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1.
Langmuir ; 40(1): 1096-1108, 2024 Jan 09.
Artículo en Inglés | MEDLINE | ID: mdl-38153401

RESUMEN

We studied the evaporation-induced formation of supraparticles from dispersions of elongated colloidal particles using experiments and computer simulations. Aqueous droplets containing a dispersion of ellipsoidal and spherical polystyrene particles were dried on superamphiphobic surfaces at different humidity values that led to varying evaporation rates. Supraparticles made from only ellipsoidal particles showed short-range lateral ordering at the supraparticle surface and random orientations in the interior regardless of the evaporation rate. Particle-based simulations corroborated the experimental observations in the evaporation-limited regime and showed an increase in the local nematic ordering as the diffusion-limited regime was reached. A thin shell of ellipsoids was observed at the surface when supraparticles were made from binary mixtures of ellipsoids and spheres. Image analysis revealed that the supraparticle porosity increased with an increasing aspect ratio of the ellipsoids.

2.
Langmuir ; 40(9): 4801-4810, 2024 Mar 05.
Artículo en Inglés | MEDLINE | ID: mdl-38386540

RESUMEN

Strongly attractive forces act between superhydrophobic surfaces across water due to the formation of a bridging gas capillary. Upon separation, the attraction can range up to tens of micrometers as the gas capillary grows, while gas molecules accumulate in the capillary. We argue that most of these molecules come from the pre-existing gaseous layer found at and within the superhydrophobic coating. In this study, we investigate how the capillary size and the resulting capillary forces are affected by the thickness of the gaseous layer. To this end, we prepared superhydrophobic coatings with different thicknesses by utilizing different numbers of coating cycles of a liquid flame spraying technique. Laser scanning confocal microscopy confirmed an increase in gas layer thickness with an increasing number of coating cycles. Force measurements between such coatings and a hydrophobic colloidal probe revealed attractive forces caused by bridging gas capillaries, and both the capillary size and the range of attraction increased with increasing thickness of the pre-existing gas layer. Hence, our data suggest that the amount of available gas at and in the superhydrophobic coating determines the force range and capillary growth.

3.
Macromol Rapid Commun ; : e2400532, 2024 Aug 01.
Artículo en Inglés | MEDLINE | ID: mdl-39090528

RESUMEN

A dual zwitterionic diblock copolymer (M100C100) consisting of poly(2-(methacryloyloxy)ethyl phosphorylcholine) (PMPC, M) and poly(3-((2-(methacryloyloxy)ethyl) dimethylammonio) propionate) (PCBMA, C) is synthesized via reversible addition-fragmentation chain transfer (RAFT) polymerization. A double hydrophilic diblock copolymer (M100S100) consist of PMPC and anionic poly(3-sulfopropyl methacrylate potassium salt) (PMPS, S) is synthesized via RAFT. The degrees of polymerization of each block are 100. The charges of PMPC are neutralized intramolecularly. At neutral pH, the charges in PCBMA are also neutralized intramolecularly due to its carboxybetaine structure. Under acidic conditions, PCBMA exhibits polycation behavior as the pendant carboxy groups become protonated, forming cationic tertiary amine groups. PMPS shows permanent anionic nature independent of pH. Charge neutralized mixture of cationic M100C100 and anionic M100S100 in acidic aqueous solution forms water-soluble polyion complex (PIC) micelle owing to electrostatic attractive interactions. The core is composed of the cationic PCBMA and anionic PMPS blocks, with the PMPC blocks serving as shells that covered the core surface, forming spherical core-shell PIC micelles. Above pH 4 the pendant carboxy groups in PCBMA undergo deprotonation, transitioning to a zwitterionic state, thereby eliminating the cationic charge in PCBMA. Therefore, above pH 4 the PIC micelles are dissociated due to the disappearance of the charge interactions.

