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Hydrogels are promising supports for nanoemulsion drops since the skeleton provides a physical barrier to coalescence and possibly a thermodynamic barrier to Ostwald ripening. How these factors pla... more...

Dynamic mobility spectra of sodium dodecyl sulphate (SDS)-stabilized hexadecane nanodrops in aqueous NaCl electrolytes are measured using the electrokinetic-sonic amplitude, and interpreted using a... more...

As a first step toward understanding the electroacoustic response of polyelectrolyte hydrogel nanocomposites, we systematically vary the linear charge density of acrylic acid-co-acrylamide polymer ... more...

We examine the swelling and dissolution of hydrogels cross-linked by a combination of physical and chemical junctions, focusing on the technologically important DNA- and “bis”-cross-linked polyacry... more...

We examine networks of complementary-DNA-strand cross-linked polyacrylamide, with and without covalent N,N′-methylene(bis)acrylamide cross-linking, using rheological time–temperature superposition ... more...

An electrokinetic model for a surfactant-stabilized nano-drop under oscillatory forcing is solved. This generalizes a model for which an analytical solution was recently proposed for large, highly charged drops. Calculations of the dynamic electrophoretic mobility and the accompanying electrostatic polarization for a single drop provide a theoretical foundation for interpreting electrokinetic sonic amplitude and complex-conductivity spectra for dilute surfactant-stabilized oil-in-water emulsions and bubbly liquids. The model is distinguished from earlier models by accounting for the internal fluid and interfacial dynamics at finite frequencies ( ). This dynamics accounts for the electro-migration, diffusion and advection of surfactant ions on the interface, and exchange of these ions with the immediately adjacent electrolyte. Surface gradients induce Marangoni stresses, which couple to the electrical and hydrodynamic stresses, modulating the magnitude and phase of the drop velocity and electrostatic polarization induced by the electric field. Of particular interest, for sodium dodecyl sulphate stabilized oil-in-water drops, is how the high surface-charge density manifests in a breakdown of the Smoluchowski-slip approximation, even for drops with very thin diffuse layers. More generally, the model furnishes dynamic mobilities for drops with arbitrary size and charge, thus permitting appropriate averaging for polydisperse systems. Such calculations may help to resolve long-standing challenges and controversy with regards to the surface-charge density of nano-drops and their macro-scale counterparts, and may pave the way to quantitative interpretations of more complex dynamic interfacial rheology and exchange kinetics, e.g. for Pickering emulsions. more...

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 Schrodinger-type equation, providing a general theoretical framework for modeling confined polymer solut... more...

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. more...

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. more...

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 c... more...

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 diffusio... more...

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. more...

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. more...

This paper examines the nanoparticle (NP) influence on energy storage and dissipation in hydrogel nanocomposites (HNCs). To obtain fundamental insights into mechanical enhancement, a model system involving the in situ free-radical polymerization of acrylamide with bis-acrylamide (bis) and silica NPs is adopted. The loss tangents of the unmodified polymer networks span three orders of magnitude, and the weak attraction between silica and poly(acrylamide) (PA)—as compared to composites with a stronger NP-polymer interaction—makes these HNCs particularly sensitive to systematic variations in (i) NP size and concentration and (ii) monomer and crosslinker concentrations. From the dynamic shear moduli during polymerization, and their spectra at steady-state, silica NPs in PA behave as multi-functional, physical crosslinking centers that increase the storage modulus, particularly in very weakly bis-crosslinked PA (in which NP aggregates are proposed to form elastically effective clusters). The loss modulus for HNCs reflects adsorption/desorption and friction at the NP surfaces, varying with the NP, monomer and crosslinker concentrations. Silica NPs were also found to slow the polymerization and crosslinking of acrylamide according to the specific NP surface area (set by the NP size and concentration), suggesting that silica NPs reduce the free-radical concentration. more...

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 Δ = 0.70 ± 0.02) that are consistent with the de Gennes [“On a relation betwee... more...

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. more...

