Inelastic effects in bulge formation of inflated polymer tubes.

When a soft tube is inflated, it may sometimes show a bulge instability wherein a portion of the tube inflates much more than the rest. The bulge instability is well-understood for hyperelastic materials. We examine inflation of polyurethane tubes whose material behavior is not strictly hyperelastic. Upon inflating at constant rate, the tubes deform into a variety of shapes including irregular axisymmetric shapes with multiple localized bulges, a single axially-propagating bulge, or homogeneous cylindrical shapes. In all cases regardless of the inflation mode, the pressure first rises to a maximum, and then gradually reduces towards a plateau. We document numerous differences as compared to hyperelastic tubes. Most notably a pressure maximum can appear even without bulging, whereas for hyperelastic tubes, a pressure maximum is necessarily accompanied by bulging. Further, the decrease in pressure beyond the maximum occurs gradually over timescales as long as an hour, whereas bulging of hyperelastic tubes induces an instantaneous drop in pressure. We also observe permanent deformation upon deflation, a decrease in the pressure maximum during a subsequent second inflation, and more severe bulge localization at low inflation rates. Existing theory of hyperelastic tube inflation cannot capture the observed behaviors, even qualitatively. Finite element simulations suggest that many of the observations can be explained by viscoelasticity, specifically that a slow material response allows the pressure to remain high for long durations, which in turn allows growth of multiple bulges.

Salt Effects on the Phase Behavior and Cocrystallization Kinetics of POCB-Water Mixtures.

Mixtures of water with polyoxacyclobutane (POCB) have a unique phase diagram which combines liquid-liquid equilibrium (LLE) at high temperatures and cocrystallization of a POCB-hydrate at low temperatures. Such cocrystal hydrate formation is extremely rare among polymers. We report on the effects of adding NaCl salt on the phase behavior of POCB-water mixtures and the kinetics of hydrate crystallization from such mixtures. Salt loadings of less than 0.1 wt % were found to greatly expand the LLE region. Salt loadings of ∼10 wt % were found to significantly decrease the melting temperature of the hydrate below its ∼37 °C value under salt-free conditions. The hydrate was found to be remarkably tolerant of salt and persists at room temperature even when equilibrated with salt-saturated water. Salt was found to slow down hydrate crystallization, and the degree of slowing was greater than that expected from the salt-induced decrease in undercooling due to melting point depression.

Ridge localization driven by wrinkle packets.

While buckling is a time independent phenomenon for filaments or films bonded to soft elastic substrates, time evolution plays an important role when the substrate is a viscous fluid. Here we show that buckling instabilities in fluid-structure interactions can be reduced to the analysis of a growth function that amplifies the initial noise characterizing experimental or numerical error. The convolution between a specific growth function and noise leads to natural imperfections that emerge in the form of wave packets with a large scale modulation that can transform into localized structures depending on nonlinear effects. Specifically, we provide an experimental example where these wave packets are amplified into ridges for sufficiently low compression rates or are diluted into wrinkles for high compression rates.

Crimped fiber composites: mechanics of a finite-length crimped fiber embedded in a soft matrix.

Composites comprising crimped fibers of finite length embedded in a soft matrix have the potential to mimic the strain-hardening behavior of tissues containing fibrous collagen. Unlike continuous fiber composites, such chopped fiber composites would be flow-processable. Here, we study the fundamental mechanics of stress transfer between a single crimped fiber and the embedding matrix subjected to tensile strain. Finite element simulations show that fibers with large crimp amplitude and large relative modulus straighten significantly at small strain without bearing significant load. At large strain, they become taut and hence bear increasing load. Analogous to straight fiber composites, there is a region near the ends of each fiber which bears much lower stress than the midsection. We show that the stress-transfer mechanics can be captured by a shear lag model where the crimped fiber can be replaced with an equivalent straight fiber whose effective modulus is lower than that of the crimped fiber, but increases with applied strain. This allows estimating the modulus of a composite at low fiber fraction. The degree of strain hardening and the strain needed for strain hardening can be tuned by changing relative modulus of the fibers and the crimp geometry.

Topographic de-adhesion in the viscoelastic limit.