4.
Small ; 19(37): e2301561, 2023 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-37096929

RESUMEN

Atmospheric water harvesting is considered a viable source of freshwater to alleviate water scarcity in an arid climate. Water condensation tends to be more efficient on superhydrophobic surfaces as the spontaneous coalescence-induced droplet jumping on superhydrophobic surfaces enables faster condensate removal. However, poor water nucleation on these surfaces leads to meager water harvest. A conventional approach to the problem is to fabricate micro- and nanoscale biphilic structures. Nonetheless, the process is complex, expensive, and difficult to scale. Here, the authors present an inexpensive and scalable method based on manipulating the water-repellent coatings of superhydrophobic surfaces. Flexible siloxane can facilitate water nucleation, while a branched structure promotes efficient droplet jumping. Moreover, ToF-SIMS analysis indicated that branched siloxane provides a better water-repellent coating coverage than linear siloxane and the siloxanes comprise hydrophilic and hydrophobic molecular segments. Thus, the as-prepared superhydrophobic surface, TiO2 nanorods coated with branched siloxanes harvested eight times more water than a typical fluoroalkylsilane (FAS)-coated surface under a low 30% relative humidity and performed better than most reported biphasic materials.

5.
Langmuir ; 39(30): 10367-10374, 2023 Aug 01.
Artículo en Inglés | MEDLINE | ID: mdl-37466052

RESUMEN

Surface tension is a physical property that is central to our understanding of wetting phenomena. One could easily measure liquid surface tension using commercially available tensiometers (e.g., Wilhelmy plate method) or by optical imaging (e.g., pendant drop method). However, such instruments are designed for bulk liquid volumes on the order of milliliters. In order to perform similar measurements on extremely small sample volumes in the range of femtoliters, atomic force microscope (AFM) is considered as a promising tool. It was previously reported that by fabricating a special "nanoneedle"-shaped cantilever probe, a Wilhelmy-like experiment can be performed with AFM. By measuring the capillary force between such special probes and a liquid surface, surface tension could be calculated. Here, we carried out measurements on microscopic droplets with AFM, but instead, using standard pyramidal cantilever tips. The cantilevers were coated with a hydrophilic polyethylene glycol-based polymer brush in a simple one-step process, which reduced its contact angle hysteresis for most liquids. Numerical simulations of a liquid drop interacting with a pyramidal or conical geometry were used to calculate surface tension from the experimentally measured force. The results on micrometer-sized drops agree well with bulk tensiometer measurement of three test liquids (mineral oil, ionic liquid, and glycerol), within a maximum error of 10%. Our method eliminates the need for specially fabricated "nanoneedle" tips, thus reducing the complexity and cost of measurement.

6.
J Theor Biol ; 557: 111315, 2023 01 21.
Artículo en Inglés | MEDLINE | ID: mdl-36332666

RESUMEN

Several creatures can climb on smooth surfaces with the help of hairy adhesive pads on their legs. A rapid change from strong attachment to effortless detachment of the leg is enabled by the asymmetric geometry of the tarsal hairs. In this study, we propose mechanisms by which the hairy pad can be easily detached, even when the hairs possess no asymmetry. Here, we examine the possible function of the tibia-tarsus leg joint and the claws. Based on a spring-based model, we consider three modes of detachment: vertically pulling the pad while maintaining either a (1) fixed or a (2) free joint, or by (3) flexing the pad about the claw. We show that in all cases, the adhesion force can be significantly reduced due to elastic forces when the hairs deform non-uniformly across the array. Our proposed model illustrates the design advantage of such fibrillar adhesive systems, that not only provide strong adhesion, but also allow easy detachment, making them suitable as organs for fast locomotion and reliable hold. The presented approaches can be potentially used to switch the adhesion state in bio-inspired fibrillar adhesives, by incorporating artificial joints and claws into their design, without the need of asymmetric or stimuli-responsive fibrillar structures.


Asunto(s)
Adhesivos , Citoesqueleto , Locomoción , Estaciones del Año , Tibia
7.
Soft Matter ; 19(6): 1241-1248, 2023 Feb 08.
Artículo en Inglés | MEDLINE | ID: mdl-36688683

RESUMEN

When a particle, such as dust, contacts a thin liquid film covering a surface it is trapped by the liquid. This effect is caused by the formation of a meniscus, resulting in a capillary force that makes the particle adhere to the surface. While capillary adhesion is well-characterised in static situations, the dynamic formation of the liquid bridge after the initial contact is highly intricate. Here, we experimentally study the evolution of a liquid bridge after a glass sphere is gently brought into contact with a thin viscous film. It is found that the contact creates a ripple on the thin film, which influences the growth of the meniscus. Initially, the ripple and the meniscus are coupled and exhibit similar dynamics. This initial regime is well accounted for by a scaling law derived from lubrication theory. At a later stage, the ripple is "detached" from the liquid bridge, leading to a second regime of bridge dynamics. As a result, capillary forces are time-dependent, highlighting the importance of dynamics on adhesion.