Nanoparticle zeta-potentials are relatively easy to measure, and have consistently been proposed in guidance documents as a particle property that must be included for complete nanoparticle characterization. There is also an increasing interest in integrating data collected on nanomaterial properties and behavior measured in different systems (e.g. in vitro assays, surface water, soil) to identify the properties controlling nanomaterial fate and effects, to be able to integrate and reuse datasets beyond their original intent, and ultimately to predict behaviors of new nanomaterials based on their measured properties (i.e. read across), including zeta-potential. Several confounding factors pose difficulty in taking, integrating and interpreting this measurement consistently. Zeta-potential is a modeled quantity determined from measurements of the electrophoretic mobility in a suspension, and its value depends on the nanomaterial properties, the solution conditions, and the theoretical model applied. The ability to use zeta-potential as an explanatory variable for measured behaviors in different systems (or potentially to predict specific behaviors) therefore requires robust reporting with relevant meta-data for the measurement conditions and the model used to convert mobility measurements to zeta-potentials. However, there is currently no such standardization for reporting in the nanoEHS literature. The objective of this tutorial review is to familiarize the nanoEHS research community with the zeta-potential concept and the factors that influence its calculated value and interpretation, including the effects of adsorbed macromolecules. We also provide practical guidance on the precision of measurement, interpretation of zeta-potential as an explanatory variable for processes of interest (e.g. toxicity, environmental fate), and provide advice for addressing common challenges associated with making meaningful zeta-potential measurements using commercial instruments. Finally, we provide specific guidance on the parameters that need to be reported with zeta-potential measurements to maximize interpretability and to support scientific synthesis across data sets. more...

Gel-electrophoresis has been demonstrated in recent decades to successfully sort a great variety of nanoparticles according to their size, charge, surface chemistry, and corona architecture. However, quantitative theoretical interpetations have been limited by the number and complexity of factors that influence particle migration. Theoretical models have been fragmented and incomplete with respect to their counterparts for free-solution electrophoresis. This paper unifies electrokinetic models that address complex nanoparticle corona architectures, corona and gel charge regulation (e.g., by the local pH), multi-component electrolytes, and non-linear electrostatics and relaxation effects. By comprehensively addressing the electrokinetic aspects of the more general gel-electrophoresis problem, in which short-ranged steric interactions are significant, a stage is set to better focus on the physicochemical and steric factors. In this manner, it is envisioned that noparticle gel-electrophoresis may eventually be advanced from a nanoparticle-characterization tool to one that explicitly probes the short-ranged interactions of nanoparticles with soft networks, such as synthetic gels and biological tissues. In this paper, calculations are undertaken that identify a generalized Hückel limit for nanoparticles in low-conductivity gels, and a new Smoluchowski limit for polyelectrolyte-coated particles in high-conductivity gels that is independent of the gel permeability. Also of fundamental interest is a finite, albeit small, electrophoretic mobility for uncharged particles in charged gels. Electrophoretic mobilities and drag coefficients (with electroviscous effects) for nanoparticles bearing non-uniform coronas show that relaxation effects are typically weak for the small nanoparticles (radius ≈3-10 nm) to which gel-electrophoresis has customarily been applied, but are profound for the larger nanoparticles (radius ≳ 40 nm in low conductivity gels) to which passivated gel-electrophoresis experiments have recently been applied. To demonstrate its practical application, the model is applied to (pH charge regulating) carboxylated polystyrene nanospheres in low-density passivated agarose gels (weak steric effects). This furnishes a new theoretical interpretation of literature data for which a finite diffuse-layer-thickness, pH-charge regulation, high charge, and relaxation effects dominate over the steric influences. more...

