Showing papers on "Laplace pressure published in 2010"

Use of a porous membrane for gas bubble removal in microfluidic channels: physical mechanisms and design criteria

Abstract: We demonstrate and explain a simple and efficient way to remove gas bubbles from liquid-filled microchannels, by integrating a hydrophobic porous membrane on top of the microchannel. A prototype chip is manufactured in hard, transparent polymer with the ability to completely filter gas plugs out of a segmented flow at rates up to 7.4 μl/s/mm2 of membrane area. The device involves a bubble generation section and a gas removal section. In the bubble generation section, a T-junction is used to generate a train of gas plugs into a water stream. These gas plugs are then transported toward the gas removal section, where they slide along a hydrophobic membrane until complete removal. The system has been successfully modeled, and four necessary operating criteria have been determined to achieve a complete separation of the gas from the liquid. The first criterion is that the bubble length needs to be larger than the channel diameter. The second criterion is that the gas plug should stay on the membrane for a time sufficient to transport all the gas through the membrane. The third criterion is that the gas plug travel speed should be lower than a critical value: otherwise a stable liquid film between the bubble and the membrane prevents mass transfer. The fourth criterion is that the pressure difference across the membrane should not be larger than the Laplace pressure to prevent water from leaking through the membrane.

Understanding pattern collapse in photolithography process due to capillary forces.

Abstract: Photolithography is the most widely used mass nanoproduction process. Technology requirements demand smaller nanodevices. However, smaller features risk collapse during the drying of rinse liquid because of capillary forces. In the present study, progress is made on two fronts: (i) The importance of surface tension force (STF) on three-phase line on the pattern collapse is investigated. The STF was ignored in previous pattern collapse studies. It is found that inclusion of STF increases the pattern deformation. The calculated deformation error from neglecting STF increases by increasing contact angle, pattern height to width ratio, and trough to width ratio. The deformation error decreases with an increase in elasticity module of pattern. (ii) A more accurate representation for the interface curvature (and related Laplace pressure), that is, using Surface Evolver (SE) simulation rather than cylindrical interface model (CIM), is presented. Curvature values of two-line parallel and box-shaped patterns are derived from SE and compared with the curvature values from CIM. It was found that CIM for the case of two-line parallel overestimates the curvature value and for the case of box-shaped underestimates it. SE simulations also showed that the error of calculating curvature values using CIM for both shapes is only a function of LAR (ratio of pattern length to trough width). For LAR values less than 20, the curvature values from CIM are not accurate for calculating pattern deformation.

Use of a porous membrane for gas bubble removal in microfluidic channels: physical mechanisms and design criteria

Abstract: We demonstrate and explain a simple and efficient way to remove gas bubbles from liquid-filled microchannels, by integrating a hydrophobic porous membrane on top of the microchannel. A prototype chip is manufactured in hard, transparent polymer with the ability to completely filter gas plugs out of a segmented flow at rates up to 7.4 microliter/s per mm2 of membrane area. The device involves a bubble generation section and a gas removal section. In the bubble generation section, a T-junction is used to generate a train of gas plugs into a water stream. These gas plugs are then transported towards the gas removal section, where they slide along a hydrophobic membrane until complete removal. The system has been successfully modeled and four necessary operating criteria have been determined to achieve a complete separation of the gas from the liquid. The first criterion is that the bubble length needs to be larger than the channel diameter. The second criterion is that the gas plug should stay on the membrane for a time sufficient to transport all the gas through the membrane. The third criterion is that the gas plug travel speed should be lower than a critical value: otherwise a stable liquid film between the bubble and the membrane prevents mass transfer. The fourth criterion is that the pressure difference across the membrane should not be larger than the Laplace pressure to prevent water from leaking through the membrane.