The superiority of many natural surfaces at resisting soft, sticky biofoulants have inspired the integration of dynamic topography with mechanical instability to promote self-cleaning artificial surfaces. The physics behind this novel mechanism is currently limited to elastic biofoulants where surface energy, bending stiffness and topographical wavelength are key factors. However, the viscoelastic nature of many biofoulants causes a complex interplay between these factors with time-dependent characteristics such as material softening and loading rate. Here, we enrich the current elastic theory of topographic de-adhesion using analytical and finite-element models to elucidate the nonlinear, time-dependent interaction of three physical, dimensionless parameters: biofoulant's stiffness reduction, the product of relaxation time and loading rate, and the critical strain for short-term elastic de-adhesion. Theoretical predictions, in good agreement with numerical simulations, provide insight into tuning these control parameters to optimize surface renewal via topographic de-adhesion in the viscoelastic regime.

Flat, wrinkled, or ridged: Relaxation of an elastic film on a viscous substrate undergoing continuous compression.

We conduct a finite element computational study of the dynamics of a thin elastic film bonded to a much thicker viscous substrate undergoing compression at a fixed rate. The applied compression tends to continuously increase the strain, and hence the elastic energy, of the film. In contrast to the well-studied case of a soft elastic substrate, a viscous substrate cannot store elastic energy; instead it regulates the kinetics of the various mechanisms that dissipate elastic energy of the film. Sufficiently short films remain flat because shear flow in the liquid near the ends allows rapid relaxation of the strain over the entire film length. In longer films, end-relaxation cannot relax film strain in the mid-section, which therefore buckles. Buckles initially appear as packets of approximately-sinusoidal wrinkles. With increasing strain, these packets transform into tall localized ridges separated by nearly flat regions. In all cases, the buckles cause end-relaxation to become dynamically confined to a narrow region near the ends We construct a state map identifying regions of the parameter space of strain vs film length in which the film remains flat, develops wrinkle packets, or develops localized ridges. The evolution of the film energy during continuous compression shows that ridge localization appears due to a competition between two effects: a well-spaced ridges offer a lower energy state than uniform wrinkles, but wrinkles can develop faster because they require the viscous fluid to move over shorter distances.

Interfacially compatibilized PI/PDMS blends with reduced octadecylamine-functionalized graphene oxide: morphological and rheological properties.

We investigate the interfacial compatibilization effect of reduced octadecylamine-functionalized graphene oxide (ODA-GO) on the morphological and rheological properties of immiscible homopolymer blends of polydimethylsiloxane (PDMS) and polyisoprene (PI). We prepared droplet-matrix blends with a PI : PDMS ratio of 30 : 70 or 70 : 30 and interfacially localized ODA-GO stabilizer loadings from 0.1% to 1%. Blends were examined by optical microscopy and rheometry. Both blends show typical droplet-matrix morphology with stabilized round drops that do not stick together. With the addition of ODA-GO, smaller drops were observed in PI-continuous blends as compared to the PDMS-continuous blends suggesting that the effects of particles are not symmetric in the two cases. At sufficiently high ODA-GO loadings, flow-induced coalescence is suppressed almost completely. Dynamic oscillatory rheology broadly confirms the morphological observations. Specifically, all the blends show an interfacial relaxation process that is distinct from the bulk viscoelasticity, and the dependence of this process on GO content and flow conditions confirms the compatibilizing effect of the ODA-GO. This work provides a strategy for interfacially-compatibilizated polymer blends with specific properties for practical applications.

Drop Spreading and Confinement in Swelling-Driven Folding of Thin Films.

Surface instabilities are a versatile method for generating three-dimensional (3D) surface microstructure. When an elastomeric film weakly bonded to a substrate is swollen with solvent, buckle delamination and subsequent sliding of the film on the substrate lead to the formation of tall, self-contacting, and permanent folds. This paper explores the mechanics of fold development when such folding is induced by placing a drop on the surface of the film. We show that capillary effects can induce a strong coupling between folding and drop spreading: as folds develop, they wick the solvent toward the periphery of the drop, further propagating radially aligned folds. Accordingly, a solvent drop spreads far more on films that are weakly adhered to the substrate. As drop size reduces and folding becomes increasingly confined, debonding propagates along the perimeter of the wetted region, thus leading to corral-shaped fold patterns. On the other hand, as drop size increases and confinement effects weaken, isotropically oriented folds appear at a spacing that reduces as swelling increases. The spacing between the folds and the size of the corrals are both determined by the extent to which a single fold relieves compressive stress in its vicinity by sliding. We develop a model for folding which explicitly accounts for the fact that folds must initiate with near-zero volume under the buckle. The model shows that folds can appear even at very low swelling if there are large pre-existing debonded regions at the film-substrate interface.