8.
Langmuir ; 38(41): 12610-12616, 2022 Oct 18.
Artículo en Inglés | MEDLINE | ID: mdl-36190842

RESUMEN

When a drop of a polar liquid slides over a hydrophobic surface, it acquires a charge. As a result, the surface charges oppositely. For applications such as the generation of electric energy, lubricant-infused surfaces (LIS) may be important because they show a low friction for drops. However, slide electrification on LIS has not been studied yet. Here, slide electrification on lubricant-infused surfaces was studied by measuring the charge generated by series of water drops sliding down inclined surfaces. As LIS, we used PDMS-coated glass with micrometer-thick silicone oil films on top. For PDMS-coated glass without lubricant, the charge for the first drop is highest. Then it decreases and saturates at a steady state charge per drop. With lubricant, the drop charge starts from 0, then it increases and reaches a maximum charge per drop. Afterward, it decreases again before reaching its steady-state value. This dependency is not a unique phenomenon for lubricant-infused PDMS; it also occurs on lubricant-infused micropillar surfaces. We attribute this dependency of charge on drop numbers to a change in surface conductivity and depletion of lubricant. These findings are helpful for understanding the charge process and optimizing solid-liquid nanogenerator devices in applications.

9.
Langmuir ; 38(48): 14666-14672, 2022 Dec 06.
Artículo en Inglés | MEDLINE | ID: mdl-36410035

RESUMEN

Superhydrophobic surfaces have long been the center of attention of many researchers due to their unique liquid repellency and self-cleaning properties. However, these unique properties rely on the stability of the so-called Cassie state, which is a metastable state with air-filled microstructures. This state tends to transit to the stable Wenzel state, where the inside of the microstructures eventually wets. For potential industrial applications, it is therefore critical to maintain the Cassie state. We investigate the Cassie-to-Wenzel transition on superhydrophobic micropillar surfaces by squeezing a water drop between the surface and a transparent superhydrophobic force probe. The probe's transparency allows the use of top-view optics to monitor the area of the drop as it is squeezed against a micropillared surface. The impalement, or Cassie-to-Wenzel transition, is identified as a sharp decrease in force accompanied by an abrupt change in the drop's contact area. We compare the force measured by the sensor with the capillary pressure force calculated from the observed drop shape and find a good agreement between both quantities. We also study the force and pressure at impalement as a function of the pillar's slenderness ratio. Finally, we compare the impalement pressure with three literature predictions and find that our experimental values are consistently lower than the theoretical values. We find that a possible cause of this earlier Cassie-to-Wenzel transition may be the coalescence of the squeezed drop with microdroplets that nucleate around the base of the micropillars.

10.
Langmuir ; 38(42): 12961-12967, 2022 10 25.
Artículo en Inglés | MEDLINE | ID: mdl-36239606

RESUMEN

The attachment of bio-fluids to surfaces promotes the transmission of diseases. Superhydrophobic textiles may offer significant advantages for reducing the adhesion of bio-fluids. However, they have not yet found widespread use because dried remnants adhere strongly and have poor mechanical or chemical robustness. In addition, with the massive use of polymer textiles, features such as fire and heat resistance can reduce the injuries and losses suffered by people in a fire accident. We developed a superhydrophobic textile covered with a hybrid coating of titanium dioxide and polydimethylsiloxane (TiO2/PDMS). Such a textile exhibits low adhesion to not only bio-fluids but also dry blood. Compared to a hydrophilic textile, the peeling force of the coated textile on dried blood is 20 times lower. The textile's superhydrophobicity survives severe treatment by sandpaper (400 mesh) at high pressure (8 kPa) even if some of its microstructures break. Furthermore, the textile shows excellent heat resistance (350 °C) and flame-retardant properties as compared to those of the untreated textile. These benefits can greatly inhibit the flame spread and reduce severe burns caused by polymer textiles adhering to the skin when melted at high temperatures.