The Interaction between a Very Small Rising Bubble and a Hydrophilic Titania Surface

Abstract: Very small bubbles are ideal for making measurements of both the film drainage process and the disjoining force between a bubble and a hydrophilic titania surface, immersed in water. Their small buoyancy, combined with high Laplace pressure, minimizes bubble deformation, in a flow regime where the Reynolds number approaches zero. We have used high-speed, dynamic, thin-film interferometry to measure film drainage rate and film thickness as a function of buoyancy force. Single gas bubbles, in the diameter range of 15−120 μm, were allowed to rise freely, before collision with a planar, hydrophilic titania surface. Experiments were conducted in 0 to 10−1 M aqueous KCl or (CH3)4NBr at pH 3.5 or pH 6.3, both below and above the titania isoelectric point. We have observed a transition in bubble boundary condition from full-slip to no-slip. Importantly, this effect is reversible and dependent on electrolyte pH, ionic strength, and film thickness. The true origin of these effects remains obscure; however, they see...

Effect of impurities in description of surface nanobubbles

Abstract: Surface nanobubbles emerging at solid-liquid interfaces of submerged hydrophobic surfaces show extreme stability and very small (gas-side) contact angles. In a recent paper Ducker [ W. A. Ducker Langmuir 25 8907 (2009)]. conjectured that these effects may arise from the presence of impurities at the air-water interface of the nanobubbles. In this paper we present a quantitative analysis of this hypothesis by estimating the dependence of the contact angle and the Laplace pressure on the fraction of impurity coverage at the liquid-gas interface. We first develop a general analytical framework to estimate the effect of impurities (ionic or nonionic) in lowering the surface tension of a given air-water interface. We then employ this model to show that the (gas-side) contact angle and the Laplace pressure across the nanobubbles indeed decrease considerably with an increase in the fractional coverage of the impurities, though still not sufficiently small to account for the observed surface nanobubble stability. The proposed model also suggests the dependencies of the Laplace pressure and the contact angle on the type of impurity

Laplace barriers for electrowetting thresholding and virtual fluid confinement.

Abstract: Reported are Laplace barriers consisting of arrayed posts or ridges that impart ∼100 to 1000 s of N/m(2) Laplace pressure for fluid confinement, but the Laplace pressure is also small enough such that the barriers are porous to electrowetting control. As a result, the barriers are able to provide electrowetting flow thresholding and virtual fluid confinement in noncircular fluid geometries. A simple theoretical model for the barriers and experimental demonstrations validate functionality that may be useful for lab-on-chip, display devices, and passive matrix control, to name a few applications.

Different measures for the capillarity-driven deformation of a nanoporous metal

Abstract: We present an experimental study of the deformation of nanoporous gold electrodes, wetted by aqueous electrolytes, subject to variation of the capillary forces at the solid surface. The macroscopic dimensional change measured by dilatometry and the lattice parameter change measured by X-ray diffraction differ consistently by a factor of 2. The apparent discrepancy points towards a distinct difference between the action of the surface stress at the solid surface as opposed to the Laplace pressure of the fluid in the pore space. Whereas sorption strain in porous solids is typically discussed in relation to the pressure in the fluid alone, the present observations can only be understood as the consequence of a modified bonding between the (surface) atoms of the solid. We suggest that the distinction impacts the interpretation of previous findings of sorption strain in porous solids.

The role of interdroplet interaction in the physics of highly concentrated emulsions

Abstract: The osmotic pressure and shear modulus of highly concentrated emulsions were modelled by considering both interfacial energy and interdroplet interaction. This was performed for two- and three-dimensional cases and by optimization and approximation methods of predicting film thickness. The results show that even a small source of interaction can result in non-superimposition of scaled osmotic pressure and shear modulus by Laplace pressure for different droplet sizes, and also significant deviation from the models which consider interfacial interaction as the sole source of energy. The model was used to explain the reciprocal squared diameter dependency of elastic modulus: an interaction similar to the van der Waals type can be responsible for this observation. The model can also be used to analyze the interdroplet interactions in highly concentrated emulsions.