Caveolin-1 mediates soft scaffold-enhanced adipogenesis of human mesenchymal stem cells.

BACKGROUND: Human bone marrow-derived mesenchymal stem cells (hBMSCs) can differentiate into adipocytes upon stimulation and are considered an appropriate cell source for adipose tissue engineering. In addition to biochemical cues, the stiffness of a substrate that cells attach to has also been shown to affect hBMSC differentiation potential. Of note, most current studies are conducted on monolayer cultures which do not directly inform adipose tissue engineering, where 3-dimensional (3D) scaffolds are often used to create proper tissue architecture. In this study, we aim to examine the adipogenic differentiation of hBMSCs within soft or stiff scaffolds and investigate the molecular mechanism mediating the response of hBMSCs to substrate stiffness in 3D culture, specifically the involvement of the integral membrane protein, caveolin-1 (CAV1), known to regulate signaling in MSCs via compartmentalizing and concentrating signaling molecules. METHODS: By adjusting the photo-illumination time, photocrosslinkable gelatin scaffolds with the same polymer concentration but different stiffnesses were created. hBMSCs were seeded within soft and stiff scaffolds, and their response to adipogenic induction under different substrate mechanical conditions was characterized. The functional involvement of CAV1 was assessed by suppressing its expression level using CAV1-specific siRNA. RESULTS: The soft and stiff scaffolds used in this study had a compressive modulus of ~0.5 kPa and ~23.5 kPa, respectively. hBMSCs showed high viability in both scaffold types, but only spread out in the soft scaffolds. hBMSCs cultured in soft scaffolds displayed significantly higher adipogenesis, as revealed by histology, qRT-PCR, and immunostaining. Interestingly, a lower CAV1 level was observed in hBMSCs in the soft scaffolds, concomitantly accompanied by increased levels of Yes-associated protein (YAP) and decreased YAP phosphorylation, when compared to cells seeded in the stiff scaffolds. Interestingly, reducing CAV1 expression with siRNA was shown to further enhance hBMSC adipogenesis, which may function through activation of the YAP signaling pathway. CONCLUSIONS: Soft biomaterials support superior adipogenesis of encapsulated hBMSCs in 3D culture, which is partially mediated by the CAV1-YAP axis. Suppressing CAV1 expression levels represents a robust method in the promotion of hBMSC adipogenesis.

Improved chemosensitivity following mucolytic therapy in patient-derived models of mucinous appendix cancer.

Abundant intraperitoneal (IP) accumulation of extracellular mucus in patients with appendiceal mucinous carcinoma peritonei (MCP) causes compressive organ dysfunction and prevents delivery of chemotherapeutic drugs to cancer cells. We hypothesized that reducing extracellular mucus would decrease tumor-related symptoms and improve chemotherapeutic effect in patient-derived models of MCP. Mucolysis was achieved using a combination of bromelain (BRO) and N-acetylcysteine (NAC). Ex vivo experiments of mucolysis and chemotherapeutic drug delivery/effect were conducted with MCP and non-MCP tissue explants. In vivo experiments were performed in mouse and rat patient-derived xenograft (PDX) models of early and late (advanced) MCP. MCP tumor explants were less chemosensitive than non-MCP explants. Chronic IP administration of BRO + NAC in a mouse PDX model of early MCP and a rat PDX model of late (advanced) MCP converted solid mucinous tumors into mucinous ascites (mucolysis) that could be drained via a percutaneous catheter (rat model only), significantly reduced solid mucinous tumor growth and improved the efficacy of chemotherapeutic drugs. Combination of BRO + NAC efficiently lyses extracellular mucus in clinically relevant models of MCP. Conversion of solid mucinous tumors into mucinous ascites decreases tumor bulk and allows for minimally invasive drainage of liquified tumors. Lysis of extracellular mucus removes the protective mucinous coating surrounding cancer cells and improves chemotherapeutic drug delivery/efficacy in cancer cells. Our data provide a preclinical rationale for the clinical evaluation of BRO + NAC as a therapeutic strategy for MCP.

