Showing papers on "Laplace pressure published in 2006"

Physical Properties of Nanobubbles on Hydrophobic Surfaces in Water and Aqueous Solutions

Abstract: In recent years there has been an accumulation of evidence for the existence of nanobubbles on hydrophobic surfaces in water, despite predictions that such small bubbles should rapidly dissolve because of the high internal pressure associated with the interfacial curvature and the resulting increase in gas solubility. Nanobubbles are of interest among surface scientists because of their potential importance in the long-range hydrophobic attraction, microfluidics, and adsorption at hydrophobic surfaces. Here we employ recently developed techniques designed to induce nanobubbles, coupled with high-resolution tapping-mode atomic force microscopy (TM-AFM) to measure some of the physical properties of nanobubbles in a reliable and repeatable manner. We have reproduced the earlier findings reported by Hu and co-workers. We have also studied the effect of a wide range of solutes on the stability and morphology of these deliberately formed nanobubbles, including monovalent and multivalent salts, cationic, anionic, and nonionic surfactants, as well as solution pH. The measured physical properties of these nanobubbles are in broad agreement with those of macroscopic bubbles, with one notable exception: the contact angle. The nanobubble contact angle (measured through the denser aqueous phase) was found to be much larger than the macroscopic contact angle on the same substrate. The larger contact angle results in a larger radius of curvature and a commensurate decrease in the Laplace pressure. These findings provide further evidence that nanobubbles can be formed in water under some conditions. Once formed, these nanobubbles remain on hydrophobic surfaces for hours, and this apparent stability still remains a well-recognized mystery. The implications for sample preparation in surface science and in surface chemistry are discussed.

Formation of self-organized nanoscale porous structures in anodic aluminum oxide

Abstract: A theory of the spontaneous formation of nanoscale porous structures in aluminum oxide films growing during aluminum anodization is presented. The main elements of this theory are the Butler-Volmer relation describing the exponential dependence of the current on the overpotential and the dependence of the activation energies of the oxide-electrolyte interfacial reactions on the Laplace pressure and the elastic stress in the oxide layer. Two cases are considered, distinguished by whether the elastic stress dependence is significant or not. In the case when the effect of elastic stress is negligible, a linear stability analysis predicts a long-wave instability resulting from the field-assisted dissolution reaction; its competition with the stabilizing effect of the Laplace pressure due to the surface energy provides the wavelength selection mechanism. A weakly nonlinear analysis near the instability threshold reveals that the nonlinear dynamics of the interface perturbations is governed by the Kuramoto-Sivashinsky equation. The spatiotemporally chaotic solutions of this equation can explain the formation of spatially irregular pore arrays that are observed in experiments. In the case when the effect of elastic stress in the oxide layer is significant we show that the instability can transform from the long-wave type to the short-wave type. A weakly nonlinear analysis of the short-wave instability shows that it leads to the growth of spatially regular, hexagonally ordered pore arrays, as observed experimentally.

Bubble Kinetics in a Steady-State Column of Aqueous Foam

Abstract: We measure the liquid content, the bubble speeds, and the distribution of bubble sizes, in a vertical column of aqueous foam maintained in steady state by continuous bubbling of gas into a surfactant solution. Nearly round bubbles accumulate at the solution/foam interface, and subsequently rise with constant speed. Upon moving up the column, they become larger due to gas diffusion and more polyhedral due to drainage. The size distribution is monodisperse near the bottom and polydisperse near the top, but there is an unexpected range of intermediate heights where it is bidisperse with small bubbles decorating the junctions between larger bubbles. We explain the evolution in both bidisperse and polydisperse regimes, using Laplace pressure differences and taking the liquid fraction profile as a given.

Sessile-drop-induced bending of atomic force microscope cantilevers: a model system for monitoring microdrop evaporation

Abstract: To monitor the evaporation kinetics of drops from solid surfaces, and to investigate the interaction between liquids and solids, microscopic drops of liquids were deposited onto atomic force microscope cantilevers. Due to the surface tension of the liquid, the Laplace pressure inside the drop, and the change of the interfacial stress at the solid–liquid boundary, the cantilever bends and is deflected by typically a few hundred nanometers. We used liquids with different vapour pressures and surface tensions, in order to vary the evaporation time and also the magnitude of the surface forces exerted by the drops. For fast evaporating drops the cantilever bending along the longitudinal axis was measured versus time. In the case of non-evaporating drops the overall bending was recorded with optical methods. We developed a FEM model for cantilever bending as an improvement to a previously presented analytical model. FEM simulations are confirmed by experimental results.

Light-induced deformation and instability of a liquid interface. I. Statics.