Uptake of water droplets by nonwetting capillaries

Abstract: We present direct experimental evidence that water droplets can spontaneously penetrate non-wetting capillaries, driven by the action of Laplace pressure due to high droplet curvature. Using high-speed optical imaging, microcapillaries of radius 50 to 150 micron, and water microdroplets of average radius between 100 and 1900 micron, we demonstrate that there is a critical droplet radius below which water droplets can be taken up by hydrophobised glass and polytetrafluoroethylene (PTFE) capillaries. The rate of capillary uptake is shown to depend strongly on droplet size, with smaller droplets being absorbed more quickly. Droplet size is also shown to influence meniscus motion in a pre-filled non-wetting capillary, and quantitative measurements of this effect result in a derived water-PTFE static contact angle between 96 degrees and 114 degrees. Our measurements confirm recent theoretical predictions and simulations for metal nanodroplets penetrating carbon nanotubes (CNTs). The results are relevant to a wide range of technological applications, such as microfluidic devices, ink-jet printing, and the penetration of fluids in porous materials.

Various Modes of Void Closure during Dry Sintering of Close-Packed Nanoparticles

Abstract: Film formation from aqueous suspensions of polymer nanoparticles is an important process in many environmental friendly applications and particularly for waterborne coatings. This process occurs via three mains steps: concentration, sintering, and interdiffusion. During the sintering step, the particles in close-packed morphology deform and the interstices between them close under Laplace pressure. This step is crucial in the film formation process since it is where the suspension turns into a uniform defect-free film. Most of the experimental and theoretical studies on sintering assume that the interstices close uniformly over the entire film. We use small-angle neutron scattering to probe void closure between polystyrene nanoparticles. We show that the voids close simultaneously and uniformly throughout the annealing process in large particles. For particles with a diameter smaller than 60 nm, we interpret the results to show that the interstices close heterogeneously at the nanoscopic level: in the beginning of annealing, some interstices close while others enlarge, and eventually they all vanish. The difference between the behavior of large and small particles is related to the high polydispersity of small particles compared to the larger ones.

An experimental study of interactions between droplets and a nonwetting microfluidic capillary

Abstract: We present a detailed experimental study of water drops coming into contact with the end of vertical polytetrafluoroethane (PTFE) capillary tubes. The drops, supported on a superhydrophobic substrate, were between 0.06 and 1.97 mm in radius, and the inner radius of the vertical tube was 0.15 mm. These experiments expand on our recent work, which demonstrated that small water droplets can spontaneously penetrate non-wetting capillaries, driven by the action of Laplace pressure within the droplet, and that the dynamics of microfluidic capillary uptake are strongly dependent on the size of the incident drop. Here we quantitatively bound the critical drop radius at which droplets can penetrate a pre-filled capillary to the narrow range between 0.43 and 0.50 mm. This value is consistent with a water–PTFE contact angle between 107.8° and 110.6°. Capillary uptake dynamics were not significantly affected by the initial filling height, but other experimental factors have been identified as important to the dynamics of this process. In particular, interactions between the droplet, the substrate and the tubing are unavoidable prior to and during droplet uptake in a real microfluidic system. Such interactions are classified and discussed for the experimental set-up used, and the difficulties and requirements for droplet penetration of a dry capillary are outlined. These results are relevant to research into microfluidic devices, inkjet printing, and the penetration of fluids in porous materials.

Drying of complex suspensions.

Abstract: We investigate the 3D structure and drying dynamics of complex mixtures of emulsion droplets and colloidal particles, using confocal microscopy. Air invades and rapidly collapses large emulsion droplets, forcing their contents into the surrounding porous particle pack at a rate proportional to the square of the droplet radius. By contrast, small droplets do not collapse, but remain intact and are merely deformed. A simple model coupling the Laplace pressure to Darcy's law correctly estimates both the threshold radius separating these two behaviors, and the rate of large-droplet evacuation. Finally, we use these systems to make novel hierarchical structures.