Design of Thermoresponsive Polyamine Cross-Linked Perfluoropolyether Hydrogels for Imaging and Delivery Applications.

Perfluorocarbons are versatile compounds with applications in 19F magnetic resonance imaging (MRI) and chemical conjugation to drugs and pH sensors. We present a novel thermoresponsive perfluorocarbon emulsion hydrogel that can be detected by 19F MRI. The developed hydrogel contains perfluoro(polyethylene glycol dimethyl ether) (PFPE) emulsion droplets that are stabilized through ionic cross-linking with polyethylenimine (PEI). Specifically, PFPE ester undergoes hydrolysis upon contact with aqueous PEI solution, resulting in an ionic bond between the PFPE acid and charged PEI amino groups. Due to the ionic nature of the PFPE/PEI bond, potassium buffer is required to preserve the hydrogel's pH and rheological and emulsion droplet stability. The presence of the surface cross-linked PFPE droplets does not affect the hydrogel's rheological behavior, drug loading, or drug release, and the hydrogel is nontoxic. We propose that the presented hydrogel can be adapted to a broad range of biomedical imaging and delivery applications.

Dynamic Luminal Topography: A Potential Strategy to Prevent Vascular Graft Thrombosis.

AIM: Biologic interfaces play important roles in tissue function. The vascular lumen-blood interface represents a surface where dynamic interactions between the endothelium and circulating blood cells are critical in preventing thrombosis. The arterial lumen possesses a uniform wrinkled surface determined by the underlying internal elastic lamina. The function of this structure is not known, but computational analyses of artificial surfaces with dynamic topography, oscillating between smooth and wrinkled configurations, support the ability of this surface structure to shed adherent material (Genzer and Groenewold, 2006; Bixler and Bhushan, 2012; Li et al., 2014). We hypothesized that incorporating a luminal surface capable of cyclical wrinkling/flattening during the cardiac cycle into vascular graft technology may represent a novel mechanism of resisting platelet adhesion and thrombosis. METHODS AND RESULTS: Bilayer silicone grafts possessing luminal corrugations that cyclically wrinkle and flatten during pulsatile flow were fabricated based on material strain mismatch. When placed into a pulsatile flow circuit with activated platelets, these grafts exhibited significantly reduced platelet deposition compared to grafts with smooth luminal surfaces. Constrained wrinkled grafts with static topography during pulsatile flow were more susceptible to platelet accumulation than dynamic wrinkled grafts and behaved similar to the smooth grafts under pulsatile flow. Wrinkled grafts under continuous flow conditions also exhibited marked increases in platelet accumulation. CONCLUSION: These findings provide evidence that grafts with dynamic luminal topography resist platelet accumulation and support the application of this structure in vascular graft technology to improve the performance of prosthetic grafts. They also suggest that this corrugated structure in arteries may represent an inherent, self-cleaning mechanism in the vasculature.

Esophageal extracellular matrix hydrogel mitigates metaplastic change in a dog model of Barrett's esophagus.

Chronic inflammatory gastric reflux alters the esophageal microenvironment and induces metaplastic transformation of the epithelium, a precancerous condition termed Barrett's esophagus (BE). The microenvironmental niche, which includes the extracellular matrix (ECM), substantially influences cell phenotype. ECM harvested from normal porcine esophageal mucosa (eECM) was formulated as a mucoadhesive hydrogel, and shown to largely retain basement membrane and matrix-cell adhesion proteins. Dogs with BE were treated orally with eECM hydrogel and omeprazole (n = 6) or omeprazole alone (n = 2) for 30 days. eECM treatment resolved esophagitis, reverted metaplasia to a normal, squamous epithelium in four of six animals, and downregulated the pro-inflammatory tumor necrosis factor-α+ cell infiltrate compared to control animals. The metaplastic tissue in control animals (n = 2) did not regress. The results suggest that in vivo alteration of the microenvironment with a site-appropriate, mucoadhesive ECM hydrogel can mitigate the inflammatory and metaplastic response in a dog model of BE.

Wrinkling instabilities for biologically relevant fiber-reinforced composite materials with a case study of Neo-Hookean/Ogden-Gasser-Holzapfel bilayer.