Abstract: We study in detail the deformations of a liquid-liquid interface induced by the electromagnetic radiation pressure of a focused cw laser beam. Using a simple linear model of static equilibrium of the interface under the effect of radiation pressure, buoyancy, and Laplace pressure, we explain the observed hump height variations for any value of the optical Bond number ( is the capillary length and is the waist of the beam) in the regime of weak deformations and show that the deformations are independent of the direction of propagation of the laser. By increasing the beam power, we observe an instability of the interface leading to the formation of a long jet when the laser propagates from the more refringent phase to the less refringent one. We propose that the total internal reflection of the incident light on the highly deformed interface could be at the origin of this instability. Using a nonlinear model of static equilibrium of the interface taking account of the angular dependance of radiation pressure, we explain the measured beam power threshold of the instability , as well as the shape of the interface deformations observed at large waists just below the instability onset. According to this model, the instability should occur when the interface slope reaches the angle of total reflection, . We find experimentally that, just below the instability threshold, the maximum incidence angle along the interface, , is significantly smaller than and that our nonlinear model does not present any instability up to . Thus, although the proposed instability model correctly predicts the instability threshold , it fails to describe the actual instability mechanism. We finally discuss possible additional effects that could explain the instability.

Bubble kinetics in a steady-state column of aqueous foam

Abstract: We measure the liquid content, the bubble speeds, and the distribution of bubble sizes, in a vertical column of aqueous foam maintained in steady-state by continuous bubbling of gas into a surfactant solution. Nearly round bubbles accumulate at the solution/foam interface, and subsequently rise with constant speed. Upon moving up the column, they become larger due to gas diffusion and more polyhedral due to drainage. The size distribution is monodisperse near the bottom and polydisperse near the top, but there is an unexpected range of intermediate heights where it is bidisperse with small bubbles decorating the junctions between larger bubbles. We explain the evolution in both bidisperse and polydisperse regimes, using Laplace pressure differences and taking the liquid fraction profile as a given.

Laplace pressure as a surface stress in fluid vesicles

Abstract: Consider a surface enclosing a fixed volume, described by a free energy depending only on the local geometry; for example, the Canham–Helfrich energy quadratic in the mean curvature describes a fluid membrane. The stress at any point on the surface is determined completely by geometry. In equilibrium, its divergence is proportional to the Laplace pressure, normal to the surface, maintaining the constraint on the volume. It is shown that this source itself can be expressed as the divergence of a position-dependent surface stress. As a consequence, the equilibrium can be described in terms of a conserved effective surface stress. Various non-trivial geometrical consequences of this identification are explored. In a cylindrical geometry, the cross-section can be viewed as a closed planar Euler elastic curve. With respect to an appropriate centre the effective stress itself vanishes; this provides a remarkably simple relationship between the curvature and the position along the loop. In two or higher dimensions, it is shown that the only geometry consistent with the vanishing of the effective stress is spherical. It is argued that the appropriate generalization of the loop result will involve null stresses.

Flow Characteristics of Liquid with Pressure-Dependent Viscosities in Microtubes

Abstract: It is obvious that the pressure gradient along the axial direction in a pipe flow keeps constant according to the Hagen-Poiseuille equation. However, recent experiments indicated that the distribution of the pressure seemed no longer linear for liquid flows in microtubes driven by high pressure (1-30MPa). Based on H-P equation with slip boundary condition and Bridgman's relation of viscosity vs. static pressure, the nonlinear distribution of pressure along the axial direction is analyzed in this paper. The revised standard Poiseuille number with the effect of pressure-dependent viscosity taken into account agrees well with the experimental results. Therefore, the dependence of the viscosity on the pressure is one of the dominating factors under high driven pressure, and is represented by an important property coefficient α of the liquid.

Collapse dynamics of smectic-A bubbles

Abstract: The collapse dynamics of smectic-A bubbles are analyzed experimentally and theoretically. Each bubble is expanded from a flat film stretched at the end of a hollow cylinder and deflated through a pressure release by means of a capillary tube. Its total collapse time can be varied between 0.1s and 20s by suitably choosing the length and the internal diameter of the capillary. This experiment allowed us to show that the collapse takes place in two steps: an initial one, which lasts a fraction of a second, where the meniscus destabilizes and fills up with focal conics, followed by a much longer period during which the bubble collapses and exchanges material with the meniscus. By measuring simultaneously the Laplace pressure and the internal pressure inside the bubble, we were able to fully characterize the shear-thinning behavior of the smectic phase within the meniscus. We emphasize that this method is generic and could be applied as well to other systems such as soap bubbles, on condition that inertial effects are negligible.