Dynamic wetting on superhydrophobic surfaces: Droplet impact and wetting hysteresis

Abstract: We study the wetting energetics and wetting hysteresis of sessile and impacting water droplets on superhydrophobic surfaces as a function of surface texture and surface energy. For sessile drops, we find three wetting regimes on these surfaces: equilibrium Cassie at small feature spacing, equilibrium Wenzel at large feature spacing, and an intermediate state at medium feature spacing. We observe minimum wetting hysteresis not on surfaces that exhibit Cassie wetting but rather on surfaces in the intermediate regime. We argue that droplets on these surfaces are metastable Cassie droplets whose internal Laplace pressure is insufficient to overcome the energy barrier required to homogeneously wet the surface. These metastable Cassie droplets show superior roll-off properties because the effective length of the contact line that is pinned to the surface is reduced. We develop a model that can predict the transition between the metastable Cassie and Wenzel regimes by comparing the Laplace pressure of the drop to the capillary pressure associated with the wetting-energy barrier of the textured surface. In the case of impacting droplets the water hammer and Bernoulli pressures must be compared with the capillary pressure. Experiments with impacting droplets show very good agreement with this simple pressure-balance model.

On the surface properties of a nanodiamond

Abstract: The dependences of the specific surface energy, the surface tension, and the surface pressure on the size, the surface shape, and the temperature of a nanodiamond with a free surface have been investigated using the Mie-Lennard-Jones interatomic interaction potential. The nanocrystal has the form of a parallelepiped faceted by the (100) planes with a square base. The number of atoms N in the nanocrystal varies from 5 to ∞. The isothermal isomorphic dependences of the specific surface energy, its isochoric derivative with respect to the temperature, the surface tension, and the surface pressure on the nanodiamond size have been calculated at temperatures ranging from 20 to 4300 K. According to the results of the calculations, the surface energy under this conditions is positive, which indicates that the nanodiamond cannot be fragmented at temperatures up to 4300 K. The surface pressure for the nanodiamond Psf(N) ∼ N−1/3 is considerably less than the Laplace pressure Pls(N)−1/3 ∼ N−1/3 for the same nanocrystal at the given values of the temperature, the density, and the number of atoms N. As the temperature increases from 20 to 4300 K, the lowering of the isotherm Psf(N) is considerably more pronounced than that of the isotherm Pls(N). At high temperatures, the isotherm Psf(N) changes the shape of the size dependence and goes to the range of extension of small nanocrystals. It has been demonstrated that the lattice parameter of the nanodiamond can either decrease or increase with a decrease in the nanocrystal size. The most significant change in the lattice parameter of the nanodiamond is observed at temperatures below 1000 K.

Effect of contact angle on gas slug formation, shape and flow in a microchannel T-junction by numerical simulation

Abstract: The effect of the contact angle on two-phase flow slug formation in a microchannel Tjunction was studied by numerical simulation. The contact angle, varied from 0 to 120, determined the interaction of the gas and liquid phases with the channel wall, affecting their shape, size and velocity. The interface shape was also found to vary due to the Laplace pressure, which is a function of the contact angle and the slug velocity. The visualisation of the cross-sectional area of gas slugs allowed for insight into the existence of liquid flow along rectangular microchannel corners, which was affected by the contact angle value and determined the occurrence of velocity slip. For the hydrophobic case, the gas completely fills the channel cross-section and experiences no velocity slip. In hydrophilic channels a stationary liquid fraction remains in the channel corners, allowing for the gas phase to achieve higher average velocity, and hence inducing velocity slip. The velocity profile within the gas slugs was also found to change as a function of contact angle, with hydrophilic channels inducing greater internal circulation, compared to greater channel wall contact in the case of hydrophobic channels. These effects play a role in heat from mass transfer from channels walls and highlight the value of numeral simulation in microfluidic design.

