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We study the stability and breakup of liquid bridges with a free contact line on a surface with contact-angle hysteresis under zero-gravity conditions. Theoretical predictions of the stability limits are validated by experimental measurements. Experiments are conducted in a water-methanol-silicon oil system where the gravity force is offset by buoyancy. We highlight cases where stability is lost during the transition from a pinned-pinned to pinned-free interface when the receding contact angle is approached---rather than a critical state, indicating that the breakup length is not always associated with the static maximum-length stability limit. We demonstrate that the dynamic contact angle controls the contact-line radius following stability loss, and that interface evolution following stability loss can increase the dispensed-drop size if the contact angle is fixed., Comment: To be submitted to Phys. Fluids

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 elatocapillary 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.

Contact-drop dispensing is central to many small-scale applications, such as direct-scanning probe lithography and micromachined fountain-pen techniques. Accurate and controllable dispensing required for nanometer-resolved surface patterning hinges on the stability and breakup of liquid bridges. Here, 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 non-axisymmetric perturbations. We apply a variational formulation to derive the corresponding stability criteria. The maximal stability region and stability region are represented in the favourable and canonical phase diagrams, providing a complete description of catenoid equilibrium and stability. All catenoids are stable with respect to non-axisymmetric 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.

Electroosmotic pumping through uncharged hydrogels can be achieved by embedding the polymer network with charged colloidal inclusions. Matos and co-workers (2006) recently used the concept to enhance the diffusion-limited flux of uncharged molecules across polyacrylamide hydrogel membraness 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. 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 nano-particle 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.

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.

This paper examines the response of electrolyte-saturated polymer gels, embedded with charged spherical inclusions, to a weak gradient of electrolyte concentration. These composites present a model system to study microscale electrokinetic transport processes, and a rigorous theoretical prediction of the bulk properties will benefit novel diagnostic applications. 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 $\zeta$-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.

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.

A theoretical model of electromigrative, diffusive and convectivetransport 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 `exact' 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 theory may also be accurate at moderate volume fractions. In this work, the model is used to compute ion fluxes, electrical current density, and convective flow induced by an applied electric field. The electric-field-induced (electro-osmotic) flow is a sensitive indicator of the inclusion zeta-potential and size, electrolyte concentration, and Darcy permeability of the gel, while the electrical conductivity increment is most often independent of the polymer gel, and is much less sensitive to particle and electrolyte characteristics.

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.