Free volume and polymer chain architecture play important roles in controlling the glass transition temperature $$T_g$$ of polymer nanocomposites. Various changes in $$T_g$$ with respect to nanoparticle (NP) loading have been reported, depending, in part, on whether there are attractive or repulsive interactions between the polymer and NPs. However, even with no enthalpic interaction, there are ostensible changes in $$T_g$$ that must be attributed to topological factors, such as chain stiffness and nanoparticle size. Here we adopt a macroscopic granular model to help understand frustrated dynamics in glassy polymer nanocomposites. Mixtures of granular chains with spherical inclusions were prepared with prescribed sphere size, chain length, and mixture composition. We measured the time to reach a close–packed, jammed state when these composites were subjected to controlled mechanical shaking. The compaction dynamics reveal that spherical inclusions profoundly influence the chain relaxation dynamics. In the long-chain limit, increasing the NP loading furnishes a minimum in the chain relaxation time, which may be loosely associated with an intermediate minimum in $$T_g$$ with respect to nanoparticle loading for polymer nanocomposites. This minimum occurs for spheres having different sizes, but only at concentrations where the characteristic sphere separation is comparable to the chain loop size. This observation may explain the variety of contrasting trends that have been found in the literature for the dependence of $$T_g$$ on nanoparticle loading in polymeric nanocomposites. more...

Tools to measure transmembrane-protein diffusion in lipid bilayer membranes have advanced in recent decades, providing a need for predictive theoretical models that account for interleaflet leaflet friction on tracer mobility. Here we address the fully three-dimensional flows driven by a (nonprotruding) transmembrane protein embedded in a dual-leaflet membrane that is supported above and below by soft porous supports (e.g., hydrogel or extracellular matrix), each of which has a prescribed permeability and solvent viscosity. For asymmetric configurations, i.e., supports with contrasting permeability, as realized for cells in contact with hydrogel scaffolds or culture media, the diffusion coefficient can reflect interleaflet friction. Reasonable approximations, for sufficiently large tracers on low-permeability supports, are furnished by a recent phenomenological theory from the literature. Interpreting literature data, albeit for hard-supported membranes, provides a theoretical basis for the phenomenological Stokes drag law as well as strengthening assertions that nonhydrodynamic interactions are important in supported bilayer systems, possibly leading to overestimates of the membrane/leaflet viscosity. Our theory provides a theoretical foundation for future experimental studies of tracer diffusion in gel-supported membranes. more...

We study the stability and breakup of liquid bridges with a free contact line on surfaces with contact-angle hysteresis (CAH) under zero-gravity conditions. Non-ideal surfaces exhibit CAH because of surface imperfections, by which the constraints on three-phase contact lines are influenced. Given that interfacial instabilities are constraint-sensitive, understanding how CAH affects the stability and breakup of liquid bridges is crucial for predicting the drop size in contact-drop dispensing. Unlike ideal surfaces on which contact lines are always free irrespective of surface wettability, contact lines may undergo transitions from pinned to free and vice versa during drop deposition on non-ideal surfaces. Here, we experimentally and theoretically examine how stability and breakup are affected by CAH, highlighting cases where stability is lost during a transition from a pinned–pinned (more constrained) to pinned-free (less constrained) interface—rather than a critical state. This provides a practical means of expediting or delaying stability loss. We also demonstrate how the dynamic contact angle can control the contact-line radius following stability loss. more...

Dynamics of colloidal particles adhering to soft, deformable substrates, such as tissues, biofilms, and hydrogels play a key role in many biological and biomimetic processes. These processes, including, but not limited to colloid-based delivery, stitching, and sorting, involve microspheres exploring the vicinity of soft, sticky materials in which the colloidal dynamics are affected by the fluid environment (e.g., viscous coupling), inter-molecular interactions between the colloids and substrates (e.g., Derjaguin-Landau-Verwey-Overbeek (DLVO) theory), and the viscoelastic properties of contact region. To better understand colloidal dynamics at soft interfaces, an optical tweezers back-focal-plane interferometry apparatus was developed to register the transverse Brownian motion of a silica microsphere in the vicinity of polyacrylamide (PA) hydrogel films. The time-dependent mean-squared displacements are well described by a single exponential relaxation, furnishing measures of the transverse interfacial diffusion coefficient and binding stiffness. Substrates with different elasticities were prepared by changing the PA crosslinking density, and the inter-molecular interactions were adjusted by coating the microspheres with fluid membranes. Stiffer PA hydrogels (with bulk Young's moduli ≈1-10 kPa) immobilize the microspheres more firmly (lower diffusion coefficient and position variance), and coating the particles with zwitterionic lipid bilayers (DOPC) completely eliminates adhesion, possibly by repulsive dispersion forces. Remarkably, embedding polyethylene glycol-grafted lipid bilayers (DSPE-PEG2k-Amine) in the zwitterionic fluid membranes produces stronger adhesion, possibly because of polymer-hydrogel attraction and entanglement. This study provides new insights to guide the design of nanoparticles and substrates with tunable adhesion, leading to smarter delivery, sorting, and screening of micro- and nano-systems. more...