Asunto(s)
Retardadores de Llama , Humanos , Textiles , Interacciones Hidrofóbicas e Hidrofílicas , Dimetilpolisiloxanos , Polímeros
11.
Soft Matter ; 18(8): 1628-1635, 2022 Feb 23.
Artículo en Inglés | MEDLINE | ID: mdl-35113106

RESUMEN

When neutral water drops impact and rebound from superhydrophobic surfaces, they acquire a positive electrical charge. To measure the charge, we analyzed the trajectory of rebounding drops in an external electric field by high-speed video imaging. Although this charging phenomenon has been observed in the past, little is known about the controlling parameters for the amount of drop charging. Here we investigate the relative importance of five of these potential variables: impact speed, drop contact area, contact line retraction speed, drop size, and type of surface. We additionally apply our previously reported model for sliding drop electrification to the case of impacting drops, suggesting that the two cases contain the same charge separation mechanism at the contact line. Both our experimental results and our theoretical model indicate that maximum contact area is the dominant control parameter for charge separation.

12.
J Exp Biol ; 224(20)2021 10 15.
Artículo en Inglés | MEDLINE | ID: mdl-34581416

RESUMEN

Many insects can climb smooth surfaces using hairy adhesive pads on their legs, mediated by tarsal fluid secretions. It was previously shown that a terrestrial beetle can even adhere and walk underwater. The naturally hydrophobic hairs trap an air bubble around the pads, allowing the hairs to make contact with the substrate as in air. However, it remained unclear to what extent such an air bubble is necessary for underwater adhesion. To investigate the role of the bubble, we measured the adhesive forces in individual legs of live but constrained ladybird beetles underwater in the presence and absence of a trapped bubble and compared these with its adhesion in air. Our experiments revealed that on a hydrophobic substrate, even without a bubble, the pads show adhesion comparable to that in air. On a hydrophilic substrate, underwater adhesion is significantly reduced, with or without a trapped bubble. We modelled the adhesion of a hairy pad using capillary forces. Coherent with our experiments, the model demonstrates that the wetting properties of the tarsal fluid alone can determine the ladybird beetles' adhesion to smooth surfaces in both air and underwater conditions and that an air bubble is not a prerequisite for their underwater adhesion. This study highlights how such a mediating fluid can serve as a potential strategy to achieve underwater adhesion via capillary forces, which could inspire artificial adhesives for underwater applications.


Asunto(s)
Adhesivos , Escarabajos , Adhesividad , Animales , Interacciones Hidrofóbicas e Hidrofílicas , Insectos , Humectabilidad
13.
Phys Chem Chem Phys ; 23(31): 16754-16766, 2021 Aug 12.
Artículo en Inglés | MEDLINE | ID: mdl-34319323

RESUMEN

Responsive poly-N-isopropylacrylamide-based microgels are commonly used as model colloids with soft repulsive interactions. It has been shown that the microgel-microgel interaction in solution can be easily adjusted by varying the environmental parameters, e.g., temperature, pH, or salt concentration. Furthermore, microgels readily adsorb to liquid-gas and liquid-liquid interfaces forming responsive foams and emulsions that can be broken on-demand. In this work, we explore the interactions between microgel monolayers at the air-water interface and a hard colloid in the water. Force-distance curves between the monolayer and a silica particle were measured with the Monolayer Particle Interaction Apparatus. The measurements were conducted at different temperatures and lateral compressions, i.e., different surface pressures. The force-distance approach curves display long-range repulsive forces below the volume phase transition temperature of the microgels. Temperature and lateral compression reduce the stiffness of the monolayer. The adhesion increases with temperature and decreases with a lateral compression of the monolayer. When compressed laterally, the interactions between the microgels are hardly affected by temperature, as the directly adsorbed microgel fractions are nearly insensitive to temperature. In contrast, our findings show that the temperature-dependent swelling of the microgel fractions in the aqueous phase strongly influences the interaction with the probe. This is explained by a change in the microgel monolayer from a soft to a hard repulsive interface.

