in the sludge cake was similar in all layers, increasing with time, suggesting that oxidants and extreme pH are secondary inactivation factors. Finally, electrodes were cooled to maintain a temperature less than 34 °C. Although pH decreased significantly after 12 min of electro-dewatering, there was no significant bacterial pathogen indicator inactivation at low temperature. [Copyright &y& Elsevier]

For over half a century, alternating electric fields have been used to induce particle transport, furnishing the ζ-potential of analytes with sizes ranging from a few nanometers to several micrometers. Concurrent advances in nanotechnology have provided new materials for catalysis, self-assembly, and biomedical applications, all of which benefit from a thorough understanding of particle surface charge. [ABSTRACT FROM AUTHOR]

Many systems of biophysical and technological interest consist of multiple interpenetrating chains in a confined volume, i.e., a confined polymer solution. Using nanofluidic approaches developed originally for the study of single chains in confined geometries, we develop an assay to create confined polymer solutions on-chip and then probe the solution response to applied compressive forcing. In our approach, multiple chains are introduced into a nanoslit via hydrodynamic flow and are then concentrated against a barrier that is permeable only to solvent. For sufficiently high concentration, the compressed solution profile can be described by a mean-field polymer model based on Doi's two-fluid approach, with the chain free energy described by a Ginzburg-type free energy functional. This theory furnishes a partial differential equation based description of the concentration profile in terms of a nonlinear Schrödinger-type equation, providing a general theoretical framework for modeling confined polymer solution dynamics. [ABSTRACT FROM AUTHOR]

Electromigration of nanoparticles (NPs) is relevant to many technological and biological applications. We correlate the experimentally observed electromigration of Au NPs with a closed-form theoretical model that furnishes key NP characteristics, including the previously unknown values of Au NP core ζ-potential, PEG-corona permeability, and particle-hydrogel friction coefficient. More generally, the theory furnishes new understanding of NP electromigration in complex environments, establishing a robust and predictive model to guide the design and characterization of functionalized NPs. [ABSTRACT FROM AUTHOR]

Vesiculation of hydrous melts at 1 atm was studied in situ by synchrotron X-ray tomographic microscopy at the TOMCAT beamline of the Swiss Light Source (Villigen, Switzerland). Water-undersaturated basaltic, andesitic, trachyandesitic, and dacitic glasses were synthesized at high pressures and then laser heated at 1 atm. on the beamline, causing vesiculation. The porosity, bubble number density, size distributions of bubbles, and pore throats, as well as their tortuosity and connectivity, were measured in three-dimensional tomographic reconstructions of sample volumes, which were also used for lattice Boltzmann simulations of viscous permeabilities. Connectivity of bubbles by pore throats varied from ~ 100 to 105 mm−3, and for each sample correlated with porosity and permeability. Consideration of the results of this and previous studies of the viscous permeabilities of aphyric and crystal-poor magmatic samples demonstrated that at similar porosities permeability can vary by orders of magnitude, even for similar compositions. Comparison of the permeability relationships from this study with previous models (Degruyter et al., Bull Vulcanol 72:63–74, 2010; Burgisser et al., Earth Planet Sci Lett 470:37–47, 2017) relating porosity, characteristic pore-throat diameters, and tortuosity demonstrated good agreement. Modifying the Burgisser et al. model by using the maximum pore-throat diameter, instead of the average diameter, as the characteristic diameter reproduced the lattice Boltzmann permeabilities to within 1 order of magnitude. Correlations between average bubble diameters and maximum pore-throat diameters, and between porosity and tortuosity, in our experiments produced relationships that allow application of the modified Burgisser et al. model to predict permeability based only upon the average bubble diameter and porosity. These experimental results are consistent with previous studies suggesting that increasing bubble growth rates result in decreasing permeability of equivalent porosity foams. This effect of growth rate substantially contributes to the multiple orders of magnitude variations in the permeabilities of vesicular magmas at similar porosities. [ABSTRACT FROM AUTHOR]