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. more...

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. more...

Anchoring poly(ethylene glycol) (PEG) to inorganic nanoparticles (NPs) permits control over NP properties for a variety of technological applications. However, the core-shell structure tremendously complicates the interpretation of the ubiquitous ζ-potential, as furnished by electrophoretic light-scattering, capillary electrophoresis or gel electrophoresis. To advance the ζ-potential-and the more fundamental electrophoretic mobility-as a quantitative diagnostic for PEGylated NPs, we synthesized and characterized Au NPs bearing terminally anchored 5 kDa PEG ligands with univalent carboxymethyl end groups. Using the electrophoretic mobilities, acquired over a wide range of ionic strengths, we developed a theoretical model for the distributions of polymer segments, charge, electrostatic potential, and osmotic pressure that envelop the core: knowledge that will help to improve the performance of soft NPs in fundamental research and technological applications. more...

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. more...

When an electric field is applied to an electrolyte-saturated polymer gel embedded with charged colloidal particles, the force that must be exerted by the hydrogel on each particle reflects a delicate balance of electrical, hydrodynamic and elastic stresses. This paper examines the displacement of a single charged spherical inclusion embedded in an uncharged hydrogel. We present numerically exact solutions of coupled electrokinetic transport and elastic-deformation equations, where the gel is treated as an incompressible, elastic Brinkman medium. This model problem demonstrates how the displacement depends on the particle size and charge, the electrolyte ionic strength, and Young's modulus of the polymer skeleton. The numerics are verified, in part, with an analytical (boundary-layer) theory valid when the Debye length is much smaller than the particle radius. Further, we identify a close connection between the displacement when a colloid is immobilized in a gel and its velocity when dispersed in a Newtonian electrolyte. Finally, we describe an experiment where nanometer-scale displacements might be accurately measured using back-focal-plane interferometry. The purpose of such an experiment is to probe physicochemical and rheological characteristics of hydrogel composites, possibly during gelation. more...

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 so-called 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. more...

The permeability of certain polymer membranes with impenetrable nanoinclusions increases with the particle volume fraction (Merkel et al., Science, 296, 2002). This intriguing observation contradicts even qualitative expectations based on Maxwell's classical theory of conduction/diffusion in composites with homogeneous phases. This letter presents a simple theoretical interpretation based on classical models of diffusion and polymer physics. An essential feature of the theory is a polymer-segment depletion layer at the inclusion-polymer interface. The accompanying increase in free volume leads to a significant increase in the local penetrant diffusivity, which, in turn, increases the bulk permeability while exhibiting reverse selectivity. This model captures the observed dependence of the bulk permeability on the inclusion size and volume fraction, providing a straightforward connection between membrane microstructure and performance. more...

A theoretical model of electromigrative, diffusive and convective transport in polymer-gel composites is presented. Bulk properties are derived from the standard electrokinetic model with an impenetrable charged sphere embedded in an electrolyte-saturated Brinkman medium. Because the microstructure can be carefully controlled, these materials are promising candidates for enhanced gel-electrophoresis, chemical sensing, drug delivery, and microfluidic pumping technologies. The methodology provides solutions for situations where perturbations from equilibrium are induced by gradients of electrostatic potential, concentration and pressure. While the volume fraction of the inclusions should be small, Maxwell's well-known theory of conduction suggests that the model may also be accurate at moderate volume fractions. In this work, the theory is used to compute ion fluxes, electrical current density, and convective flow driven by an electric field applied to an homogeneous composite. The electric-field-induced (electro-osmotic) flow is a sensitive indicator of the inclusion (-potential and size, electrolyte concentration, and Darcy permeability of the gel, while the electrical conductivity is usually independent of the polymer gel and is relatively insensitive to characteristics of the inclusions and electrolyte. more...