Streaming Potentials of Hyaluronic Acid Hydrogel Films.

The streaming potentials of hyaluronic acid (HA) hydrogel films are measured and theoretically interpreted by systematically varying the HA concentration and the streaming electrolyte pH and ionic strength. While Donnan potentials are expected to vanish with sufficient added salt, apparent ζ-potentials from the Helmholtz-Smoluchowski interpretation remain of the order -20 mV. To theoretically interpret these data, we derived an electrokinetic model (valid in the Debye-Hückel regime) that accounts for ionic and hydrodynamic permeability of the gels. The films could then be ascribed an effective acid dissociation constant pKa ≈ 4.2, specific HA charge ≈-0.1e mmol g-1, and Brinkman/hydrodynamic permeability l2 ∼ l02S1/3, where l0 is the Brinkman length for HA solutions in the as-prepared reference state and S is the hydrogel swelling ratio. At an ionic strength of 10 mmol L-1, for example, the HA surface potentials are only ψD/2 ≈ -8 mV, where ψD is the Donnan potential, considerably lower than ζ-potentials furnished by the Helmholtz-Smoluchowski interpretation. This insight significantly changes how the films are expected to interact with other surfaces and colloids via Derjaguin-Landau-Vervey-Overbeek-type forces. Our analysis furnishes formulas for the swelling ratio S and hydrodynamic permeability l2, expressed explicitly as simple power-law functions of the as-prepared HA concentration cha (wt %), consistent with independent assessments of the HA solution permeability and polyelectrolyte-hydrogel swelling theory. These may prove valuable for extrapolating the results to other combinations of ionic strength, pH, and HA and cross-linking concentrations.

Electrokinetics of nanoparticle gel-electrophoresis.

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.

Liquid-bridge stability and breakup on surfaces with contact-angle hysteresis.

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.

Hydrogel-colloid interfacial interactions: a study of tailored adhesion using optical tweezers.

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.

Electrophoretic Interpretation of PEGylated NP Structure with and without Peripheral Charge.

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.

Capillary Force between Flexible Filaments.

Liquid droplets bridging filaments are ubiquitous in nature and technology. Although the liquid-surface shape and the capillary force and torque have been studied extensively, the effect of filament flexibility is poorly understood. Here, we show that elastic deformation (at large values of the elasto-capillary number) can significantly affect the liquid-surface shape and capillary force. The equilibrium state of parallel filaments is calculated using analytical approximations and numerical solutions for the fluid interface. The results compare well, and the numerical solution is then applied to crossing filaments. In the investigated range of parameters, the capillary force increases rapidly when the filaments touch. The force decreases continuously when decreasing the liquid volume for parallel hydrophilic filaments but produces a maximum for crossed filaments. The liquid volume at the maximum force is reported when changing the filament flexibility, crossing angle, and contact angle. These results may be beneficial in applications where the strength and structure of wet fibrous materials are important, such as in paper formation and when welding flexible components.

Impact of Joule Heating and pH on Biosolids Electro-Dewatering.

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 electro-osmotic 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 the dewatering efficiency. Thus, process optimization depends on trade-offs between speed and efficiency, according to physicochemical properties of the biosolids microstructure.

Transmembrane protein diffusion in gel-supported dual-leaflet membranes.

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.

Effects of Surface Topography and Cellular Biomechanics on Nanopillar-Induced Bactericidal Activity.