14.
Langmuir ; 36(39): 11581-11588, 2020 Oct 06.
Artículo en Inglés | MEDLINE | ID: mdl-32897726

RESUMEN

When a liquid drop gets into contact with a soft array of microstructures, capillary forces at the three-phase contact line can lead to critical deformations. Microstructures may collapse and form bundles or even patterns. So far, viewing the kinetics of bundling at the menisci scale has remained elusive. Here, we use laser scanning confocal microscopy to directly image the menisci between micropillars. We image structural changes in polydimethylsiloxane micropillar arrays during the Cassie-to-Wenzel transitions of a water drop evaporating on top of the array. We demonstrate how the regular pillar array undergoes a spontaneous symmetry breaking as the first step to the formation of pillar bundles. A comparison of the Cassie-to-Wenzel transition in air and FC40 indicates that the local contact angle determines the outcome of the bundling process. Based on these observations, we develop a simple model using the local contact angle, stiffness of the pillars, and interfacial tension of the liquid to predict the onset of the symmetry breaking.

15.
Small ; 15(35): e1902376, 2019 08.
Artículo en Inglés | MEDLINE | ID: mdl-31310426

RESUMEN

A substrate mimicking the surface topography and temperature sensitivity of skin goosebumps is fabricated. Close-packed arrays of thermoresponsive microgel particles undergo topographical changes in response to temperature changes between 25 and 37 °C, resembling the goosebump structure that human skin develops in response to temperature changes or other circumstances. Specifically, positively charged poly[2-(methacryloyloxy)ethyltrimethylammonium chloride] (PMETAC) brushes serve as an anchoring substrate for negatively charged poly(NIPAm-co-AA) microgels. The packing density and particle morphology can be tuned by brush layer thickness and pH of the microgel suspension. For brush layer thickness below 50 nm, particle monolayers are observed, with slightly flattened particle morphology at pH 3 and highly collapsed particles at pH above 7. Polymer brush films with thickness above 50 nm lead to the formation of particle multilayers. The temperature responsiveness of the monolayer assemblies allows reversible changes in the film morphology, which in turn affects underwater adhesion and friction at 25 and 37 °C. These results are promising for the design of new functional materials and may also serve as a model for biological structures and processes.

16.
Langmuir ; 35(43): 14042-14048, 2019 Oct 29.
Artículo en Inglés | MEDLINE | ID: mdl-31589055

RESUMEN

Controlling the droplet evaporation on surfaces is desired to get uniform depositions of materials in many applications, for example, in two- and three-dimensional printing and biosensors. To explore a new route to control droplet evaporation on surfaces and produce asymmetric particles, sessile droplets of aqueous dispersions were allowed to evaporate from surfaces coated with oil films. Here, we applied 1-50 µm thick films of different silicone oils. Two contact lines were observed during droplet evaporation: an apparent liquid-liquid-air contact line and liquid-liquid-solid contact line. Because of the oil meniscus covering part of the rim of the drop, evaporation at the periphery is suppressed. Consequently, the droplet evaporates mainly in the central region of the liquid-air interface rather than at the droplet's edge. Colloidal particles migrate with the generated upward flow inside the droplet and are captured by the receding liquid-air interface. A uniform deposition ultimately forms on the substrate. With this straightforward approach, asymmetric supraparticles have been successfully fabricated independent of particle species.

17.
Soft Matter ; 15(40): 8175-8183, 2019 Oct 28.
Artículo en Inglés | MEDLINE | ID: mdl-31596303

RESUMEN

When a supersaturated aqueous solution flows over a microstructured, hydrophobic surface, bubbles tend to nucleate. Here, we control heterogeneous nucleation of gas bubbles from supersaturated CO2 solution. By designing the shape, size, and arrangement of hydrophobic micropillars and by adjusting the flow we obtain uniform nucleation patterns. It is possible to selectively turn nucleation on and off. We use laser scanning confocal microscopy to resolve nucleation in early stages at the micropillar-substrate intersection. Numerical simulations show a correlation between minute pressure drops behind micropillars and nucleation sites. Bubbles nucleate uniformly behind pillars of the same size. The flow profile further contributes to the uniform growth of the bubbles. We control heterogeneous nucleation by varying micropillar geometry or size, flow direction and rate. While nucleation behind square pillars is independent of the flow direction, nucleation behind round micropillars is coupled with the direction. Nucleation behind triangular micropillars is bifurcated. These observations pave the way for the replenishment of the gas layer entrapped in between hydrophobic surface features, needed for superhydrophobicity.