Demixing, remixing and cellular networks in binary liquids containing colloidal particles

Abstract: We present a confocal-microscopy study of demixing and remixing in binary liquids containing colloidal particles. First, particle-stabilized emulsions have been fabricated by nucleation and growth of droplets upon cooling from the single-fluid phase. We show that their stability mainly derives from interfacial particles; the surplus of colloids in the continuous phase possibly provides additional stability. Upon heating these emulsions, we have observed the formation of polyhedral cellular networks of colloids, just before the system remixes. Given a suitable liquid–liquid composition, the initial emulsions cross the binary-liquid symmetry line due to creaming. Therefore, upon heating, the droplets do not shrink and they remain closely packed. The subsequent network formation relies on a delicate balance between the Laplace pressure and the pressure due to creaming/remixing. As high concentrations of colloids in the cell walls inhibit film thinning and rupture, the networks can be stabilized for more than 30 min. This opens up an avenue for their application in the fabrication of advanced materials.

On the Application of Laplace Pressure in the Science of Sintering

Abstract: An equation of the Laplace pressure derived using the Gibbs thermodynamic method have been discussed and the correct applications of the equation have been substantiated. It has been shown that the expression is applicable only to macrovolumes for the description of surfaces with a constant curvature, but not to the description of nanodisperced systems and surfaces with variable curvature. The expression of the Laplace pressure applicable to a crystal and the cavity limited by a surface of any geometrical shape have been derived.

Numerical simulation of the absorption of a droplet in a porous medium

Abstract: In this paper we study the behavior of a droplet printed on a porous substrate by an inkjet printer. An extended model for absorption of a droplet in a porous substrate is proposed. The model is based on a model proposed by Alleborn et al.[1][2], with the extension of the dynamics of the wetting front due to capillary forces and radial velocity. As a basic assumption, an initially spherically shaped droplet is considered such that the model can be simplified as an axially symmetric problem. The droplet dynamics is driven by pressure that acts on the droplet, and consists of Laplace pressure, disjoining pressure and gravity. Hence, fluid flow in the droplet is modeled by the Navier‐Stokes equation and continuity equation, where the lubrication approximation is taken into account. The mass loss due to sorption is modeled by the Darcy equation. Here, we extend our model by considering the radial velocity of the fluid inside the porous medium. The extension implies the spreading of the fluid inside the substrate in radial direction. Hence the dynamics of the wetting front due to the radial velocity is modeled using the mass balance principle. For the condition in the surface of the substrate, we use continuity of velocity and pressure. In the wetting front, a discontinuous pressure is assumed, in order to distinguish between the saturated and unsaturated porous medium. The numerical method has good stability properties. Numerical results agree well with simulations from a commercial CFD package where the full Navier‐Stokes equation is solved numerically.

Quantitative spreading kinetics of a three molecular layer liquid patch.

Abstract: The late stage kinetics of the spreading of a smectic nanodrop on a solid surface was investigated by direct and real time imaging of a three molecular layer patch using the SEEC microscopy. Experimental data do not conform to the only available theory, which covers only weakly stratified liquids. A new model is proposed, in remarkable agreement with experiments, in which the spreading mechanism appears to be a quasi-static process ruled by solid/liquid interactions, 2D Laplace pressure, and separate edge and surface permeation coefficients.

On the thermodynamic interpretation of the Laplace pressure

Abstract: An equation of the Laplace pressure derived using the Gibbs thermodynamic method have been discussed and the correct applications of the equation have been substantiated. It has been shown that the expression is applicable only to macrovolumes for the description of surfaces with a constant curvature, namely, spherical, cylindrical, and plane, but not to the description of nanodisperced systems and surfaces with variable curvature.

Molecular-dynamical study of surface tension in nanostructures

Abstract: In the present paper, we perform a molecular-dynamical study of the surface tension in nanodimensional structures. In this case, we find three types of surface characteristics corresponding to different mechanisms of the surface reaction to the external actions: 1. Compression of clusters by the system of surface atoms in the absence of external actions (the Laplace pressure) and the dependence of the internal pressure on the radius. 2. Reaction of the already compressed cluster to the additional external compressive or expansive pressure, which results in surface deformation and in variations both in the energy of the surface atoms and in the binding energy of the surface and the bulk atoms. 3. Energy necessary to form a new surface under unloading (the Griffith energy).