Bacteria are mechanically resistant biological structures that can sustain physical stress. Experimental data, however, have shown that high-aspect-ratio nanopillars deform bacterial cells upon contact. If the deformation is sufficiently large, it lyses the bacterial cell wall, ultimately leading to cell death. This has prompted a novel strategy, known as mechano-bactericide technology, to fabricate antibacterial surfaces. Although adhesion forces were originally proposed as the driving force for mechano-bactericidal action, it has been recently shown that external forces, such as capillary forces arising from an air-water interface at bacterial surfaces, produce sufficient loads to rapidly kill bacteria on nanopillars. This discovery highlights the need to theoretically examine how bacteria respond to external loads and to ascertain the key factors. In this study, we developed a finite element model approximating bacteria as elastic shells filled with cytoplasmic fluid brought into contact with an individual nanopillar or nanopillar array. This model elucidates that bacterial killing caused by external forces on nanopillars is influenced by surface topography and cell biomechanical variables, including the density and arrangement of nanopillars, in addition to the cell wall thickness and elastic modulus. Considering that surface topography is an important design parameter, we performed experiments using nanopillar arrays with precisely controlled nanopillar diameters and spacing. Consistent with model predictions, these demonstrate that nanopillars with a larger spacing increase bacterial susceptibility to mechanical puncture. The results provide salient insights into mechano-bactericidal activity and identify key design parameters for implementing this technology.

Nanoparticle ζ -potentials.

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. Therefore, the measurement of the ζ-potential via electrophoretic light scattering (ELS) has become essential for nanoparticle (NP) research. However, the interpretation of NP electrophoretic mobility, especially that of ligand-coated NPs, can be a complex undertaking. Despite the inherent intricacy of these data, key concepts from colloidal science can help to distill valuable information from ELS. In this Account, we adopt PEGylated Au NPs as an illustrative example to explore extensions of the classical theories of Smoluchowski, Hückel, and Henry to more contemporary theories for ligand-coated NP systems such as those from Ohshima, and Hill, Saville, and Russel. First, we review the basic experimental considerations necessary to understand NP electrophoretic mobility, identifying when O'Brien and White's numerical solution of the standard electrokinetic model should be adopted over Henry's closed-form analytical approximation. Next, we explore recent developments in the theory of ligand-coated particle electrophoresis, and how one can furnish accurate and meaningful relationships between measured NP mobility, ζ-potential, and surface charge. By identifying key ligand-coated NP parameters (e.g., coating thickness, permeability, molecular mass, and hydrodynamic segment size), we present a systematic method for quantitatively interpreting NP electrophoretic mobility. In addition to reviewing theoretical foundations, we describe our recent results that examine how the unique surface curvature of NPs alters and controls their properties. These data provide guidelines that can expedite the rational design of NPs for advanced uses, such as heterogeneous catalysis and in vivo drug delivery. As a practical demonstration of these concepts, we apply the ligand-coated theory to a recently developed noncovalent PEGylated Au NP drug-delivery system. Our analysis suggests that anion adsorption on the Au NP core may enhance the stability of these NP-drug conjugates in solution. In addition to providing useful nanochemistry insights, the information in this Account will be useful to biomedical and materials engineers, who use ELS and ζ-potentials for understanding NP dynamics.

Bubbles and drops on curved surfaces.

Surface curvature affects the shape, stability, and apparent contact angle of sessile and pendant drops. Here, we develop an approximate analytical solution for non-axisymmetric perturbations to small spherical drops on a flat substrate, assuming a fixed contact angle and fixed drop volume. The analytical model is validated using numerical solutions of the Laplace equation from the Surface Evolver software. We investigate the effects of surface curvature on drop shape, pressure, and surface energy, ascertaining the energy-gradient force that drives lateral drop migration. By balancing this force with the viscous resistance/drag force, in the lubrication approximation, we predict velocities of the order of 0.1 mm s(-1) for 1 mm diameter drops of water with a 30° contact angle on a substrate with a curvature gradient of 0.01 mm(-2), achieved, for example, on a harmonic surface with a wavelength of 4 cm and an amplitude of 4 mm.

Surface Wettability Is a Key Feature in the Mechano-Bactericidal Activity of Nanopillars.