18.
Nanotechnology ; 30(6): 065301, 2019 Feb 08.
Artículo en Inglés | MEDLINE | ID: mdl-30523814

RESUMEN

We found that platinum (Pt) nanoparticles, upon annealing at high temperature of 1000 °C, are engulfed into amorphous fused-silica or thermal oxide silicon substrates. The same phenomenon was previously published for gold (Au) nanoparticles. Similar to the Au nanoparticles, the engulfed Pt nanoparticles connect to the surface of the substrates through conical nanopores, and the size of the Pt nanoparticles decreases with increasing depth of the nanopores. We explain the phenomena as driven by the formation of platinum oxide by reaction of the platinum with atmospheric oxygen, with platinum oxide evaporating to the environment. We found that the use of Pt provides much better controllability than the use of Au. Due to the high vapor pressure of platinum oxide, the engulfment of the Pt nanoparticles into oxidized silicon (SiO2) substrates is faster than of Au nanoparticles. At high temperature annealing we also find that the aggregation of Pt nanoparticles on the substrate surface is insignificant. As a result, the Pt nanoparticles are uniformly engulfed into the substrates, leading to an opportunity for patterning dense nanopore arrays. Moreover, the use of oxidized Si substrates enables us to precisely control the depth of the nanopores since the engulfment of Pt nanoparticles stops at a short distance above the SiO x /Si interface. After subsequent etching steps, a membrane with dense nanopore through-holes with diameters down to sub-30 nm is obtained. With its simple operation and high controllability, this fabrication method provides an alternative for rapid patterning of dense arrays of solid-state nanopores at low-cost.

19.
Macromol Rapid Commun ; 40(21): e1900395, 2019 Nov.
Artículo en Inglés | MEDLINE | ID: mdl-31507007

RESUMEN

The synthesis of ionogels with a responsive, self-replenishing surface for combating biofouling is described. Ionogels are prepared by infiltrating poly(vinylidene fluoride-co-hexafluoropropylene) with binary mixtures of ionic liquids (IL): 1-octadecyl-3-methylimidazolium bis(trifluoromethyl sulfonyl)imide ([C18 C1 im][NTf2 ], melting point Tm = 55 °C) and 1-hexyl-3-methylimidazolium bis(trifluoromethyl sulfonyl)imide ([C6 C1 im][NTf2 ], Tm = -9 °C). The IL mixtures release spontaneously from the gel matrix and eventually crystallize on the surface. This leads to self-replenishment of the surface of ionogels even after mechanical damage. The incorporation of [C6 C1 im][NTf2 ] provides the antimicrobial efficacy of ionogels while the crystals of [C18 C1 im][NTf2 ] serve as a skeleton maintaining [C6 C1 im][NTf2 ] on the surface. By heating, the ionogel surface transforms from solid to liquid-infused state-the removal of biofilms/bacteria developed under a long time of colonization is facilitated. The antimicrobial efficacy is maintained even after several cycles of biofilm formation and detachment. This work provides an opportunity to apply ionogels as functional coatings with renewable antibiofouling properties.


Asunto(s)
Incrustaciones Biológicas/prevención & control , Líquidos Iónicos/farmacología , Polivinilos/farmacología , Líquidos Iónicos/química , Estructura Molecular , Tamaño de la Partícula , Polivinilos/química , Propiedades de Superficie
20.
Phys Rev Lett ; 121(4): 048002, 2018 Jul 27.
Artículo en Inglés | MEDLINE | ID: mdl-30095942

RESUMEN

The work required to detach microparticles from fluid interfaces depends on the shape of the liquid meniscus. However, measuring the capillary force on a single microparticle and simultaneously imaging the shape of the liquid meniscus has not yet been accomplished. To correlate force and shape, we combined a laser scanning confocal microscope with a colloidal probe setup. While moving a hydrophobic microsphere (radius 5-10 µm) in and out of a 2-5 µm thick glycerol film, we simultaneously measured the force and imaged the shape of the liquid meniscus. In this way we verified the fundamental equations [D. F. James, J. Fluid Mech. 63, 657 (1974)JFLSA70022-112010.1017/S0022112074002126; A. D. Scheludko, A. D. Nikolov, Colloid Polymer Sci. 253, 396 (1975)] that describe the adhesion of particles in flotation, deinking of paper, the stability of Pickering emulsions and particle-stabilized foams. Comparing experimental results with theory showed, however, that the receding contact angle has to be applied, which can be much lower than the static contact angle obtained right after jump in of the particle.

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