Wrinkling is a ubiquitous surface phenomenon in many biological tissues and is believed to play an important role in arterial health. As arteries are highly nonlinear, anisotropic, multilayered composite systems, it is necessary to investigate wrinkling incorporating these material characteristics. Several studies have examined surface wrinkling mechanisms with nonlinear isotropic material relationships. Nevertheless, wrinkling associated with anisotropic constitutive models such as Ogden-Gasser-Holzapfel (OGH), which is suitable for soft biological tissues, and in particular arteries, still requires investigation. Here, the effects of OGH parameters such as fibers' orientation, stiffness, and dispersion on the onset of wrinkling, wrinkle wavelength and amplitude are elucidated through analysis of a bilayer system composed of a thin, stiff neo-Hookean membrane and a soft OGH substrate subjected to compression. Critical contractile strain at which wrinkles occur is predicted using both finite element analysis and analytical linear perturbation approach. Results suggest that besides stiffness mismatch, anisotropic features associated with fiber stiffness and distribution might be used in natural layered systems to adjust wrinkling and subsequent folding behaviors. Further analysis of a bilayer system with fibers in the (x-y) plane subjected to compression in the x direction shows a complex dependence of wrinkling strain and wavelength on fiber angle, stiffness, and dispersion. This behavior is captured by an approximation utilizing the linearized anisotropic properties derived from OGH model. Such understanding of wrinkling in this artery wall-like system will help identify the role of wrinkling mechanisms in biological artery in addition to the design of its synthetic counterparts.

Self-assembly of multiscale anisotropic hydrogels through interfacial polyionic complexation.

Polysaccharides are explored for various tissue engineering applications due to their inherent cytocompatibility and ability to form bulk hydrogels. However, bulk hydrogels offer poor control over their microarchitecture and multiscale hierarchy, parameters important to recreate extracellular matrix-mimetic microenvironment. Here, we developed a versatile platform technology to self-assemble oppositely charged polysaccharides into multiscale fibrous hydrogels with controlled anisotropic microarchitecture. We employed polyionic complexation through microfluidic flow of positively charged polysaccharide, chitosan, along with one of the three negatively charged polysaccharides: alginate, gellan gum, and kappa carrageenan. These hydrogels were composed of microscale fibers, which in turn were made of submicron fibrils confirming multiscale hierarchy. Fibrous hydrogels showed strong tensile mechanical properties, which were further modulated by encapsulation of shape-specific antioxidant cerium oxide nanoparticles (CNPs). Specifically, hydrogels with chitosan and gellan gum showed more than eight times higher tensile strength compared to the other two pairs. Incorporation of sphere-shaped cerium oxide nanoparticles in chitosan and gellan gum further reinforced fibrous hydrogels and increased their tensile strength by 40%. Altogether, our automated hydrogel fabrication platform allows fabrication of bioinspired biomaterials with scope for one-step encapsulation of small molecules and nanoparticles without chemical modification or use of chemical crosslinkers.

Tuning of thermoresponsive pNIPAAm hydrogels for the topical retention of controlled release ocular therapeutics.

Low patient compliance and poor bioavailability of ophthalmic medications are the main limitations of topical eye drops. A potential solution to these disadvantages could be provided by thermoresponsive hydrogels, which could be used as the basis for a gelling eye drop for long-term release of therapeutics. We previously reported such a system capable of being retained in the lower fornix of rabbits, continuously releasing an anti-glaucoma drug for one month. Here, we sought to improve the properties of the existing gels as most relevant to patient use without altering the drug release profile. Specifically, we optimized the sol-to-gel transition temperature and de-swelling kinetics of pNIPAAm gels to avoid risk of the gelled drop reverting to liquid during cold or windy weather, and ensure quick gelation upon administration. A reduction of the gel LCST, faster gelation kinetics, and suitable viscosity for the administration as an eye drop were successfully achieved through modification of the poly(ethylene glycol) content in the water phase and its molecular weight. Our data suggest that drug release is not affected by these changes, with representative drug concentration profiles of the previous and new formulations demonstrating comparable anti-glaucoma release kinetics.

Active wrinkles to drive self-cleaning: A strategy for anti-thrombotic surfaces for vascular grafts.