Effects of Laplace Pressure on Propagation and Termination in Aqueous Heterogeneous Free Radical Polymerization

Abstract: The influence of the Laplace pressure in polymer emulsion particles during aqueous heterogeneous free radical polymerization on the polymerization kinetics has been investigated. Calculations were carried out based on experimentally reported pressure dependences of propagation and termination rate coefficients. The results suggest that in most cases the effects are not likely to be significant, although under conditions of very small particles (diameter <20 mm) and high interfacial tensions effects of the order of a few percent on propagation (increase in rate) and termination (decrease in rate) were predicted.

Self-Directed Movements of Droplets on Radially Patterned Surfaces Based on Self-Assembled Monolayers

Abstract: This paper demonstrates macroscopic (millimetre-scale), self-directed transport of droplets on radially patterned silicon surfaces to induce wettability gradients based on self-assembled monolayers (SAMs). A difference in wettability between the opposite sides of the droplet edge creates a Laplace pressure gradient inside the droplet, forcing the droplet to move forward. Circulating wedge-shaped features with alternate hydrophobic and hydrophilic regions were photographically patterned and combined with selective coating of silanol- and thiol-based SAMs to transport the droplets right to the centre passively. Positions and velocities of the droplets were measured using high speed CCD camera.

Coolant film flow over the edge of a nozzle in a rarefied gas

Abstract: The flow of a thin liquid film over the nozzle wall under the action of tangential friction and pressure gradient is considered. For the slow flow of the film with constant thermal physical properties, analytical dependences of the film thickness and temperature at the interface on the coordinate along the nozzle edge are derived. The flow of the film over the variable-curvature nozzle edge when the gas expands into vacuum is considered. At the initial section of the curvilinear edge, the film thickness increases in inverse proportion to the root of the friction stress at the interface. Near the end point of the nozzle, the film thickens drastically because of a decrease in the friction and, consequently, the curvature of the interface diminishes. As a result, the deceleration of the liquid by the Laplace pressure gradient drops, which causes an additional sharp growth of the thickness of the film with the possibility of its dynamic and thermal disintegration and, eventually, contamination of the spacecraft surface.

Laplace pressure as a surface stress in fluid vesicles

Abstract: Consider a surface, enclosing a fixed volume, described by a free-energy depending only on the local geometry; for example, the Canham-Helfrich energy quadratic in the mean curvature describes a fluid membrane. The stress at any point on the surface is determined completely by geometry. In equilibrium, its divergence is proportional to the Laplace pressure, normal to the surface, maintaining the constraint on the volume. It is shown that this source itself can be expressed as the divergence of a position-dependent surface stress. As a consequence, the equilibrium can be described in terms of a conserved `effective' surface stress. Various non-trivial geometrical consequences of this identification are explored. In a cylindrical geometry, the cross-section can be viewed as a closed planar Euler elastic curve. With respect to an appropriate centre the effective stress itself vanishes; this provides a remarkably simple relationship between the curvature and the position along the loop. In two or higher dimensions, it is shown that the only geometry consistent with the vanishing of the effective stress is spherical. It is argued that the appropriate generalization of the loop result will involve `null' stresses.

Performance of an Electrokinetic Shuttle Polymerase Chain Reactor

Abstract: An alternative polymerase chain reactor (PCR) driven by electrokinetic flow was developed and tested. A single straight microchannel and a double-T intersection were designed for injection of DNA samples and thermal cycling by shuttling between constant temperature zones. Thermal performance of the device was studied using numerical and analytical models to understand the temperature distribution. Devices were made on a polycarbonate substrate by hot embossing with a micromilled brass mold insert. A PID control system, with a tolerance of ± 0.2°C, was used to maintain the temperatures in each zone during experiments. Power consumption in each zone was predicted using thermal simulations. Molecular diffusion of 500 bp DNA was evaluated using two methods, an empirical equation and an analytical model, and the diffusion length after 20 cycles from both models was 100 μm with a 0.97 μm difference. Electroosmotic flow (EOF) was minimized by using dynamic coating and Joule heating was reduced by decreasing the KCl component in the DNA cocktail. Successful amplification of 500 bp DNA fragments at shuttle velocities of 1mm s-1 (620 seconds), 2mm s-1 (310 seconds), and 3mm s-1 (207 seconds) was demonstrated for 20 thermal cycles. The amplification efficiencies were 31%, 28%, and 18%, respectively. Unintentional flows resulting from siphoning phenomenon due to hydrostatic pressure, and Laplace pressure due to surface tension, may be responsible for the reduced amplification performance.Copyright © 2006 by ASME