Nanopillar-textured surfaces are of growing interest because of their ability to kill bacteria through physical damage without relying on antimicrobial chemicals. Although research on antibacterial nanopillars has progressed significantly in recent years, the effect of nanopillar hydrophobicity on bactericidal activity remains elusive. In this study, we investigated the mechano-bactericidal efficacy of etched silicon nanopillars against Pseudomonas aeruginosa at nanopillar hydrophobicities from superhydrophilic to superhydrophobic. Assessing cell viability and bacterial morphology in immersed wet conditions, we observed negligible bactericidal activity; however, air/liquid interface displacement during water evaporation established a bactericidal effect that strongly depends on substrate hydrophobicity. Specifically, bactericidal activity was highest on superhydrophilic surfaces but abated with increasing hydrophobicity, diminishing at substrate contact angles larger than 90°. Calculation of the surface tension and Laplace pressure forces during water evaporation for each substrate subsequently highlighted that the total capillary force, as an external driving force responsible for bacterial deformation, is significantly weaker on hydrophobic substrates. These findings suggest that superhydrophilic nanopillared surfaces are a superior choice for mechano-bactericidal activity, whereas superhydrophobic surfaces, although not bactericidal, may have antibiofouling properties through their self-cleaning effect. These findings provide new insights into the design and application of nanopillared surfaces as functional antibacterial materials.

Self-assembled calcium pyrophosphate nanostructures for targeted molecular delivery.

Nanostructured, inorganic microspheres have many industrial applications, including catalysis, electronics, and particularly drug delivery, with several advantages over their organic counterparts. However, many current production methods require high energy input, use of harmful chemicals, and extensive processing. Here, the self-assembly of calcium pyrophosphate into nanofibre microspheres is reported. This process takes place at ambient temperature, with no energy input, and only salt water as a by-product. The formation of these materials is examined, as is the formation of nanotubes when the system is agitated, from initial precipitate to crystallisation. A mechanism of formation is proposed, whereby the nanofibre intermediates are formed as the system moves from kinetically favoured spheres to thermodynamically stable plates, with a corresponding increase in aspect ratio. The functionality of the nanofibre microspheres as targeted enteric drug delivery vehicles is then demonstrated in vitro and in vivo, showing that the microspheres can pass through the stomach while protecting the activity of a model protein, then release their payload in intestinal conditions.

Preparation and characterization of multilayered polymer nanotube dispersions.

Despite considerable efforts to synthesize nanotubes using porous alumina or polycarbonate membrane templates, few studies have addressed the resulting nanotube dispersion. We prepared dispersions of multilayered polyethylenimine/maleic anhydride alternating copolymer (PEI/MAAC) nanotubes synthesized with porous alumina templates. After mechanical polishing to remove the residual polymer surface layer from templates and subsequent template dissolution, the multilayered PEI/MAAC nanotubes were easily dispersed in water at neutral pH by polyelectrolyte adsorption, producing nanotube dispersions that were stable for at least 3 months. We characterized the dispersions using phase-contrast optical microscopy, electro-optics, electrophoresis, and viscometry to help understand their colloidal properties in the dilute and semidilute regimes. The dispersions were resistant to salt-induced aggregation up to at least 1 mM NaCl and were optically anisotropic when subjected to an electric field or flow. Interestingly, the electrophoretic mobility of polystyrene sulfonate (PSS)-stabilized nanotubes increases with increasing ionic strength, because of the high surface charge and softness of the adsorbed polyelectrolyte. Furthermore, unlike many rod-like colloid systems, the polymer nanotube dispersion has low viscosity because of weak rotary Brownian motions and strong tendency to shear thinning. At the high shear rates achieved in capillary viscometry experiments, however, we observed a slight shear thickening, which can be attributed to transient hydrocluster formation.

Dynamic electrical response of colloidal micro-spheres in compliant micro-channels from optical tweezers velocimetry.