The inner surfaces of arteries and veins are naturally anti-thrombogenic, whereas synthetic materials placed in blood contact commonly experience thrombotic deposition that can lead to device failure or clinical complications. Presented here is a bioinspired strategy for self-cleaning anti-thrombotic surfaces using actuating surface topography. As a first test, wrinkled polydimethylsiloxane planar surfaces are constructed that can repeatedly transition between smooth and wrinkled states. When placed in contact with blood, these surfaces display markedly less platelet deposition than control samples. Second, for the specific application of prosthetic vascular grafts, the potential of using pulse pressure, i.e. the continual variation of blood pressure between systole and diastole, to drive topographic actuation was investigated. Soft cylindrical tubes with a luminal surface that transitioned between smooth and wrinkled states were constructed. Upon exposure to blood under continual pressure pulsation, these cylindrical tubes also showed reduced platelet deposition versus control samples under the same fluctuating pressure conditions. In both planar and cylindrical cases, significant reductions in thrombotic deposition were observed, even when the wrinkles had wavelengths of several tens of µm, far larger than individual platelets. We speculate that the observed thrombo-resistance behavior is attributable to a biofilm delamination process in which the bending energy within the biofilm overcomes interfacial adhesion. This novel strategy to reduce thrombotic deposition may be applicable to several types of medical devices placed into the circulatory system, particularly vascular grafts.

Necking and drawing of rubber-plastic bilayer laminates.

We examine the stretching behavior of rubber-plastic composites composed of a layer of styrene-ethylene/propylene-styrene (SEPS) rubber, bonded to a layer of linear low density polyethylene (LLDPE) plastic. Dog-bone shaped samples of rubber, plastic, and rubber-plastic bilayers with rubber : plastic thickness ratio in the range of 1.2-9 were subjected to uniaxial tension tests. The degree of inhomogeneity of deformation was quantified by digital image correlation analysis of video recordings of these tests. In tension, the SEPS layer showed homogeneous deformation, whereas the LLDPE layer showed necking followed by stable drawing owing to its elastoplastic deformation behavior and post-yield strain hardening. Bilayer laminates showed behavior intermediate between the plastic and the rubber, with the degree of necking and drawing reducing as the rubber : plastic ratio increased. A simple model was developed in which the force in the bilayer was taken as the sum of forces in the plastic and the rubber layers measured independently. By applying a mechanical energy balance to this model, the changes in bilayer necking behavior with rubber thickness could be predicted qualitatively.

Topography Driven Surface Renewal.

Natural surfaces excel in self-renewal and preventing bio-fouling, while synthetic materials placed in contact with complex fluids quickly foul [1, 3]. We present a novel biophysics inspired mechanism [4, 5] for surface renewal using actuating surface topography, generated by wrinkling. We calculate a critical surface curvature, given by an intrinsic characteristic length scale of the fouling layer that accounts for its effective flexural or bending stiffness and adhesion energy, beyond which surface renewal occurs. The effective bending stiffness includes the elasticity and thickness of the fouling patch, but also the boundary layer depth of the imposed wrinkled topography. The analytical scaling laws are validated using finite element simulations and physical experiments. Our data span over five orders of magnitude in critical curvatures and are well normalized by the analytically calculated scaling. Moreover, our numerics suggests an energy release mechanism whereby stored elastic energy in the fouling layer drives surface renewal. The strategy is broadly applicable to any surface with tunable topography and fouling layers with elastic response.

A microstructure-composition map of a ternary liquid/liquid/particle system with partially-wetting particles.

We examine the effect of composition on the morphology of a ternary mixture comprising two molten polymeric liquid phases (polyisobutylene and polyethylene oxide) and micron-scale spherical silica particles. The silica particles were treated with silanes to make them partially wetted by both polymers. Particle loadings up to 30 vol% are examined while varying the fluid phase ratios across a wide range. Numerous effects of particle addition are catalogued, stabilization of Pickering emulsions and of interfacially-jammed co-continuous microstructures, meniscus-bridging of particles, particle-induced coalescence of the dispersed phase, and significant shifts in the phase inversion composition. Many of the effects are asymmetric, for example particle-induced coalescence is more severe and drop sizes are larger when polyisobutylene is the continuous phase, and particles promote phase continuity of the polyethylene oxide. These asymmetries are likely attributable to a slight preferential wettability of the particles towards the polyethylene oxide. A state map is constructed which classifies the various microstructures within a triangular composition diagram. Comparisons are made between this diagram vs. a previous one constructed for the case when particles are fully-wetted by polyethylene oxide.