Droplet Impingement and Wetting Hysteresis on Textured Hydrophobic Surfaces

Abstract: We study the wetting energetics and wetting hysteresis of sessile and impacting water droplets on superhydrophobic surfaces as a function of surface texture and surface energy Detailed experiments tracking contact line motion simultaneously with contact angle provides new insights on the wetting hysteresis, stick-slip behavior and dependence on contact line velocity For sessile drops, we find three wetting regimes on these surfaces: equilibrium Cassie at small feature spacing, equilibrium Wenzel at large feature spacing, and an intermediate state at medium feature spacing We observe minimum wetting hysteresis not on surfaces that exhibit Cassie wetting but rather on surfaces in the intermediate regime We argue that droplets on these surfaces are metastable Cassie droplets whose internal Laplace pressure is insufficient to overcome the energy barrier required to homogeneously wet the surface These metastable Cassie droplets show superior roll-off properties because the effective length of the contact line that is pinned to the surface is reduced We develop a model that can predict the transition between the metastable Cassie and Wenzel regimes by comparing the Laplace pressure of the drop to the capillary pressure associated with the wetting-energy barrier of the textured surface In the case of impacting droplets the water hammer and Bernoulli pressures must be compared with the capillary pressure Experiments with impacting droplets show very good agreement with this simple pressure-balance modelCopyright © 2010 by ASME

A Finite Element Model for Predicting the Collapse of Short and Large Two-Line Patterns During Drying Process in Photolithography

Abstract: Photolithography is one of the main mass nano-production processes. Smaller devices are always aimed to save material and energy. Manufacturing small devices by photolithography is a challenge, due to the risk of collapse of patterns during the drying of rinse liquid. One of the main pattern shapes is the two-line parallel. In our previous study, an analytical model was developed for predicting the collapse of large (L/d, LAR>20; see Fig. 1) two-line parallel patterns [1]. This model assumes the rinse interface shape is cylindrical. Knowledge of the rinse interface shape is needed to define the forces contribute to collapse, i.e. Laplace pressure and surface tension force at the three-phase line. In the current study, a Finite Element (FE) model is developed to predict the collapse of short (LAR 20) two-line parallel patterns. Rinse liquid shape and its curvature are found using Surface Evolver (an interactive program for the study of surfaces shaped by surface tension, gravitational and other energies). Another finite element method (i.e. ANSYS 11.0) is used to find the pattern deformation. It was found that the pattern deformation decreases by decreasing the LAR value. It is important as for the cases that due to the design specifications, selection of the pattern material and rinse liquid is restricted, by changing the LAR value one may resolve the collapse problem.Copyright © 2010 by ASME

Simulation Study on Dynamics of Resin-Air Interface during Resin-Air Flows between Filaments Using Phase-Field Navier-Stokes Model

Abstract: To investigate void formation during resin transfer molding (RTM) processes, we developed a numerical code of a multiphase fluid model that employs Navier-Stokes equation including the interfacial tension term and Cahn-Hilliard equation for capturing the resin-air interface. We performed preliminary numerical simulations of microscale resin-air flow around a regular-lattice array of four single filaments. From the analysis, we found that (1) Laplace pressure arisen from the finite curvature of the resin-air interface could drive a capillary-driven flow penetrating into the gap between the two filaments located in longitudinal direction; (2) there was another dual time scale even at the microscale on the determination of flow patters: one was caused by the main flow, and the other by capillary driven transverse flow; (3) voids could be formed when the time scale of the main flow was shorter than that of capillary flow; (4) two modes of void formations were revealed numerically: longitudinal gaps fully capped by the resin-air interface leading to the void formation under a high interfacial tension coefficient; and a small bubble left at the back-step of the filament under a relatively weak interfacial tension coefficient.

P‐111: Distinguished Poster: Reliable Electrofluidic Display Pixels without Liquid Splitting

Abstract: Liquid splitting has been observed in electrofluidic displays when colored pigment dispersion recoils back into reservoir. Application of Laplace pressure to liquid film causes the liquid splitting problem. As demonstrated herein, the liquid splitting problem can be effectively solved by increasing interfacial surface tension or decreasing pixel size.