We report the dynamic response of colloidal silica in aqueous electrolytes to oscillatory electric fields at frequencies up to approximately 50 kHz. Particles were optically trapped at various positions across the gap of straight and crossed parallel-plate micro-channels. Using back-focal-plane interferometry, we measured the apparent electrophoretic mobility in NaCl and CaCl(2) electrolytes over a wide range of salt concentrations. The mobility has a strikingly complex dependence on channel position and forcing frequency that cannot be understood on the basis of standard electrokinetic theory for rigid micro-channels. We ascribe the anomalous dynamics to coupling of electro-osmotic flow and elastic modes of the micro-channel and auxiliary hardware. By integrating into the classical theory a complex-valued channel-compliance parameter--that modulates the phase and amplitude of the dynamic electro-osmotic flow--theoretical interpretation of the frequency-dependent mobility furnishes robust measurements of the intrinsic particle electrophoretic mobility and the upper and lower channel-wall zeta-potentials. Together, the single-particle experiments and accompanying theoretical interpretation highlight--for the first time--how spatially and temporally resolved particle dynamics are exquisitely sensitive to channel compliance. Accordingly, specially designed compliant micro-fluidic channels and flexible tube connections might be tailored for dynamic electrical micro-fluidic diagnostic applications.

Electrophoretic mobilities of PEGylated gold NPs.

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.

Steady electrodiffusion in hydrogel-colloid composites: macroscale properties from microscale electrokinetics.

A rigorous microscale electrokinetic model for hydrogel-colloid composites is adopted to compute macroscale profiles of electrolyte concentration, electrostatic potential, and hydrostatic pressure across membranes that separate electrolytes with different concentrations. The membranes are uncharged polymeric hydrogels in which charged spherical colloidal particles are immobilized and randomly dispersed with a low solid volume fraction. Bulk membrane characteristics and performance are calculated from a continuum microscale electrokinetic model (Hill 2006b, c). The computations undertaken in this paper quantify the streaming and membrane potentials. For the membrane potential, increasing the volume fraction of negatively charged inclusions decreases the differential electrostatic potential across the membrane under conditions where there is zero convective flow and zero electrical current. With low electrolyte concentration and highly charged nanoparticles, the membrane potential is very sensitive to the particle volume fraction. Accordingly, the membrane potential--and changes brought about by the inclusion size, charge and concentration--could be a useful experimental diagnostic to complement more recent applications of the microscale electrokinetic model for electrical microrheology and electroacoustics (Hill and Ostoja-Starzewski 2008, Wang and Hill 2008).

Electric-field-induced displacement of charged spherical colloids in compressible hydrogels.

This paper concerns the electric-field-induced displacement of a charged spherical colloid embedded in an uncharged compressible hydrogel. Previous theoretical calculations for incompressible polymer skeletons predict sub-nanometre particle displacements within the experimentally accessible parameter space (e.g., particle surface charge density, polymer shear modulus, and electric field strength). Accordingly, the prevailing expectation is that an experimental test of the theory would be extraordinarily difficult. In this work, however, we solved the electrokinetic model for compressible polymer skeletons with arbitrary Poisson's ratio. The most striking result, obtained from numerically exact solutions of the full model and an analytical boundary-layer approximation, is that polymer compressibility admits particle displacements that increase linearly with particle size when the radius is greater than the Debye length. This scaling is qualitatively different than previously obtained for incompressible skeletons, where the ratio of the particle displacement to the electric field approaches a particle-size-independent constant. The displacement is also much more sensitive to the hydrodynamic permeability of the polymer skeleton. Therefore, when compressible hydrogels are deformed at frequencies below their reciprocal draining time, our theory identifies the parameter space where displacements could be registered using optical microscopy. In turn, this will help to establish a quantitative connection between the electric-field-induced particle displacement and physicochemical characteristics of the particle-polymer interface.

Electric-field-induced displacement of a charged spherical colloid embedded in an elastic Brinkman medium.

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. Finally, we identify a close connection between the displacement when a colloid is immobilized in a gel and its velocity (electrophoretic mobility) when dispersed in a Newtonian electrolyte.

Electric-field-enhanced transport in polyacrylamide hydrogel nanocomposites.

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.